DEPARTMENT OF THE INTERIOR

BULLETIN

OF THK

UNITED STATES

GEOLOGICAL SURVEY

No. 73

THE VISCOSITY OF SOLIDS

WASHINGTON

GOVERNMENT PRINTING OFFICE

1891
r\
Private Library 

N. W. LORD

LIBRARY CATALOGUE SLIPS.

United States. Department of the interior. ( U. S. geological survey).

Department of the Interior | | Bulletin | of the | United 

States | geological survey | no. 73 | [Seal of the department] | 

Washington | government printing office | 1891

Second title: United States geological survey | J. W. Powell, director | | The viscosity of solids | by | Carl Barns | [Vignette] | 

Washington | government printing office | 1891 

8°. xii, 139pp. 6 pi.

Barus (Carl).

United States geological survey | J. W. Powell, director | | 

The viscosity of solids | by | Carl Barus | [Vignette] | 

Washington | government printing office | 1891 

8°. xii, 139 pp. 6 pi.

[UNITED STATES. Department of the interior. (U. S. geological survey). 

Bulletin 73.]

United States geological survey | J. W. Powell, director | |

The viscosity of solids | by | Carl Barus | [Vignette] |

Washington | government printing office | 1891

8°. xii, 139 pp. 6 pi.

[UNITED STATES. Department of the interior. (U. S. geological survey). 

Bulletin 73.]

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[Bulletin No. 73.]

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Survey should be addressed To THE DJUECTOR OK THE

UNITED STATES GEOLOGICAL SURVEY,

WASHINGTON, D. C. 

WASHINGTON, D. C., July, 1891.

DEPARTMENT OF THE INTERIOB

BULLETIN

OF THE

UNITED STATES

GEOLOGICAL SURVEY

No. 73

WASHINGTON

GOVERNMENT PRINTING OFFICE 

1891

UNITED STATES GEOLOGICAL SURVEY

J. W. POWELL, DIEECTOR

THE

YISCOSITY OF SOLIDS

BY

CARL BARUS.

WASHINGTON

GOVERNMENT PRINTING OFFICE 

1891

CONTENTS.

Page.

Preface..................................................................... xi

Chapter I. The Viscosity of Steel and its Relations to Temper, by C. Barns

and V.Strouhal............................................... 1

Introduction ...........^...................^........... .................. 1

Literary notes............................ - ........................ 2

Plan of research.................................................... 2

Method of experiment.................................................. 3

Apparatus.......................................................... 3

Bifilar apparatus................................................. 3

Tubular apparatus............................ .................. 5

Unifilar, apparatus .............................................. 6

Method of observing................................'................ 6

Method of tempering................................................ 6

Quenching...................................................... 6

Annealing ...................................................... 8

Elimination of errors.................................................. 9

Experimental data...................................................... 12

Notation.................................................... ........ 12

Introductory explanations .......................................... 12

Experiments proper................................................. 14

Notation........................................................ 14

Eods annealed at 25° and 100° .................................. 14

Eods annealed at 190°........................................... 18

Rods annealed at 360°........................................... 21

Rods annealed at 450°........................................... 23

Soft rods....................................................... 25

Remarks on the tables............................................... 28

Miscellaneous experiments . J-........................................ 29

Glass fibers ..................................................... 29

Iron, soft and drawn........... 4 ................................. 31

Nickel and copper .............................................. 35

Steels annealed at 450° and 1000°................................ 37

Quadrifilar arrangement ........................ ................ 37

Tabular apparatus.............................................. 38

Discussion.............................................................. 39

Interpretation of (q>-<p').... .................................... 39

Viscosity and temper................................................ 41

Graphic digest.............................................. .... 41

Immediate results.................................. ............ 42

Viscosity and electrics of steel................................... 44

Viscosity and hardness.......................................... 44

Residual phenomenon .......................................... 45

Sectional areas of the bifilar wires................................... 45

V
VI CONTENTS.

Page.

Chapter I. The Viscosity of Steel and its Eolations to Temper Continued. f

Discussion Continued.

Viscosity and strain................................................. 47

Steel and glass................................................... 47

Steel and iron.................................................. 47

Effect of quenching............................................. 48

Steel and cast-iron.............................................. 49

Stress intensity estimated ....................................... 49

Magnetic relations.................................................. 50

Viscosity and magnetic intensity................................ 50

Magnetic and viscous maxima in steel........................... 50

Steel and iron.......................................... ......... 51

Remarks........................................................ ....... 51

Chapter II. The Viscosity of Steel and its Relations to Temperature ........ 53

Introduction............................................................ 53

Method of measurement................................................. 53

Apparatus ...................................................... 53

Theory of apparatus...... ....................................... 55

Digression...................................................... 57

Experimental results...... .... .^i....................................... 58

Residual twist.................................................. 58

Torsional viscosity and temperature................................. 59

Notation........................................................ 59

Viscosity at 100°................................................ CO

Viscosity at 190°................................................ 64

Viscosity at 360°................................................ 66

Remarks on the tables........................................... 68

Deductions ............................................................. 68 ^

Viscosity and temperature ...................................... 68

Behavior of other metals........................................ 70

Viscosity and pressure........................................... 71

Sudden and gradual deformation ................................ 72

Chapter III. Maxwell's Theory of the Viscosity of Solids and its Physical

Verification... ....................'.......................... 74

Introduction............................................................ 74

Historical sketch of the theories of solid viscosity ....................... 75 <

0. E. Meyer's theory ............................................ 75

Boltzmann's theory.............................................. 75

Neesen's theory ................................................. 76

Warburg's theory............................................... 77

Nissen's theory .........................s....................... 77

Maxwell's theory ............................................... 77

Experimental results.................................................... 79

Apparatus ............................................................ 79

Theory of the apparatus........................................ 79

Measurements with steel........................................ 79

Viscous behavior of the rods.................................... 80

Mean values deduced............................................ 82

Data of the measurements with platinum alloys.................. 83

Deductions from platinum alloys........................................ 86

Viscous effect of alloying........................................ 86

Effect of annealing and hardening platinum...................... 87

Summary........................................................... 88

Deductions for steel..................................................... 88 ,

"Accommodation" in glass-hard steel................................ 88
CONTENTS. VII

Page. 

Chapter III. Maxwell's Theory of the Viscosity of Solids, etc. Continued.

Deductions for steel Continued.

The phenomena proper.......................................... 88

Motional effects estimated...................................... 92

"Accommodation" and hysteresis .............................. 92

Viscous and electrical behavior compared........................ 93

Viscosity at mean atmospheric temperature...................... 94

Viscosity at 100°................................................ 95

Viscosity at higher temperatures.................... .... ........ 96

Annealing and viscous deformations superposed ................. 96

Viscosity and stress............................................. 97

The phenomenon of glass-hardness............................... 99

The phenomena of annealing.................................... 100

The temper-strain in other substances....'....................... 101

Extremes of complex and of simple molecular structuroi......... 101

Thermal stability of magnetic configuration..................... 102

Intensity of magnetic configuration............................. 103

Summary............................................................... 104

Clausius's and Maxwell's theories compared.......................... 104

Chapter IV. The Effect of Magnetization on the Viscosity and on the Rigidity of Iron and Steel....................................... 105

Introduction............................................................ 105

Viscosity of magnetized steel and iron.................................. 106

Apparatus and method.......................................... 106

Results...--..-.-.....,-...-......-...-..........-......:....... 107

Eigidity of magnetized iron............................................. HO

Definitions and results.......................................... no

Deductions ......................................................... 11:3

Constant fields.................................................. 113

Intermittent fields .............................................. 116

Eigidity of magnetized steel............................................. 118

Chapter V. The Change of the Order of Absolute Viscosity encountered

on passing from Fluid to Solid............................... 120

Introduction............................................................ 120

Gases and vapors ....................................................... 120

Liquids................................................................. 121

Viscous fluids................ ...... ...... ............................ 121

Apparatus...................................................... 121

Computation. Example: Glycerine.... .......................... 121

Data for marine glue............................................ 123

Eesultsfor parafflne............................................. 124

Solids ...I...-.........--.....-.....--.-... ............................. 124

Method of comparison........................................... 124

Discussion of results............................................ 125

Errors encountered.............................................. 125

General remarks on solid viscosity............................... 126

Apparatus for direct method .................................... 126

Method of computation.......................................... 128

Data obtained .................................................. 128

Discussion.............................................................. 132

Eetrospective................................................... 132

Spontaneous breaking .......................................... 132

Time variation of absolute viscosity............................. 132

Solidity of the three states of aggregation........................ 134

ILLUSTRATIONS.

Page. 

PL. I. Unifilar apparatus.................................................. 54

II. Viscous deformation at 100° for different states of temper............ 62

III. Viscous deformation at 190°, for different states of temper and strain. 64

IV. Viscous deformation at 360°, for different states of temper............ 66

V-. Effect of magnetization on the viscosity and the rigidity of iron; q>

varying with time............................................ 108

VI. Chart showing the absolute viscosity of hard steel (Tables 78 and 80), 

and of soft steel (Tables 79 and 81), during the first hour after 

twisting just within the elastic limits......................... 132

FiG. 1. Bifilar apparatus for torsional viscosity ............................. 3

2. Device for suspension............................................... 4

3. Side elevation of the apparatus shown in Fig. 1.... _............... 5

4. Sectional elevation of the tubular apparatus ........................ 6

5. Galvanic apparatus for quenching steel.............................. 7

6. Apparatus for annealing long steel wire ........................;.... 8

7. " W" crucible for annealing........................................ 9

8. Viscous deformation of steel annealed at 20° and at 100°, compared

with glass-hard steel ............................................. 18

9. Viscous deformation of steel annealed at 190°, compared with glasshard steel........................................................ 20

10. Viscous deformation of steel annealed at 360°, compared with glasshard steel........................................................ 22

11. Viscous deformation of steel annealed at 450°, compared with glasshard steel........................................................ 24

12. Viscous deformation of steel annealed at 1,000° ("soft")> compared

with glass-hard steel.............................................. 28

13. Viscous deformation of steel as compared with glass ................. 31

14. Viscous deformation of steel compared with iron, soft and drawn..... 33

15. Viscous deformation of steel compared with iron..................... 35

16. Viscous deformation of copper and nickel compared with steel annealed

at 450°........................................................... 36

17. Viscous deformation of steel annealed at 450°, compared with soft

steel ..............'............................................... 37

18. Eesults obtained with the tubular apparatus ........................ 39

19. Diagram ........................................................... 40

20. Viscous deformation of steel, as related to temper.................... 43

21. Diagram ...... ..................................................... 56

22. Effect of annealing twisted systems of glass-hard steel wire (diameter

0-82 centimetres) at 360°.......................................... 59

23. Viscous deformation increasing with time, for different states of

temper and of temperature. Mean values......................... 68

IX
X ILLUSTRATIONS.

FIG. 24. Viscous accommodation of glass-hard steel .......................... 91

25. Increments of rigidity varying with obliquity of fibers. Increments

of rigidity varying with diameter of wire.......................... 114

26. Apparatus for the secular transpiration of viscous liquids............ 122

27. Viscous deformation of a bar of marine glue compared with a hard

steel wire ...............................................-.......: 125

28. Apparatus for measuring the absolute viscosity of solids............. 127
PREFACE.

This bulletin is a second contribution to the general investigation of 

the physical contents of rocks, the experiments concerning which follow a general plan devised by Mr. Clarence King.

Questions bearing directly On. the viscosity of rock masses make up 

so large a part of Mr. King's geological observations, that the duty of 

inquiring into the physics of this enormously complicated subject devolved seriously upon me. Above all things some form of reliable 

working hypothesis was to be discovered; and this is what the present bulletin endeavors to accomplish. I believe the physical hypothesis has been found and that the data afford substantial corroboratiou of Maxwell's theory of the viscosity of solids.

The method by which I attempt to arrive at the result in question 

consists in investigating the details of viscous behavior of steel. Steel 

has a phenomenal quality, in that it can be made to pass continuously 

from an extreme of brittle hardness almost to soft plasticity. Hence 

its value in serving as a test of any theory.

Curiously enough, viscous deformation (Nachwirkung) is strikingly 

pronounced at the hard and brittle end of the scale, whereas soft steel 

is relatively rigid. These facts are established in Chapter I, of which 

they form the larger part. To interpret the striking results of Chapter 

I it is necessary to consider them from a more general point of view. 

Consequently Chapter II investigates them further with regard to their 

general truth under variable conditions of temperature and of stress. 

But the full interpretation is not attempted until Chapter III, where, 

together with other relevant matter, they are shown to bear directly 

on the fundamental hypotheses of Maxwell's theory of the viscosity of 

solids.

Chapter IV applies a magnetic method to the study of the behavior 

of a strained atomic configuration, and is thus an important deduction 

from Chapter III.

Chapter Y finally exhibits the solidity of the three states of aggregation. The results show an astounding range of variation, inasmuch as 

viscosity on passing from extreme fluid to extreme solid changes from 

at most JO-5 , to at least 1020.

By selecting steel as the chief source of evidence I gain a second important advantage. The researches of Dr. Strouhal and myself have
XII PREFACE.

thrown new light on a number of the physical qualities of steel, some 

of which are closely allied to the subject in hand. Thus there exists a 

reciprocal relation between the earlier bulletins of the Geological Survey, No. 14, No. 27 (pp. 30-60), No. 35, and No. 42 (pp. 98-131), and the 

present bulletin, by which clearness of conception regarding the physics 

of the iron-carburets is promoted.

The notation has been made uniform throughout the work, and the 

data reduced to the same standard. This occasioned much extra labor, 

since it involved a new computation of the chief results of Chapters II 

and III. However, seeing that the unity of the book could be much 

enhanced thereby, the time was not grudgingly spent.

Meantime the researches on solid viscosity have been considerably 

extended. I have now nearly ready for the press a sequel 1 to this volume, in which the molecular changes which promote viscous motion 

are specially discussed. The results enable me to submit a general 

theory of solid molecular structure, and they therefore fitly make up a 

second part of the continued series of researches of which this bulletin constitutes the first part.

I may add in concluding, that the researches on steel were begun by 

Dr. Strouhal and myself and continued to such a stage of progress as 

made it advisable for us to publish subsequent investigations together. 

But the serious delays incident to epistolary communication at best, 

and the great distance between us (Prague-Washington), has dictated, 

very much to our regret, a dissolution of literary partnership. The 

science of to-day is more and more exactingly a science of specialized 

responsibilities, aud the connection between a statement and its author 

can not be too direct or too obvious.

GAEL BARUS.

LABORATORY U. S. GEOLOGICAL SURVEY,

Washington, D. C., March 15,1890.

1 Cf. Annual Report of the Director for the fiscal year 1888-'89.
THE VISCOSITY OF SOLIDS.

BY CARL BARUS.

CHAPTBE I.

BY CARL BARUS AND VINCENT STROUHAL.

THE VISCOSITY OF STEEL AND ITS RELATIONS TO TEMPER.

INTRODUCTION.

1. In Bulletin No. 42, U. S. Geol. Survey, p. 131, we expressed the 

belief that the qualities of retaining magnetism exhibited by steel would 

probably stand in relation to the viscous properties of thja metal. In 

the present chapter we make a first search for such a relation. The 

work is restricted to torsional viscosity because it usually exists in 

larger amount, and is much more accurately measurable than any of 

the other manifestations of viscosity. Possibly it may be brought more 

rationally into comparison with magnetic phenomena. We therefore 

develop partially (i. e. so far as is necessary for our especial purposes) a 

very sensitive differential method for the study of torsional viscosity.1 

Having applied it to steel, we compare the results obtained with the 

known behavior of permanent linear magnets, tempered under like conditions. During the course of the experiments we incidentally come 

upon certain ulterior results (viscosity of iron, glass).

In our magnetic comparisons we have endeavored to avoid prematurity. Many inferences of the original draught have been cropped. 

We do not wish to ignore the magnetic effect of the chemical changes 

of steel. We have merely endeavored to circumscribe the magnetic 

effect of carburation, by exploring the magnetic importance of certain 

mechanical properties of steel. To do this we have studied, abstractly 

as It were, the occurence of permanent magnetism in a medium of continuously varying viscosity, without insisting on an inherent relation 

between retentiveness and viscosity.

1 Independently of ourselves, as we subsequently found, a similar method was used by Boltzmann 

and by 0. E. Meycr (Pogg. Ann., vol. 154, 1875, p. 357). '

Bull. 73 1 1
2 THE VISCOSITY OF SOLIDS. [BULL. 73.

LITERARY NOTES.

2. The necessary existence of viscosity in solids was pointed out, discovered, and its nature described by Weber; 1 but it is to Koblrausch's2 

extensive researches that we owe the bulk of our present knowledge. 

A new method of research was indicated by Sir William Thomson,3 

which method was developed, independent of Thomson we believe, by 

Streintz4 and by Schmidt.5 Thomson6 concisely defined the terms now 

in English use and followed by Maxwell (Heat, Chapter II).

PLAN OF RESEARCH.

3. We proposed at first to study the viscosity of steel from two distinct 

standpoints: one part of our work was to consider viscosity in its relations to temperature; the other part, viscosity in its relations to hardness. Indeed, we have as yet no data at all of this kind for steel. For 

other substances Kohlrausch7 and after him Streintz8 and Pisati9 had 

already studied viscosity and temperature with some detail though in 

a direction differing somewhat from our own. Very recently, however, 

Schroeder10 has experimented in a line of research quite identical with 

the one upon which we had determined; and though his data do not 

include steel, the results obtained for other metals are sufficiently pronounced to make a special investigation of steel appear superfluous, 

at least so far as regards its present bearing on our work. Schroeder11 

finds "Der bei 100° begonnene Yerlauf der Nachwirkung wird durch 

Abkiihlung des Drahtes auf Ziuimertemperatur uuterbrochen; nach

1 Weber: Getting. Gelehrt. Anz., St. 8, 1835; Pogg. Ann., vol. 24, 1835, p. 247; ibid., vol. 54, 1841, 

p. 1; Comm. Soc. Gotting., vol. 3, 1841, p. 45. Weber's researches express the amount of viscous deformation in terms of time by a hyperbolic formula with three constants.

2 Kohlrausch: Pogg. Ann., vol. 119,1863, p. 337; ibid., vol. 128,1866, pp. 207, 399 ; ibid., vol. 155, 1875, 

p. 579; ibid., vol. 158, 187G, p. 337. The author subjected fibers of a great number of Substances to 

torsional, tensile and flexural stress, and he discusses the amount of deformation in each case in its 

dependence on time and on temperature. The results are too elaborate to be excerpted here. The 

author finds it necessary to use exponential relations with three and even four constants to describe 

the results completely. In this place we advert, moreover, to the papers of Neesen (Pogg. Ann., vol. 

153, 1874, p. 498; ibid., vol. 157, 1876, p. 579; Wied. Ann., vol. 7, 1879, p. 460), of Braun (Pogg. Ann., 

vol. 119,1876, p. 337), of Wiedemaun (Wied. Ann., vol. 6,1879, p. 496) which supply details of critical 

discussion. Perhaps we may even add Pernet's well known thermometric researches (Carl's Eepertorium, vol. 11,1875, p. 257, and else where).

3 Sir William Thomson: Phil. Mag. (IV), vol. 30, 1865, p. 63. Thomson refers the loss of energy of 

of vibration to the existence of molecular friction.

4 Streintz: Pogg. Ann., vol. 153, 1874, p. 387; Wien. "Ber., vol. 69, part2d, 1874, p. 355. Using a 

vibration method the author discusses elaborately the effect of viscosity on the logarithmic decrement.

5 Schmidt: Wied. Ann., vol. 2, 1877, pp. 48, 241, supplements Thomson's and Streiutz's results, and is 

able to express logarithmic decrement in terms of time by Weber's formula of three constants. We 

may add Gohn( Wied. Ann., vol. 6,1879, p. 403), Hopkiuson (Phil. Trans., 1877), Warburg (Wied. Ann., 

vol. 13,1881, p. 141), Auerbach (Wied. Ann., vol. 14,1881, p. 308), Kohlrausch (Pogg. Ann., vol. 128,1886), 

Ewing (Phil. Trans., 1885, p. 545) and others who discuss viscosity as manifesting itself in phenomena 

of conductivity (Cohn), residual static charge (Hopkinson, Kohlrauscb), magnetism (Auerbach, Warburg, Ewing and others).

6 Thomson : loc. cit.

'Kohlrausch: Pogg. Ann., vol. 128, 1866, p.216; ibid., vol. 158, 1876, p. 371.

 Streiutz: Wien. Ber., vol. 69, 1874, p. 337 ; also Schmidt, loc. cit.

9 Pisati: Wien. Ber., vol. 80, 1879, p. 427. Also Gaz. Cairn, Ital, 1876,1877.

10 Schroeder: Wied. Ann., vol. 28,1876, p. 369. 

" Scbroeder: Ibid., p. 388.
BABUS.] BIFILAR APPARATUS.

erneuter Erwarmung auf 100° wird die vorher nnterbrochene Drehnug fortgesetzt." We pointed out1 that hi case of drawn metals, of 

quenched glass (Rupert's drops) and we inferred also in case of tempered steel, energy has been stored up in virtue of the rigidity of the 

material; and that on exposure to temperature (annealing), the available excess of stress is made to produce the observed viscous deformation precisely in the way in which 

Schroeder has found it for applied 

torsional stress. Nevertheless, the 

behavior of steel, when considered 

in all its details, is much more complicated and is, indeed, quite unique,

as will be indicated in the course of

this chapter.

METHOD OF EXPERIMENT.

APPARATUS.

For the reasons given the scope of 

this chapter has been limited to a 

study of the viscosity of steel, in its 

relations to temper. We endeavor 

therefore to determine the difference of viscosity which corresponds 

to a given known difference of hardness. The following differential 

method of measurement, the principle of which can be made clear in a 

few words, naturally suggests itself:

Bifilar apparatus. Given a pair of 

steel wires, one of which is always 

glass-hard, the other of known temper; let them be made the threads of 

a bifilar suspension provided with 

suitable means for the measurement 

of the angular motion of the line defined by the lower double point of 

attachment, relative to the upper line 

of attachment; finally let a twist 

of +T be imparted to one steel wire, 

a twist of T to the other. If now 

the system be left to itself, and if 

the two wires be equally viscous the FIG. 1. Bifilar apparatus for tomonal 

viscosity; scale J.

1 Bull. U. S. Geol. Survey, No. 14,1885, p. 196; Am. Jour. Sci. (Ill), vol. 31, I860, p. 452.
4 THE VISCOSITY OF SOLIDS. [BULL.73.

bifllar system cseteris paribus will remain at rest. If on the other hand 

the viscosities be unequal, the lower free part of the bifilar will move 

around the vertical let fall from the upper part. The sign of this angular 

motion will be that of the twist of the wire of greater viscosity; its 

amount caeteris paribus directly dependent on the difference of viscosity 

of the pair of wires under experiment, One of the forms of apparatus 

actually used is given in the annexed diagrams, Figs. 1 to 3, the former 

on a scale of £. The couple of steel wires awivg and axxg to be tested, 

are fastened above to a massive piece of brass ABO and below to a similar piece DEGF. ABC is fixed firmly to the wall at some distance from 

it, and all incidental motion or displacement is registered by the mirror 

Mj adj ustable at pleasure by aid of the screw-arms fed and bo. DEGF is 

free to move under the influence of the bifilar couples and motion is 

similarly registered by the'mirror N adjustable at pleasure by aid of 

the screw arms mlk and h. To keep the line of symmetry of the piece 

DEGF vertical, to deaden incidental vibrations, and to give general 

stability to the whole bifilar adjustment, we suspended a heavy lead 

disk H.Q (5 Ibs.) from the screw r. HQ is partially immersed in water 

contained in a glass bell-jar ILK also (adjustably) attached to the 

wall.

The steel wires are inserted and then fastened in the apparatus as 

follows: To keep the two steel wires (about 33CIU long) under a permanent strain of torsion, each is softened about 2cm from the ends inward. 

The soft parts are then beat into a hook-like loop just large enough to 

slide over the screws of the little brass bolts a and g. Having fastened 

the lower ends by the bolt </, the upper ends are each twisted 180° against 

each other and then also fastened by the bolt a.

The ends of this twisted system are now to be secured to the blocks 

of brass ABO and DEGF. One method of fastening is given (J actual 

size) in Fig. 2, the parts of which are lettered similarly to Fig. 1. The

two wires, w and #, are pressed firmly 

<7 H ^i ^ against a little rectangular piece of 

steel o, by aid of the bolt pp1 and the 

^ p nut qq'. The bolt is provided with a 

square hole near its head, through 

which o and the steel wires may easily 

be passed. A little pin prevents o from

FIG. 2. Device for suspension; scale,*. , ,. ... . n ,, rotating around the axis of the screw,

thus diminishing liability to breakage. In the apparatus figured it is 

necessary to slide the bolts pp' over the wires w, #, before the torsion 

is applied by fastening a.

In Fig. 3 the same apparatus is given in side elevation (sectional), 

and as the same lettering is here used as in Figs. 1, 2, this diagram is 

at once intelligible. It indicates in a clearer way the method of insert-
BAiurs.] TUBULAR APPARATUS.

ing and fastening the twisted systems ivx, wx, with reference to which 

wires the experiments are made.

In a more convenient form of apparatus, perhaps, we replace the brass 

blocks ABC and DEQF by little 

hand vises, the axle of the lower one 

of which has been perforated and 

fitted with a screw subserving the 

purposes of r in the figure. By aid 

of a disc of lead vertical symmetry 

of the whole apparatus is here also 

maintained.

The advantage of this form of apparatus, apart from our own special 

purposes, is that with a single adjustment, the viscous movement can 

be traced with extreme accuracy for 

an indefinite length of time. There 

is no doubt that in some of the cases 

examined such motion will demonstrably exist even for a year after 

the torsion has been imparted. 

Kohlrausch's method is an absolute 

method 5 but his wire must be 

twisted and untwisted once for each 

observation. The method of logarithmic decrement is difficult of interpretation, and is really a complex 

method and limited to short intervals of time.

In experimenting with glass it 

was necessary to modify the apparatus so that twists less than T=180° 

could be applied. This is easily 

done by perforating the screw of the 

upper bolt and passing the glass 

fiber through the hole. Torsion in 

any amount may then be applied to 

the projecting fiber. .

5. Tubular apparatus. Our second 

(tubular) apparatus combines with 

the advantages of the one just sketched, the ulterior desideratum of 

enabling the observer to follow the viscous detorsion immediately after 

applying stressj and therefore also the advantage of exhibiting the

FIG. 3. Side elevation of the apparatus 

shown in JTig. 1.
6 THE VISCOSITY OP SOLIDS. [HULL. 73.

effect of positive torsion immediately succeeding negative torsion and 

vice versa; or of studying the effect produced by an indefinite number 

of alternations of the sign of the twist. In the second 

form of apparatus the wire is introduced into a narrow 

tube just large enough to surround it. The tube is 

fixed above and fastened to the wire below. Twist is 

imparted to the wire and through it to the tube. The 

observations, in other respects, are conducted as 

above.

Figure 4 is a sectional elevation of the tubular apparatus. Here JE is a massive cylinder of brass, in the 

lower socket of which the reduced end of the cylinder 

B fits snugly, so as to be free to rotate around the 

vertical, unless fastened by the steel pin F. E and 

B are axially perforated, and B carries the tube tttt, 

which in its turn carries the lower massive cylinder of 

brass A. The steel wire to be tested, ag, is inserted 

through the perforations in ^7, J5, A, and securely 

fastened against rotation by the lateral screws CD and 

G'D'. N is the movable mirror, adjustably fastened 

to the lower bob A; M is the fixed mirror (fiducial 

mark) adjustably fastened to B.

The cylinder B is stationary, being secured by a 

clamp not shown in the figure. Twist is imparted to 

the system of tube tttt and wire ag, by withdrawing the 

pin jP, rotating J2, and then again inserting the pin.

6. Unifilar apparatus. A. third form of apparatus in which the wires 

are countertwisted unifilarly is described in Chapter II.

METHOD OF OBSERVING.

7. In both forms of apparatus, angles are registered by Gauss' method 

of telescope 1 and scale. We secure extreme accuracy by using two mirrors, one of which (stationary) furnishes a reliable fiducial mark for the 

other (movable). These mirrors are easily so adjusted that their respective scale-images appear simultaneously in the field of the telescope, 

one above the other and intersected by the same cross-hair. Indeed, it 

would not be difficult so to arrange this device that the stationary image 

could be used as a vernier on the moving image.

METHOD OF TEMPERING.

8. Quenching. The wires used (Stubs's steel) were hardened galvanically as described elsewhere.2 To Prof. H. A. Eowland, who placed his

1 Three wood screws, the head of one of which is planed, of another hollowed out conically, make a 

good adjustable plane-dot-slot arrangement. 

2 Ball. TJ. S. Geol. Survey, No, 14. p. 29; Wied. Ann., 1880, vol. 11, p. 932. Cf. § 55.

FIG. 4. Sectional elevation of the tubular apparatus.
BARUS. 1 METHOD OF TEMPERING.

dynamo-electric machine at our disposal for this purpose, and favored 

us with the benefit of his advice during almost the entire afternoon, we 

owe our cordial thanks.

The apparatus for quenching deserves special description, being simplified in general character and made available for divers ulterior purposes. It is given perspectively in Fig. 5, slightly tilted forward to

c'

FIG. 5. -Galvanic apparatus for quenching steel.

show the parts. Here gli is the trough of sheet iron in which quenching 

is to take place. The wire dd', kept slightly stretched by two horizontal 

beak-shaped arms die, d'~k' which are swiveled on the axle We', is suspended horizontally just above the water in gli. A spring at &, tends to 

snap the wire into the water, unless prevented by the notched stop a. 

&, therefore, tends to rotate the axle We' which to secure insulation is 

made of hard rubber. Finally the rear ends of the said beak-shaped arms, 

are bent downward and amalgamated. During the suspension of the 

steel wire they dip into oblong adjustable troughs of mercury c, c' which 

communicate with a battery or dynamo. Finally, two spiral springs, 

s, s', by drawing the rear ends of the arms together, (swivel at le and /<;') 

keep the wire stretched, as has been stated, even at red heat. The level 

of mercury in c and c' is so adjusted that the current of the battery is 

broken the moment the wire touches the surface of the water.

The method of operating is easily understood. Having closed the 

current and heated the wire to the degree of redness desired, the pin at 

a is quickly released, which whips the wire suddenly into the water and 

at the same time, as already stated, automatically breaks the. currents. 

l(he cold wire will be found quenched glass-hard, or indeed harder, so 

that specific resistance may run as high as s=50 microhms. As regards homogeneity, too, these wires are exceptionally excellent, as will 

be indicated below, twenty wires of about 150CIU each in length having 

for certain special purposes been examined per 2CIn of length of each.

The present apparatus offers many conveniences by which quenching 

is appreciably facilitated. This will be seen by comparing it with the 

older galvanic apparatus. 1 Alterations, moreover, are easily introduced 

by which quenching may be effected in water or metal of any tempera1 Bull. TJ. S. Geol. Survey, No. 14, 1885, p. 29.
8 THE VISCOSITY OF SOLIDS. [BULL. 73.

ture (simply heating the trough gh with burners placed underneath); 

and by which the rod may be quenched from any temperature of red 

heat corresponding to known intensity of the galvanic current which 

heats the wire.

9. Annealing. The annealing was effected by drawing the glass-hard 

wires through a zone of constant temperature by clockwork. 1 Of. § 55. 

This operation is also of such importance antf so difficult to accomplish in case of very long wires, that an apparatus by which it is satisfactorily done deserves description. It is given in perspective view in 

Fig. 6, and consists essentially of a Barus' boiling tube T, containing 

the substance boiling at the temperature at which annealing is to take 

place. Water 100°, aniline 185°, diphenylamine 

310°, mercury 360°, sulphur 450°, are usually 

sufficient for annealing work.. Other substances 

are given elsewhere.2 These substances are 

easily boiled by aid of the ring burner surrounding the tube, and annealing is commenced when 

the thermal distribution has become stationary. 

The central tube of the boiling-tube T is prolonged downward by attaching the closed tube 

tj long enough to envelope the cold steel wire to 

be annealed. .This wire (or wires) is suspended 

from a very fine copper filament, the upper end 

of which is fastened to the drum or disc C.of 

the adjustable clock. When the clock has been 

set in motion the wire is slowly drawn through 

the zone of ebullition, by the revolving drum C. 

All parts are attached to a ring stand as shown, 

and easily adjustable. In the figure the wires 

are given at w prolonged, in which position they 

are about half way through the zone of ebullition. If li be the height of the zone and R the 

radius of the disc G revolving once per hour,

then

h

FIG. 6. Apparatus for annealing long steel wire.

~~'27iR

is the time of annealing in hours. Again by making 7&=27r, the time of 

exposure in hours is the reciprocal of the radius of the disc in centimeters.

This method of annealing is exceedingly convenient at high temperatures, as only a very narrow zone of constant temperature is called 

for. Between 500° and 1,000° such work is done by replacing the annealing tube by an annealing crucible of porcelain or fire clay of the

1 Barus: Am. Jour. Sci. (Ill), 1886, vol. 32, p. 279.

2 Bar us: Bull. U. S. Geol. Survey, 'No. 54,1889, p. 87.
BAUDS.] THEORY OP THE APPARATUS. 9

form given in Fig. 7, the crucible being placed in a suitable Fletcher 

furnace, as shown iu Bulletin No. 54. Cadmium, zinc bismuth, may 

then be used for high temperature boiling points 

and the rods suitably protected by atmospheres 

of hydrogen or carbon dioxide.

ELIMINATION OF ERRORS.

10. The steel wire to be used in these experiments are all about 0-lcm in thickness. Hence to 

determine the condition of equilibrium or motion 

in the torsional apparatus described, it is necessary to consider the respective moments of the 

bifilar couple (M6 ), of the torsional couple (Mr) 

and of the flexural couple (M,}, by which the movable end is actuated.

The moment of the bifilar couple has the well 

known form1

M.b=^-mg sin «r .... (1)

where A and A/ are respectively the distance apart 

of the upper ends and the lower ends of the 

bifilar wires, I the vertical distance and a the 

horizontal angle between the lines A. arid A/, mg 

the weight of the whole suspended adjustment. 

To mg should be added one-half the weight of the 

wires.

The moment of the torsion couple is MT=ra, 

where T is the sum of the torsional coefficients of 

the~wires. This applies because the sum of the 

stored torsional moments, for a=0, is T+( 2')=0. 

We may give MT an experimentally convenient 

form by substituting for r the approximate value 

derived in elastics. We obtain

FIG. 7. " W" crucible for 

annealing.

where p is the ra.dius of the steel wires used, E the G. g. s. value2 of the 

modulus of elasticity of steel.

The moment of the flexural couple is more involved, If p be the distance between vertical planes passing through the bifilar wires, and 

if/ be the horizontal component of the flexural force, then the flexural 

couple is M/=fp. We have however by geometry, _p=(AA/ sin a) / s,

1 Kohlrausch Leitfaden, 1884, p. 167. Maxwell, 1881, vol. ii, p. 108.

2 Poisson's coefficient is in the following estimate taken at i: If JS' be the current technical.modulus 

referred to the kilogram and square millimeter, E=^E' g X 105 .
10 THE VISCOSITY OF SOLIDS. [BULL. 73.

where s is the sum of the horizontal projections of the wires. We have 

moreover given us in elastics

'6 np* s 

 2 

and therefore the couple in question becomes

M^* £lS*na ... (3) 

o i

The equations 1, 2, 3 enable us to choose the dimensions of the wire 

and of the apparatus as well as to select conditions of experiment such 

that the torsional couple may alone be effective. The following are extremely unfavorable phases of the best available values, in question:

A=A' <0-2cm

In view of the small values of a it is sufficient to compare the coefficients only. We obtain nearly

Mb : M T : ^=1000 : 280000 : 20.

Hence it appears that in the case of the chosen dimension the most 

unfavorable effect of the bifilar and flexural couples combined is less 

than 0-4 per cent of the torsional couple. Moreover the torsional couple 

becomes more predominant as the angle of deviation, a, increases, so 

that no serious inaccuracy from the discrepancies here enumerated need 

be apprehended.

11. When we operate with glass-hard steel, we encounter so many 

mechanical difficulties, that the conditions postulated in the foregoing 

analysis can not be immediately assumed. We can not, for instance, 

adjust the tensions of the two wires precisely to equality. Nor is it 

easy SO to Store the permanent torsion that the parallelism of the lines 

joining the upper and lower points of suspension remains intact. Under 

these circumstances flexural and bifilar couples may have very different 

values from the ones accepted, and the moments as a whole, will form 

a complex aggregate. Although it is improbable that the flexural and 

bifilar discrepancies will exceed the limits of error investigated, it is 

none the less desirable to determine them by direct experiment. This 

can be done with convenience and great accuracy.

Let the water be removed from the jar ILK, and the system be put 

in vibration around a vertical and in such a way that the angle a remains 

small. Then the circumstances of motion are given by

where K is the moment of inertia of the bifilar body, Z the time of a 

complete vibration. If we replace the steel wires by threads for which
UABUB.] THEORY OF THE APPARATUS. 11

r and 6Mf / 6 a are zero, we may find the value of the bifilar coefficient 

in terms of the other two. We cite the following typical experiment : 

Steel wires: ^=0-025 sec.; Z=26cm ; A<0-lcm ; 

Brass capillary wire: Zb= 0-35 sec.; Z=30cra ; A=0-2cm ; A'=0-3cm . 

If we reduce the results for capillary brass wire to the I and A, which 

obtain for steel, we deduce ^=0-40 sec. Hence the bifilar coefficient 

is less than 0-4 per cent of the combined torsioual and flexural coefficients, in very unfavorable values of the chosen dimensions. This experimental result agrees with the one calculated above.

12. The following static method is better, being exhaustive and final. 

Let the lower ends of the pair of identical steel wires, A and B, be fastened with the bolt. Let rotation at this end be temporarily checked. 

Then we may store like degrees of torsion by twisting the upper ends 

of the wires in the following three ways :

a. Let the wire A be twisted +360° and then fastened to B. Left to 

itself the upper end of the system will rotate 180° so that the residual 

torsion of A is +180° ; of .Bis 180°. The total couple actuating the 

bifilar body then is of the form ±Mb -\-Mr±_ Mf.

6. Let the wires A and B be twisted +180° and 180° respectively 

and then fastened together. Lei't to itself the upper end of the system 

will not move. The residual torsion is therefore the same as in case a; 

but the total couple here actuating the bifilar body is JlfT ±0. This is 

the case premised in the analysis which introduces this paragraph.

c. Let the wire B be twisted 360° and then fastened to A. Left to 

itself the upper end will rotate +180°, so that the residual torsions on 

A and B are the same as in cases a and fr; but the total couple which 

in case of viscous motion actuates the bifilar body has now the form

This is the device : We are able to commutate, as it were, the combined flexual and bifilar couples relative to the. torsional couple of 

fixed sign. In the results below this test is frequently applied and we 

will there show that for the chosen dimensions the torsion couple only 

need be considered.

13. In the case of the tubular apparatus, Fig. 4, the present precautions are at once superfluous. Here each wire is introduced into the 

tube and compared with the next wire introduced under like circumstances. The tubular apparatus is specially adapted for the iuvestiga 

tion of viscous detorsion in its dependence on the applied torsional 

stress, as well as on time. But the same work may also well be done 

with the bifilar.

The viscous effect of the relative sections of the wires and allied observations, with a bearing on viscosity proper, can more expediently be 

made after the experimental data have been communicated. It is convenient to insert a few remarks on the rigidity of efficient parts of the 

above apparatus here. In the tubular adjustment, if d be the diameter of 

the wire, d\ and DI the diameters of the tube, if I symbolize the effective
12 THE VISCOSITY OF SOLIDS. [BULL. 73.

length, Tthe amount of stored twist, G the rigidity, we have, iii view 

of the equal couples,

-~3ZT- l 321; .... 

Now in order to make sharp comparisons on the viscosity of solids, in 

order to investigate its dependence both on time and on stress, the apparatus is to be so adjusted that like stresses produce like strains in the 

substances compared. Hence put T=T^ whence

ft Gil I

This applies to the bifilar apparatus for ^,=0. The equation (2) shows 

at once how to study viscosity under conditions in which like stresses 

produce like strains upon like sectional areas of the viscous solids 

compared.

EXPERIMENTAL DATA.

NOTATION.

14. In Bulletin 14 we used the word " retentiveness " in the restricted 

German sense to designate magnetic stability, or the property in virtue 

of which a magnet resists such influences as temperature, percussion, 

time. The common English use of the term is much broader than this 

and refers to residual induction1 in a general way. Fortunately the 

context of our paper is sufficiently clear and does not admit of serious misapprehension. Inasmuch as measurement of total induction 

has not yet fallen properly within the scope of our work, we purposely 

withhold many obvious allusions to magnetic permeability. We moreover retain the term permanent magnetization to denote the magnetic 

moment per unit of mass of a permanently saturated rod, for the sake

of uniformity with our earlier notation. Its ratio to magnetic intensity 

is therefore the density of steel.

To avoid troublesome circumlocution we use the adjective "viscous" 

with the very broad meaning of " pertaining to viscosity." Such expressions as "viscous phenomena" though not elegant are convenient. 

Similarly we often speak without confusion of "linear magnetization" 

where " magnetization of a linear rod" is meant. Of. § 55.

INTRODUCTORY EXPLANATIONS.

15. The following tables, Nos. 1 to 26, contain results for the viscosity 

of steel in different states of temper. To these are appended other 

tables of a miscellaneous kind. For convenience of comparison we insert a little index. The apparatus used in obtaining the data are desig1 Mr. Ewing proposes a new and very elegant extension of the current use of " retentiveness." He 

defines it as "resistance to any change of magnetic state which (magnets) exhibit whenever the magnetic field in. which they are placed suffers any change." Phil. Trans., vol. 2, 1885, p. 526.
BAUUS.] INDEX TO THE TABLES. 13

nated by the Epniau numerals in. the first column. Nos. I to IV are 

different forms of the bifilar adjustment j No. V is the tubular instrument. The index also contains the numbers of the rods or fibers joined 

together to make the bifilar couple and gives other information readily 

understood. Glass and iron fibers are lettered. It is to be remembered 

that in the steel measurements one of the pair of wires is always glasshard, the other annealed as specified.

INDEX TO TABLES.

I. EXPERIMENTS PROPER.

Temper of the rod coupled with glass-hard.

Apparatus 

No.

I. 

II. 

III. 

IV.

Apparatus 

No.

I. 

H. 

III. 

IV.

Annealed :it20°.

Table 1, Rods 47, 48. 

Table 2, Rods 1, 2.

Annealed at 300°.

Table 13, Rods 17, 18. 

Table 14, Rods 21, 22.

Annealed at 10<P.

Table 3, Rods 3. 4. 

Table 4, Rods 43, 44. 

Table 5, Rods 5, 6. 

Table 6, Rods 45, 46. 

Table 7, Rods 7, 8.

Table 8, Hods 9, 10.

Annealed at 450°.

Table 15, Rods 23, 24. 

Table 1C, Rods 25, 26.

Annealed at 190°.

Table 9, Rods 11, 12.

Table 10, Rods 13, 14. 

Table 11, Rods 19, 20. 

Table 12, Rods 15, 16.

Annealed at 1000° (soft).

Table 17, Rods 53, 54 (drawn). 

Table 18, Rods 27, 28 (soft). 

Table 19, Rods 29,30 (commercial drawn). 

Table 20, Rods 31, 32 (commercial annealed). 

Table 21, Rods 33,34 (annealed Irom glass-hard).

II. MISCELLANEOUS EXPERIMENTS.

Apparatus

No.

I. 

IE.

IIT, IV. 

V.

Apparatus 

No.

I. 

I. 

I. 

V.

Apparatus.

IIT. 

III. 

III. 

IV. 

III. 

IV. 

I. 

I.

Glass liber, 

a.

Table 22, Rod 35.

Iron (soft). 

g, d, in, n.

Table 26. Rod 38. 

Table 28, Rod 55. 

Table 29, Rod 56.

Glass fiber, 

b.

Table 23, Rods 36, 42.

Brass tube 

(thick). 

e.

Table 38, Rods 39, 40.

Iron drawn. 

h, c, k.

Table 25, Rod 49. 

Tallin 24, Rod 37. 

Table 27, Rod 50.

Brass tube, 

(thin). 

/

Table 39, Rod 41.

Miscellaneous soft steel:

Table 30, Rods 51, 52. 

Table 31, Rods 61, p (nickel). 

Table 35, Rods 57, 58. 

Table 36, Rods 59, 60. 

Table 37, Rods 57, 58, 59, 60 (quadrifilar). 

Table 32, Rods 62, q (drawn copper). 

Table 33, Rods 63, r (soft copper). 

Table 34, Rods 04, s (soft copper).
14 THE VISCOSITY OF SOLIDS. [BOLL. 73.

EXPERIMENTS PROPER.

16. Notation. In Tables 1 to 26, R denotes the distance betwetn 

mirror and scale, I the efficient length of the steel (bifilar) wires, /I the 

distance between the upper and lower points of suspension. T (in degrees) is the stored torsion, imparted to the whole length (30cm) of wire, 

positively or negatively as specified, whereas <p (p' (in radians) is the 

amount of angular motion (differential detorsion) of the bifilar system due 

to viscosity, per centimeter of length of the system of two steel wires. 

Positive values of T and <p <p' refer to the same angular direction, and 

<p (p1 is arbitrarily put zero (to fix the co-ordinates) at the time one 

hour after the twist T has been imparted. This is the best conveniently 

available method for comparing the divers data. Other methods would 

have compelled us to wait for the subsidence of motion, certainly several 

months in each case. Moreover, to obtain extreme degrees of accuracy, 

it is necessary to study viscosity under circumstances of constant temperature, and in a place where the viscous yielding may proceed unaccompanied by tremor or vibratory motion of the apparatus. For these 

nice experiments we are not now prepared.

The tables furthermore contain the date, the number of hours (/&0 ) 

elapsed since the beginning of the experiment, and the arbitrary deflection, N (radians per centimeter of bifilar length), for each of the times 

specified. The radius of the wires is given under p. Finally the sense 

of the couples actuating the bifilar body is indicated by r (torsion), 6 

(bifilar),/(flexure).

In practice N is the angle between the nprmals of the upper and the 

lower mirror (Fig. 1) divided by the efficient length I, of the wires.

17. The symbol (<p (p'} has been chosen to indicate the essentially 

differential character of this variable, as will be fully exhibited. Here 

it is merely necessary to point out that q> refers to the viscous yielding 

of one of the counter-twisted wires and <p' to the other. In succeeding chapters we shall usually replace T by the rate of twist r=T \ I. 

In the present chapter, since there is no means of measuring the total 

viscous yield during the interval of observation, Tis the initial value 

180° given by the method of adjustment, § 12. As the experiment 

continues, T is reduced in value.

It is to be remembered that one of the two wires is always glass-hard.

18. Rods annealed at 25° and at 100°. The data obtained are given 

in Tables 1 to 8.
BARU84

12=217 ; j 

VISCOSITY OP HARD STEEL. 

TABLE 1. APPARATUS I.

15

\<o-2°' Bods: No. 47, glass-hard, .7'= 180'; No. 48, glass-hard, T= + 180°. 

2p = 0-082 .

Date.

Aug. 21, 6h 08m 

6 21

7 08

22, 9 h 57'»

5 58 

6 54

23, 9" 08'" 

12 31

*J 0 1

24, 9h 17 

5 13

IVX103

(*) 

0-438

0468

0-543

0-552 

0-555

0-568 

0-572

0-577

0-588 

0-600

/* 

o-oo

0-22

15-82

23-83

24-77

3900 

42-38

67-12

((J. ^'JXIO3

(*) 

-0-030

+0-000

0-075

0-087

o-ioo

0-104

0126

Date.

 Aug. 25, 9h 05'" 

7 01

26, 9" 10'"

4 08

27, 9" 11"' 

7 36

28, 9" 21'" 

6 55

6 17

A'XIO3

0-615 

0-632

0-653

0-670

0-695 

0-714

0-734 

0-7 f>5

n*7Bn

0.792

/to

91-92

114-52

140-20

J 64-00

1 QQ.1 1

(0-0') xio*

0-156

0-104

0-237

0'27G

0-318

" Adjusted r-b-f.

= 203cm ; {=20 ; A<0-2

TABLE 2. APPARATUS II.

Rods : No. 1, glass-hard, T= + 180°; No. 2, glass-hard, T= 180°. 

2p=0-082cm .

Date.

Juno 11, 4" 30'"

5 00

5 30

6 15

7 00

7 33

2VX103

(*)

1-896

1-905

1-909 ruio

1-913

Ao

000

0.50 i-oo

1-75

2-50

3-06

(0-0'J X106

<*)

 0-009

±0-000

+0-004

0-005

0-008

Date.

June 12, 8h 35"'

9 25

10 10

1 5

2 20

5 00

5 50

8 30

13, 8h 3fV»

#X103

.1-920

1-922

1-922

1-926

1-926

1-926

1-926

1-926

1-926

fto

16-08

16-92

17-67

20 '58

21-83

24-50

25-33

2800

40-00

(0 0') X103

0-015

0-017

0-017 0-0'Jl

0-021

0-021

0-021

0-021

0.021

JZ=209 : 1=27"";

* Adjusted T b /. 

TABLE 3. APPARATUS I.

Rods: No. 3, glass-hard, T= 180° ; 

2pr= 0-082'"-.

No. 4, annealed at 100°, 10",

Date.

June 24, 8" 30" 

9 00 

9 30 

10 56 

11 49 

12 37 

1 52 

3 15 

4 01 

4 55 

6 5

25, 8» 41'" 

11 35 

5 25 

6 58

2VX103

(*) 

0-139 

0-194 

0-277 

0-312 

0-338 

0-373 

0-401 

0-418 

0-433 

0-453

0-619 

0-640 

0-682 

0-692

Ao

o-oo

0-50 

1-00 

2-43 

3-32 

4-12 

5-37 

6-75 

7-52 

8-42 9-68

24-18 

27-08 

32-92 

34-47

(0 0') X 1C 3

(*) 

 0-055 

±0-000 

+0-083 

0-118 

0144 

0-179 

0-207 

0.224 

0-239 

0-259

0-426 

0-446 

0488 

0-498

Date.

June 26, 8h 23'" 

12 04 

3 17 

6 50

27, 8h 50"' 

3 04

28, 8" 09'" 

11 29 

5 22

29, 8" 07'"

JVX103

0-755 

0-767 

0-778 

0-792

0-825 

0-834

0-857 

0-857 

0-859 

0-864

fco

47-88 

51-57 

54-78 

5833

72-33 

78-57

95-65 

98-98 

104-87

1.1S'63

(0-0') X 10'

0-561 

0-573 

0-584 

0-598

0-631 

0-640

0-063 

0-663 

0-065

0-670

' Adjusted r b f.
16 THE VISCOSITY OF SOLIDS. [HULL. 73.

JK=217cm ,- I 27cm ; A<0-2c

TABLE 4. APPARATUS I.

Rods: No. 43, glass-hard, T= 180°; No. 44, annealed at 100°, 9h, 

T=+180°. 2p = 0-082.

Date.

Aug. 8, 5h 00"' 

5 17

6 17

7 33

9, 9" 05"' 

11 56

7 05

1 19

6 20

ll,10h 06'" 

1 15

7 06

12, 9b 22">

5 30

13, 9" 09m 

1 28 

4 41

NXW3

(*) 

1-265

1-127 

1-043

0736 

0-686

0664 

0-579

0427 

0-388 

0-333

0-184 

0147

0-035

0-042

 0117

 0-245 

 0285 

 0-316

ho

o-oo

0-28

2-55

1608 

18-93

20-10 

26-08

41-03 

44-32 

49-33

69-15

09*<m

116-10

(</>_</>') X103

(*)

 0126

+0-097

0-404 

0-454 

0-476

0561

0-713 

0752 

0-807

1-001

1220

1-422

Date.

Aug. 14, 9h llm 

5 12

15, lh 34m 

6 35

16, lh 27 

6 55

17, 9h 22 

6 55

18, 9* 15» 

5 29

19, 9h 03 

6 35

20, 9" 16m

21, 9" 07"-

JVX103

 0-447 

 0-509

 0-635 

 0-664

 0755 

 0-783

 0-858 

 e-918

 0-984 

 1-015

 1-066 

 1-094

 1-136

 1-162

 1-196

Ao

140-19

167-07

191-18

213-15

236-36

285-00

304-12

«>-</> ) X103

1-618

1-790

1-909

2-028

2-139

2-220

2-289

2-336

* Adjusted

TABLE 5. APPARATUS II.

Rods: No. 5, glass hard, T 180°; No. 6, annealed at 100°, 9h , 

T= + 180°. 2p = 0-082»".

Date.

June 13, 9" 15"-

10 15

11 15

12 05

1 25

3 16

5 05

6 50

7 30

NXW3

(*)

1-907

2-031

2-100

2-162

2-247

2-296

2-345

2-358

h0

000 1-00

2-00

283 4-17

6-02

7-83

9-58

10-25

(<f> <t>')X103

(*)

o-ooo

0-124

0-193

0-253

0-340

0-389

0-438

0-451

Date.

June 14. 9h 00m

10 30

1 3

2 6

3 50

5 27

t6 53

.ZVXIU3

2-393

2-401

2-407

2-409

2-409

2-412

2-412

h0

2375

25-25

27-80

2885

30-58

32-20

33-60

(</> <£')X103

0-486

0-494

0-500

0-502

0-502

0-505

0-505

Adjusted, T b f. t Subsequent movement apparently retrograde.

TABLE 6. APPARATUS II.

J2 = 202°»>; i=27cm ; A<0'2cm. Rods: No. 45, glass-hard, T= 180°; No. 46, annealed at 100°, 10h ,

2p=0-082 .

Date.

Aug. 8, 6" 10"- 

6 19

7 32

9, 9h 55m 

12 31 

7 52

10, 10" 02m 

1 19 

6 19

11, 10" 45"' 

1 14 

7 05

12, 9" 22m 

5 30

13, 9" 09- 

1 28 

4 41

iVXIO3

(*) 

1-502 

1-422

1-195 

1-169 

1-098

1-007 

0-993 

0-948

0-863 

0-833 

0-789

0-709 

0-658

0-576 

0-544 

0-526

Ao

o-oo

0-15 1-37

1575 

18-35 

25-70

39-87 

43-15 

48-15

68-19

91-26

114-93

(0 <£')X103

(*) 

 0062 

+0-018

0-245 

0-271 

0-342

0-433 

0-447 

0-192

0-615

0-756

0-891

Date.

Aug. 14, 9" 11 

5 12

15, 1" 34m 

6 35

16, 1" 27"1 

6 55

17, 9" 22 

6 55

18, 9h 15m 

5 29

19, 9" 03-" 

6 35

20, 9h 16" 

6 44

NXIO3

0-440 

0-399

0-316 

0-298

0-234 

0-211

0-163 

0-119

0-070 

0'046

0-007 

0-008

 0-040 

 0-056

Ao

139-03

165-91

190-02

211-98

235-20

259-65

283-83

(<t> <£')X103

1-020

1-133

1-218

1-299

1-382

1-440

1.488

'Adjusted, r + b+f.
BABU8-] VISCOSITY OF HARD STEEL. 17

 400"» ; i 27cm. A<0.2<

TABLTC 7. APPARATUS III.

Kods: No. 7, glass-hard, T= 180°; No. 8, annealed at 100°, 10h, 

2p = 0-082"".

Date.

July 1, 12h 40 

1 20 

2 45

3 25 

4 37 

5 39

6 69

2, 9h 22"' 

1 40

5 11

3, 8" 20"' 

12 14

4, 9h 47,,, 

12 09

6 00

5, 8h 40'" 

12 00 

4 44

2VX10"

(*) 

3-122 

2-904

2903 

2-809

2'027 

2-578

2-554

2-435 

2-397

£i DO L

2-233 

2-208

9-1 QQ

2-153

2-061 

2-033 

1-992

Ao

o-oo

067 2-08

2-76 

3-95 4'98

20-70 

25-10

4367 

47-57

73-10

95-80

(4>-<f>')X103

(*;

 0-128

±0-000

+0-038 

0-091 

0-125

0-162

0-307 

0-416

0-440

0-559 

0597

0-800

0-965

Date.

July 6, 8" 40- 

1 53 

5 16

7, 8" 53-n 

1 30 

5 1C

8, 9* 16"'

12 43 

5 48

9, 8" 35"'

12 11

5 18

* 10, 8h 07"'

12 09 

5 20

11, 9" 08m

2VX103

1-890 

1-854 

1-826

1-730 

1-691 

1-660

1-547

1,515 

1-465

1-366

1-339 

1-307

1-225

1-200 

1-162

1-080

A0

120-61

144-55

168-59

192-02

215-87

236-47

(0_$')X108

* 1-137

1-300

1-485

1-657

1-708

1-914

* Adjusted,

TABLE 8. APPARATUS IV.

JZ=308cm ; J=26cm ; A<0-2"°. Kods: No. 9, glass-hard, T= 180°; No. 10, annealed at 100°, 10",

T + 180°. 2p = 0.0821"".

Date.

Jnly 1, lh 40'" 

2 46 

3 26

4 39 

5 40 

7 00

2, 9" 23m 

1 48 

5 12

3, 8" 22m 

12 15 

6 30

4, 9" 491" 

12 10 

3 09

iVXIO3

(*) 

1-185 

1-213

1-246 

1-265 

1-290

1-420 

1-459 

1-482

1-577 

1-605 

1-641

1-729 

1-747 

1-770

A0

o-oo

1-10 1-77

2-82 

4-00 

5.33

19-72 

24-13 

28-53

42-70 

46-58 

52-83

72-12

(<f>_<f>') X 103

(*)

o-ooo

0-028

0-061 

0-080 

0-105

0-236 

0-274 

0-297

0-392 

0-420 

0-456

0574

Date.

July 5, 8k 41"> 

12 00 

4 45

0, 8h 42- 

1 54 

5 17

7, 8" 54'" 

1 32 

5 18

8, 9" 18m 

12 43 

5 49

9, 8h 37"1 

12 11 

5 19

10, 8" 07m

-ZVXIO3

1-876 

1-899 

1-935

2-027 

2-063 

2-088

2-185 ' 2-222 

2-249

2-362 

2-385 

2-427

2-524 

2-547 

2-581

2-655

A0

94-81

119-63

143-58

167-61

191-04

210-45

«.-</>') X103

0-718

0-874

1-034

1-200

1-360

1-470

* Adjusted, t b f.

The data of these tables are graphically given in the accompanying 

Fig. 8, deformation ((p-cp'), as ordinate, time in hours as abscissae. Some 

irregularity of behavior is visible, due to the fact to be further-indicated 

in chapters n and in, that the viscosity of glass-hard steel can be 

enormously reduced by twisting. Indeed a glass-hard wire twisted back 

and forth as far as maximum viscosity shows about the same value of 

that quality as a rod annealed at 100° to the maximum of permanent 

hardness. In their mean relations, however, the results of this figure 

are satisfactory and easily comparable with the new results now to b.e. 

adduced.

Bull. 13. 2
18 THE VISCOSITY OF SOLIDS. | BULL. 73.

The ordinates increase in the order of greater viscosity so that the 

abscissae are glass-hard wires,

1.0

OX)

' T

9-

Tc ble 2.

TaAle.3 

Table-3.

-Ta&U.

Tine JLTV

Tablet

Ttl>lt.6>

\oura

TabU4.

FIG. 8. Viscous deformation of steel annealed at 20° and at 100°, compared with glass-hard steel.

19. Rods annealed at 190°. The data obtained are as follows: 

* TABLE 9 APPARATUS II.

/e=200 ; l=27cm ; A-CO-2"". Kods: No. 11, glass-hard, T- 180°; No 12, annealed at 190°, 2»;

o. 2pz=0-082"'1 .

Date.

July 1, 4h OO4 35 

5 36 

6 58

N X 103

(*) 

2-913 

2-767 

2-655

A»

o-oo

0-58 

1-60 2-97

(4> <f>')X103,

(*) 

 0-073 

+0-073 

0-186

Date.

July 2, 9"1 20-» 

1 45 

5 09

July 3, 8h 19"' 

12 12 

6 28

2VX103

2-215 

2-133

2-080

1-891 

1-843 

1.757

Ao

17-33 

21-75 

25-15

40-32 

44-20 

50-47

(0 0') X103

0.625 

0-707 

0-760

0.949 

0-997 

1-803

* Adjusted, T + 6 +/.
BAKUB.] VISCOSITY OF TEMPERED STEEL. 19

TABLE 10 APPARATUS III.

J{=370 ; 1 = 26 ; A<0-2<"n. Hods: No. 13, glass-hard, T= 180°; No. 14, annealed at!90°, lh ;

2p=0-082 .

Date.

June 14, 12" 30 

1 10 

2 05 

3 51 

4 21 

5 29 

6 55 

7 51

15, 9" 04-" 

10 00 

11 15 

1 10 

2 58 

4 17 

5 41 

6 18

16, 81- 00'" 

9 32 

1 07 

3 19 

5 50

17, 8" 34" 

10 29 

12 43 

3 35 

5 29 

6 45

18,llh 45"' 

4 39 

t6 09

19, 9>> 07- 

12 19 

2 25 

5 50

20, 8h 53m 

10 53 

3 26 

7 44

JVX10'

(*) 

1-025 

1-198 

1-402 

1-448 

1-525 

1-600 

1-648

2-022 

2-012 

2-073 

2-121 

2-165 

2-195 

2-223 

2-233

2-467 

2-492 

2-556 

2-597 

2-638

2-861 

2-899 

2'942 

2-995 

3-043 

3-066

3-236 

3-283 

3-293

3-410 

3-432 

3-445 

3-458

3-567 

3-581 

3-622 

3-652

ha

o-oo

0-67 

1-58 

3-35 

3-85 

4-98 

6-42 7-35

20-57 

21-50 

2275 

24-67 

26-47 

27.78 

29-18 

29-80

48-26

73-43

99-02

120-92

145-23

(0-4>')X103

(*)

 0-065 

+0-108 

0.312 

0-358 

0-435 

0-516 

0.558

0-932 

0-952 

0-983 

1-031 

1-075 

1-105 

1-133 

1-143

1-460

1-878

2-181

2-346

2-515

Date.

June 21, 8" 22"° 

12 15 

5 44 

t7 17

22, 9" 10"> 

1 18 

2 20 

6 42

23, 8" 30- 

12 43 

5 42

24, 9h 02"° 

12 39 

4 58

25, 8" 44'" 

11 38 

t5 31

26, 8b 29"- 

12 1H 

3 12 

6 52

27, 8>> 52'" 

3 06

28. 8b llm 

11 30 

5 25

29, 8" IV 

3 46 

5 52

30, 8h 53"" 

12 26 

5 25

July 1, 8h 47 

JVX10'

3-732 

3-763 

3-810 

3-823

3-913 

3-943 

3-948 

3-980

4-056 

4-077 

4-111

4-197 

4-222 

4-248

4-335 

4-351 

4-383

4-448 

4-467 

4-483 

4-504

4-575 

4-609

4-699 

4-720

4-744

4-811 

4-854 

4-866

4-943 

4-962 

4-982

5-028

fto

169-91

193-38

214-86

240-38

264-13

289-18

311-49

335-87

361-44

384-41

-.404-28

(4> 4>')X103

2-692

2-856

2-971

3-132

3-266

3-385

3-502

3-631

3-754

3-872

5-028

* Adjusted, T b f. tBeadjusted after this observation.

TABLE 11 APPARATUS III.

Kode: No. 19, glass-hard, T= 180°; No. 20, annealed at 190°, 

2*=+ 180°. 2p =

Date.

.July 11, 3b 20"> 

4 10 

4 20 

5 22 

7 00

12, 7 h 37m 

7 55 

9 02 

10 55 

5 27

12 29 

5 08

14, 8" 54°' 

12 51 

4 41

N X 103

(*) 

 0-037

±0-000

+ 0-161 

0-329

0-913 

t 

0-466 

0-523 

0-696

0-952 

0-999 

1-061

1-230 

1-270 

1-314

Ao

o-oo

0-83 

1-00 

2-03 3-67

1628 

10-58 

17-70 

19-58 

26-12

41-15 

4515 

49-80

69-49

«> <f>') X103

(') 

 0-037

 t o-ooo

+0-161 

0-329

0-91^ 

t 

0-960 

1-017 

1-190

1-446 

1-493 

1-555

1-765

Date.

July 15, 10" 46-" 

4 26

16, 9h 18m 

1 44 

5 55

17, 8" 47°" 

12 53 

6 02

18, 8" 44- 

2 26

19, 9h 39°> 

12 20 

5 12

N X 103

1-491 

1-548

1-695 

1-740 

1-780

1-899 

1-940 

1-992

2-096 

2-151

2304 

3-331 

2-371

h»

94-27

118-32

141-90

164-25

189-73

(<f>_4,')X10»

2-013

2-232

2-438

2617

2-829

' Adjusted, t Adjusted, T b f.
20 THE VISCOSITY OF SOLIDS. [BULL. 7a 

TABLE 12 APPARATUS IV.

E = 300cm ; Z = 27cm ; A<0-2cm . Rods, No. 15, glass-hard, T- 80°; No. 16, anuealed at 190°, lb ;

Date.

July 11, 4" 25'" 

4 42 

4 55

5 25 

7 00

12, 7" 38"

5 28

13, 8" 29">

12 29 

5 09

14, 8" 54 

12 52 

4 42

15, 101' 47'" 

4 26

JVXIO'

(*) 

 0210 

 0-143

 0-035 

+0-153

0'685

0-937

1-179

1-222 

1-280

1-434

1-473 

1-512

1-670 

1-720

*o

o-oo

0-28 0-50

1-00 2-58

15-22

25-05

40-07

44-07 

48.73

68-40

93-20

(<f> 4>')X103

 0-175 

 0-108

±0-000

+0-188

0-720

0-972

1-214

1-257 

1-315

1-508

1-730

Date.

July 16, 9h 19* 

I 45 

5 58

17, 8" 49m 

12 54

6 03

18, 8h 45 

2 47

19, 9" 40'" 

12 21

5 13

20,. 8" 32'" 

11 40

JVX10*

1-849 

1-885 

1-917

2022 

2-052

2099

2-198

2-243

. 2-378 

2-419

2-429

2-517 

2-538

ft0

117-26

140-84

J63-35

18866

209-68

(cp-4>')X103

1-919

2-093

2-256

2-444

2-562

* Adjusted, r b f.

The results of these tables are given in Fig, 9, in the way already 

indicated in Fig. 8. The agreement here is much more uniform than 

in the former case. Kods show prououuced increase of viscosity.

jp;

FIG. 9. Viscous deformation of steel annealed at 190°, compared with glass-hard steel.
BAEUS.] VISCOSITY OF TEMPERED STEEL. 

20. Rods annealed at 300°. The data obtained are as follows: 

TABLE 13. APPARATUS II.

E - 200"-; Z=27 ; A<0-2 . Rods! No. 17, glass-hard, T= 180°; No. 18, annealed at 350°, 1",

2p 0-082"".

21

Date.

July 4, JO1' 35m 

10 53 

12 08

5 59

5, 8>' SUall 59

5 43 6, ~8 h "40~ ~

1 52 

5 15

7, 8'- 50'"

1 26 

5 15

8, 9 1' 15'"

12 42 

5 47

9, 81' 34m 

12 10 

5 17

^XlOS

(*) 

 2-707 

 2-457

 1-929

 1-423 

 1-3 '8

~ 0882"

 Q-r,3

 0'7u3

 0-455

 0-307 

 0-295

 0-056

+0-007 

0-089

0-274 

0-321 

0-383

fco

o-oo

0-30 1-55

4-53

7-40

22.07 

25-40

31-13

" 46 08

51-28 

54-67

74-59

98-66

122-09

($ <l>>)X103

(*) 

 0-207 

+0-043

0-570

1-076 

1-181

1-312 

1-617

1-720 1-7'IG

2-127

2-513

2826

Date.

July 10, 8h 05'" 

12 08 

5 19

11, 9h 08 

11 34

5 21 

6 59

12, 7 h 36"' 

5 26

13, 8'- 27m 

12 27

5 08

14, 8" 03 

12 48

4 40

15, 10 h 45 

4 25

16, 9" 17'"

iVXIO3

0-545 

0589 

0-043

0-797 

0-821

0-881 

0-892

0-993 

1-072

1-163 

1-180

1-215

1-299 

1-323

1-348

1-446 

1-483

1 565

7t0

145-93

171-67

193-93

218-10

242-20

207-00

280-70

«. £') XI 0»

3-092

3-348

3-533

3-68G

3-823

3-965

4-065

JZ=r316c

* Adj usted T b f.

TABLK 14. APPARATUS IV.

I_26cm; \<0-2cm. Rods: No. 21, glass-hard, T= 180°; No. 22, annealed at 300°, ] 

2p = 0-082 .

 +180°

Date.

June 14, '2h 45"' 

3 52 

4 22 

5 30

6 55 

7 53

15, 9h 05'" 

tlO 00

11 16 

1 11 

 3 00

1 4 36 

5 42 

6 19 "ier8h~d2'°

9 33 

1 09

5 50

17, 8h 35 

12 44 

3 36

5 30 

6 45

18, 8h 53'"

11 45 

4 40 

t6 10

19, 91' 09 

12 19 

2 27

20, 8h 54'" 

10 59 

3 25 

7 45

NXIQ3

(*) 

1-155 

1-250 

1-415

1-558 

1-632

2-198 

2-231

2-273 

2-340 

2-400

£i tta

2-478 

2-490 " """ 2-802" 

2-837 

2-928

3-028

3-302

3-405 

3-465

3-503 

3-531

3741

3-770 

3-829 

2-850

4-000 

4-026 

4-037

4-193 

4-2H 

4-250 

4-280

Ao

o-oo

1-12 

1-62 2-75

4-17 5-13

18.33 

19-25

20-52 

22-43 

24-25

t> t>/

20-95 

27-57 

46-03*

71-19

95-12

118-69

14301

(,£ </,') X103

(*) 

0-025 

0-120 

0-285

0-428 

0-502

1-068 

1-101

1-143 

] 210 

1-270

1-348 

1-360 " """1-785

2-296

2-667

2-904

3-105

Date.

June 21, 8h 23"1 

12 15 

5 45 

7 16

22, 9 h llm 

1 19

4 13 

6 43

23, 8h 30'" 

12 43 

5 42

24, 9 b 03'" 

12 40 

4 59 25, "8h~45v"" 

11 39 

5 30

26, 81' 30m

6 53

27, 8h 53" 

3 07

28, 8" 13'" 

11 31

5 26

29, 8h 12'" 

3 45 

5 53

30, 8h 54"' 

12 27 

5 26

July 1, 8h 48-"

JVX10"

4-374 

4-403 

4-447 

4-456

4-541 

4-558

4-573 

4-583

4006 

4-699 

4-732

4-829 

4-853 

4-873 4-973" 

4-997 

5-044

5-143

5-213

5-303 

5-350

5-450 

5-471

5-508

5-595 

5-647 

5-662

5-740 

5-757 

5-780

 5-848

7w

107-66

191-61

214-22

238-15 

~26l'-88~

280-87

309-25

333-64

359-19

382-18

40205

(4> <f.')X10*

3-290

3-434

3-569

3-722 

"37875"

4-048

1-396

4-346

4-505

4-629

5-818

; Adjusted r b /. t Readjusted.
22 THE VISCOSITY OF SOLIDS. [BULL. 73.

Figure 10 contains a graphic representation of the preceding tables 

on the plan already described (cf. Table 8).

4.0

3.0

2.0

2tr>ie inPIG. 10. Viscous deformation of steel annealed at 360°, compared with glass-hard steel.
BAKUS.] VISCOSITY OF TEMPERED STEEL. 

21. Rods annealed at 450°. The data in hand are as follows :

23

TABLE 15. APPARATUS I.

JK=217<-m ; A^26cm ; Z<0'2 . Rods : No. 23, glass-hard, T= 180°; No. 24, annealed at 450°, lh,

Date.

July 21, 2h 50 

3 17 

4 44

5 21

C 13

22, hh 4U m

5 30 

7 10

23, 7h 49 

12 30 

3 31

24, 9h 13 

12 52 

4 10

26, 8h 53m 

12 07

27, 8h 49">

JL.£i £i\3

4 04

28, 9» 11"- 

1 07 

4 17

NXIO3

(*) 

3-276 

2-901

2-805 

2-698

1924

1-606 

1-552

1-307 

1-141 

1-072

0-769 

0-702 

0-647

0-126 

0-081

 0-146

 0-193 

 0-235

 0-423 

 0-468 

 0-503

fco

o-oo

0'45 1-90

2-52 3-38

17-83

21-13 

26-67 

28-33

40-98 

45-67 

48-68

69-91

117-40

141-60

166-03

(<f> </>')* 103

(*)

 0-176 

+0-198

0-294 

0-401

1-175

1-301 

1-493 

1-547

1-792 

1-958 

2-027

2-393

3-019

8-290

3-564

Date.

July 29, 8'' 56 

12 36 

4 22

30, 8h 52 

1 05

« 4 07

31, 91' 28"' 

12 36 

3 55

Aug. 2, 91" 38m 

1 11 

4 05

3, 9" 38"' 

1 14 

4 18

4, 1" 3lm 

4 23

5, lh 36"'

5 25

6, 9" 12"" 

5 26

7, 9" 15"' 

6 41

JVX103

 0-673 

 0-714 

 0-758

 0-937 

 0-991

 1-030

 i-210 

 1-249 

 1.281

 1-639 

 1-672 

 1 696

 1-807 

 1-826 

 1-844

 1947 

 1-962

2-052

 2-073

 2139

 2-175

 2-225 

 2-268

A0

189-80

213-85

237-82

28613

310-22

336-12

360*67

38248

407-13

(<t> <f>') X103

3-814

4-085

4-345

4-708

4-926

5-055

5-257

5-346

* Adjusted r + b +/.

.TABLE 16. APPARATUS II.

Rods: No. 25, glass-hard, T . 180°; No. 26, annealed at 450°, lh , 

T + 180°, 2p = 0-082 .

Date.

Junel5,12h 50'" 

1 07 

1 15 

1 30

1 45 

2 55 

4 15 

5 39

16, 7" 66'" 

9 30

3 17 

5 49

17, 8h 33m 

10 26 

12 41 

3 31

5 26 

6 44

18, 8" 48m

11 43

4 38

6 07

19, 9h 05m 

12 10

2 23 

5 50

20, 8" 12«-

10 52 

3 24 

7 42

NXW3

(*) 

1-968 

2-046 

2-152

2-239 

2-475 

2-648 

2-776

3-447 

3-506

3-703 

3-780

4-134 

4-191 

4-258

J .007

4-378 

4-410

4656

4-690

4-759

4-778

4-953 

4-982

4-998 

5-031

5-170

5-179 

5-232 

5-270

7io

o-oo

0-28 

0-42 0-67

0-92 

2-08 

3-42 4-82

19-10 

20-07

24.27 

26-45 

28-98

49-06

96-53

120-71

(<f> <£')X103

<*) 

 0-282 

 0-204 

 0-098

 0-011 

+0-225 

0-398 

0-526

0-575

1-197 

1-256

1-453 

1-530

2-035

2-741

2-963

Date.

June21, 8h 20m 

12 15 

t5 40 

7 19

22, 9h 08m 

1 16 

4 10 

6 40

*> » oh 97m

12 40 

5 41

24, 9" 00"' 

12 37 

4 55

25, 8" 42 

11 36 

5 28

26, 8h 27m 

12 05

6 05

27, 8" 51°> 

3 02

28, 8" 08 

11 29 

5 24

29, 8h 09m 

3 43

5 50

30, 8" 52"> 

12 '29 

5 24

July 1, 8" 39m

NXW

5364 

5-401 

5-4C6 

5-478

5-573 

5-597 

5-617 

5-632

5-748 

5-781

5-880 

5-909 

5-941

6-045 

6-068 

6111

6-206 

6-227

6-367 

6-412

6-516

6-535 

6-678

6-662 

6-714

6-728

6-811 

6-825 

6-845

6-910

h*

145-55

169-47

1 Q9 1 A

216-01

239-76

264-29

287-11

311-51

337-07

350-08

379-82

(4> <£') X103

3-177

3-355

3 660

3-820

3-989

4-140

4-326

4-451

4-577

4-660

* Adj usted, T b f. t Readjusted.
24 THE VISCOSITY OF SOLIDS. [BULL. 73.

The results of these tables are given in the Chart Fig. 11 on the plan 

already clearly indicated. The ordinates increase in the order of greater 

viscosity.

FIG. 11. Viscous deformation of steel annealed at 450°, compared with glass-hard steel.
VISCOSITY OF SOFT STEEL. 25

22. Soft rods. The data in baud are as follows : 

TABLE 17. APPARATUS I.

&=27cm ; JR=202cm. Rods: No. 53, steel glass-hard; 2p=0f082cm ; T=r 180°; No. 54, steel drawn;

<* 

Date.

2 10 

2 30 

3 36 

8 00 

29,10 18

h

.0-00

0-17 0-50

v I 60

600 

20-30

NXVP

0-789 

0-661 

0'486 

+0-171 

 0-206

hg

017 

0-50 

1-60 

6-00 

20-30

(<£-<£') X103

 0-239

 0-111

+0-OG4 

+0-379 

+0-756

Remarks.

TABLE 18. APPARATUS 1.

A<e-2««. Rods: No. 27, glass-hard, T- 180°; No. 28, soft, 2"=+ 180°. = 0-082.

Date.

June 9, 2b 30" 

3 10 

3 13 

3 21 

3 47 

4 00 

4 10 

4 32 

5 15 

5 35 

6 00 

6 15

10, 8" 50°> 

9 35 

9 55 

10 15 

10 45 

11 20 

11 45 

12 17

10, lh 30m 

2 15 

3 05 

4 00 

4 40 

5 25 

6 25 

t7 40 

8 05 

8 20

11, 8h 06 

 9 28 

10 21 

' 10 45 

11 45. 

12 11 

2 30 

3 48 

4 50 

. 5 50 

7 00 

7 35

12, 8" 37 

9 25 

10 10 

1 05 

2 55 

4 58 

5 50 

8 30

13, 8h 40m 

10 15 

12 06 

1 25 

3 16 

5 07 

6 60 

7 30

NX103

(*) 

1-652 

1-677 

1-730 

1-860 

1-910 

1-940 

2-004 

2-102 

2-140 

2-185 

2-210

2-938 

2-964 

2-973 

2-985 

 3-002 

3-023 

3-038 

3-056

3-100 

3-128 

3-153 

3-191 

3-214 

3-238 

3-265 3'-287 

3-296 

3-304

3-512 

3-571 

3-588 

.3-598 

3-617 

3-628 

3-680 

3-709 

3-733 

3-753 

3-777 

3-787

3-989 

4-005 

4-017 

4' 076 

4-108 

4-H6 

4-162 

4-202

4376 

4-405 

4-436 

4-458 

4-485 

4-517 

4-545 

4-556

Ao

o-oo

0-67 

0-71 

0-85 

1-28 

1-50 

1-67 

2-03 

2-75 

3-08 

3-50 3-75

20-09

26-64

47-34

71-44

95-89

(<£ 4>')X103

 0-118 

 0-093 

 0;040 

+0-090 

0-140 

0-170 

0-234 

0-332 

1 0-370 

0-415 

0-440

1-227

1-448

1-895

2-318

2-702

Date.

June 14, 9h 04m 

10 30 

1 00 

2 06 

3 50 

5 27 

6 52 

7 50

15, 9h 00"> 

10 00 

11 15 

1 05 

2 55 

4 15 

- 5 38 

6 15

16, 7'1 58 

9 30 

1 05 

3 15 

5- 48

17, 8" 30°> 

10 26 

12 40 

3 30 

5 27 

7 43

18, 8" 46'" 

11. 43 

4 37 

6 08

19, 9" 04m 

12 09 

5 50

20, 8h 50'° 

10 50 

3 23 

7 40

21, 8h 20m 

12 15 

5 38 

7 19

22, 9" 07° 

1 16 

4 09 

6 40

23, 8h 28m 

12 40 

5 40

JVX10'

4-736 

4-757 

4-796 

4-813 

4-836 

4-853 

4-866 

4-873

4-990 

4-998 

5-015 

5-037 

5-060 

5-071 

5-082 

5-086

5-205 

5-223 

5-265 

5-285 

5-310

5-455 

5-485 

5-520 

5-550 

5-570 

5-590

5-705 

5-720 

5-760 

5-775

. 5-880 

* 5-890 

5-915

6-010 

6-023 

6-055 

6-080

6-140 

6-160 

6200 

6-210

6-270 

6-290 

6-305 

6315

6375 

6-405 

6-430

ha

120-33

143-30

16622

191-54

215-31

238-52

263-18

287-88

311-80

334-44

(<£ *')X103

3-046

3-272

3-488

 N

3-758 

3-970

4-125!

4-272

4-408

4-525

4-633

" Adjusted, T b f. t Readjusted.
26 THE VISCOSITY OP SOLIDS. 

TABLE 19. APPARATUS II.

[BULL.73.

JZ=202<in) ; Z--r28cm ; X<0'2cm . Rods: No. 29, glass-hard, T= 180°; No, 30, commercial, drawn,

T=+\m°. 2p = 0-082"".

Date.

July 21, 10" 45m 

11 50 

12 18 

2 03 

3 52 

5 22

22, W 40"' 

11 58 

5 31 

7 44

23, 7" 50* 

12 32 

3 33

24, 9" 16m 

12 53 

4 12

26, 8" 55m 

12 08 

3 47

27, 8h 51» 

12 27 

4 05

28, 9h 20 

1 09 

4 18

NXW3

(*) 

2-263 

2-206 

2-045 

1-926 

1-847

1-416 

1-341 

1-217 

1-187

0-984 

0-896 

0-851

0-624 

0-499 

0-456

 0-025 

 0-011 

 0-051

 0-211 

 0-255 

 0-293

 0.487 

 0-517 

 0-550

feo

0.00 

1-08 

1-55 

3-30 

5-12 

662

21-92 

25-22 

30-77 

32-98

45-08 

49-78 

52-80

74.03

121-53

145'7l

170-18

(<£ £') X103

(*)

o-ooo

0-057 

0-218 

0-337 

0-416

0-847 

0-922 

1-046 

1-076

1-279 

1-367 

1-412

1-737

2-292

2-516

2-781

Date.

July 29, 8" 56" 

12 39 

4 23

30, 8h 54'" 

1 06 

4 07

31, 9h 42'" 

12 37 

3 57

Aug. 2, 9h 39°> 

1 12 

4 06

3, 9" 40m 

1 15 

4 19

4, Ih 32» 

4 24'

5, 1" 37"> 

5 25

6, 9h 13 

5 27

7, 9" 17'" 

6 42

NXIO3

-0-709 

 0-749 

 0-788

 0-957 

 1-010 

 1-050

 1-230 

 1-263 

 1-297

 1-644 

 1-677 

 1-693

 1-780 

 1-784 

 1-793

 1 -872 

-1-880

 1-965 

 1-982

 2-044 

 2-078

 2-133 

 2-165

^0

193-90

217-96

242-01

290-23

314-33

340-22

364-77

386-59

411-24

(<t> <t>')X103

3-012'

3-269

3-526

3-934

4-040

4-139

4-237

4-324

4-412

*Adju8ted,T

TABLE 20. APPARATUS III.

72=370 ; Z-=27on'; A<0-2cm. Kods: No. 31, glass-hard, T- 180°; No. 32, commercial, softened,

T= + ISO0. 2p = 0-082c">.

Date.

July 22, 9" 00°> 

9 08 

11 59 

5 32 

7 11

23, 7" 52'- 

12 35 

3 25

24, 9h 21'" 

12 57 

4 16

26, 8h 57- 

12 10 

3 49

NXW3

(*) 

0-949 

0-331 

0-099 

 0-193

 0-643 

 0-794 

 0-880

 1 -246 

 1-320 

 1-384

 1-993 

 2-050 

 2-105

fco

o-oo

0-13 

2-98 

8-53 

10-18

22-87 

27-58 

30-42

48-35 

51-95 

55-27

99-31

(<j,_<f,')X10s

(*) 

 0-249 

+0-368 

0-600 

0-893

1-343 

1-494 

1-580

1-946 

2-020 

2-084

2-749

Date.

July 27, 8"« 54 

12 30 

4 08

28, 9" 26m 

1 11 

4 20

29, 8" 59- 

12 42 

4 28

30, 8" 57m 

1 10 

4 17

NX 10*

 2-305 

 2-356 

-2-404

-2-612 

 2-658 

 2-695

-2-875 

 2-923 

 2-974

 3-160 

 3-217 

 3-261

»o

123-51

147-98

171-72

195-80

«>-<£') X 10»

3-055

3-355

3-624

3-913

* Adjusted r+b+f.
BAHUS.] VISCOSITY OF SOFT STEEL. 

TABLE 21. APPARATUS IV.

27

A<0-2«' Kods: No. 33, glass-hard, T= 180°; No. 34, annealed at 1000°, 

T= + 180°. 2p=0-082<;m .

Date.

July 21, 4" 15" 

4 43 

5 23 

5 45 

6 12

22, 8" 42- 

12 00 

5 33 

. 7 12

23, 7" 53m 

12 36 

3 36

24, 9h 23m 

12 59 

4 19

26, 9 b 05m 

12 14 

3 52

27, 9" 03 

12 34 

4 10

1 16

4 23

NXW3

1-249 

1-089 

1-022 

0-957

0-162 

0-042 

 0-250 

 0-185

 0-559 

 0-628

 0-924 

 0-985 

 1-038

 1-540 

 1-581 

 1-633

 1-807 

 1-851 

 1-895

 2-125 

 2-159

ho

o-oo

0-47 

1-13 

1-50 1-95

16-45 

19-75 

25-30 

26-95

39-63 

44-35 

47-35

68-64

11614

140-35

(<f> 4>')X103

(*) 

 0-149 

+0-010 

0-077 

0-142

0-937 

1-057 

1-249 

1-281

1-547 

1-658 

1-727

2-082

2-685

^ 2-951

»

Date.

July 29, 91- 02-" 

12 45 

4 31

30,9" 00m 

1 13 

4 22

31, 9h 52"' 

' 12 41 

4 01

Aug. 2, 10h 02m 

1 24 

4 10

3, 9h 47m 

1 22 

4 24

4, 1" 38'" 

4 26

5, lh 40'" 

5 27-

6, 9h 14'" 

5 28

7, 9h 22'° 

6 43

N X 103

 2-324 

 2-367 

 2-409

 2-583 

 2-633 

 2-673

 2-850 

 2-882 

 2-912

 3-264 

 3-291 

 3-312

 3-428 

 3-436 

 3-442

 3-548 

 3-560

 3680 

 3-675

 3-733 

 3-777

 3-829 

 3-863

Ac

189-18

212-61

23661

284-95

308-93

334-78

359-31

381.10

405-80

(<£._<£') X 103

3-467

3-730

3'9rf2

4-389

4-534

4-654

4-768

4-855

4-946

*Adjusted,T+&i-/.
28 THE VISCOSITY OF SOLIDS. [BULL. 73.

The results of these tables are given in Fig. 12 on the plan already 

indicated. The observed differences are probably more largely due to 

the glass-hard wires than to the soft wires of the twisted system. To 

compare soft wires these must be specially countertwisted so as to secure 

greater accuracy of measurement.

I

5.0

AO

3.0 O

'9?

4<O7i,

FIG. 12. Viscous deformation of steel annealed at 1,000° (" soft") compared with glass-hard steel.

KKMARK8 ON THE TABLES.

23. In experimenting with couples of two glass-hard wires, or with 

couples in which one of the wires is annealed at 100°, the degree of 

hardness of the harder wire is an exceedingly important factor. Hence 

these curves (Tables 3, 4, 5, 6, 7, 8) appear under a variety of forms. 

Only Tables 4, 6, 7, 8 are used in the digest constructed below. The 

results in Tables 15, 19, 21 change their curvature after August 1.
REMARKS ON THE TABLES. 29

Since the same error is found in all the wires then examined it is probably a result of temperature. When minutely traced (cf. Table 18, for 

instance), the curves show a sinuous outline which is quite marked 

and probably also due to temperature or to tremors. If the curves for 

stated temperatures aud times of annealing fail to coincide, it is due to 

differences in the tempers of the glass-hard wires, to similar differences 

in the tempers of the annealed wires, to preexisting strains accidentally imparted to one wire or the other, to lack of perfect uniformity of 

temper throughout the efficient lengths, to unavoidable inequalities of 

the sectional areas of the pairs of wires. The last-named error probably 

also affects the curvature. Viscous rotation of the arms which carry the 

mirrors, or yielding of the cement, is nil and is not to be apprehended, 

since the fixed mirror is a fiducial mark for the movable mirror. In the 

above work we do not indicate the amount of permanent torsion left in 

each wire after the experiment is finished. Though an important desideratum, it does not fall within the scope of this chapter but will be 

given in Chapter III in connection with other work there discussed. 

The effect of temperature on twisted systems of pairs of identical steel 

wires we investigate in Chapter II, and then discuss the amount of 

detorsion due to annealing at stated temperatures and times. The soft 

ends introduce no serious error because soft steel is more viscous than 

hard steel. The amount of twist registered is that between the upper 

and lower points of attachment. The included wires must be of uniform 

hardness. ,

The fact that an effect of the bifilar and flexural components is wholly 

absent in these results is proved by Table 11, in which the curve for 

r+6-f/ is followed without break of continuity by the curve r b f, 

and the total curve is practically identical with the locus for Table 10. 

It is proved, moreover, by Tables 1, 2, in which couples of glass-hard 

wires show no greater difference than is at once attributable to unavoidable differences of hardness; and by Table 30 below, in which r-\-b+f 

and t 6 /produce practically identical zero-effects on two soft wires. 

It is generally proved by the distribution of the 50 rods examined in a 

diagram of viscosity conformably with the respective tempers of the 

rods. If a couple of one hard and one soft rod possessed a smaller total 

of viscosity than a couple of two hard rods, then the bifilar and flexural 

couples might produce an effect in the former case and not in the latter. 

The absence of all effect in the case of two soft rods as well as in the 

case of two hard rods shows that the discrepancy in question is nil. 

The important bearing of this result will be indicated below.

MISCELLANEOUS EXPERIMENTS.

24. Glass fibers. In Tables 22, 23 we cite the results obtained when 

one of the steel rods is replaced by a fiber of glass. The mean thickness 

or the diameter 2pg of glass was intended to be that of the steel rod 2p,; 

but it is smaller in Table 22 and considerably larger in Table 23. It is
30 THE VISCOSITY OF SOLIDS. [BULL. 73.

impossible to store a greater total torsion than TI ( T2)=90° in the 

given system, without breaking the glass fiber. The equality of TI and 

T2 is assumed merely for convenience in designation (cf. pp. 12, 40). In 

Table 23, moreover, the glass-hard rod used during the first half of the 

experiment is replaced by an annealed rod in the second half, leaving 

the glass fiber unaltered. The suspension here is practically unifilar, 

since it is nearly impossible mechanically to clutch the glass fiber without breaking it.

TABLE 22. APPARATUS I.

_B = 215cm ; Z:=27cai ; X<0-2cm. Kods: No.35,glass-hard steel, Tt = + 45°; No. a. glassflber, T2 = 45°;

p» = 0-082cm ; ft7

Date.

June 29, 3" 20"> 

3 42 

4 20 

5 30 

5 51

30, 8" 50- 

12 23 

1 57 

5 22

July 1, 8" 37" 

2 12 

4 36 

5 37 

6 57

2, 9h 19- 

1 45 

5 09

2VX103

(*) 

 0-129 -o-ioi

 0-052 

 0-031

+0-351 

0.413 

0.440 

0-486

0652 

0-706 

0-732 

0-741 

0-753

0-854 

0-879 

0-899

ho

O'OO 

0.37 

1-00 

2-17 2-52

17-50 

21-05 

22-62 

20-03

41-28 

46 '87 

49-27 

50-28 

51-62

05-98 

70-42 

73-82

(f_</>') X 10'

(*) 

-0-028

±0-000

+0-049 

0-070

0-452 

0-514 

0-541 

0-587

0-753 

0-807 

0-833 

0-842 

0-854

0955 

0-980 

1-000

Bate.

July 3, 8h 17m 

12 12 

6 27

4, 9" 45 

12 09 

3 06 

5 59

5, O1' 39-° 

12. 00 

4 43

6, 8" 40°> 

1 52 

5 15

7, 8h 49m 

1 27

JVX103

0-974 

0-991 

1-026

1-098 

1-109 

1-116 

1-145

1-213 

t-228 

1-257

1-318 

1-339 

1-355

1-420 

1-443

ft0

88-95 

92-87 

99-12

114-42 

116-82 

119-77 

122-65

138-32 

140-67 

145-38

161-33 

166-53 

169-92

185-48 

190-12

(0 0') X103

1-075 

1-092 

1-127

1-199 

1-210 

1-217 

1-240

1-314 

1-329 

1-358

1-419 

1-440 

1456

1-521 

1-444

2 = 223«m ; £=23 Kods:

* Adjusted. 

TABLE 23. APPARATUS I.

No. 36, glass-hard steel, 2I) = + 45°; No. b, glass fiber, T2 

2ps = 0'082cm ; O t085cm<2p3<0-120cro .

= 45°;

Date.

July 7, 4" 15°> 

4 26 

4 38 

5 15

8, 9" 14m 

12 41 

4 07 

5 47

9, 8h 33m 

12 10 

5 16

10, 8" 04m 

12 08 

5 18

11, 9" 07°> 

11 23 

5 21 

6 59

NXW

(*) 

2995 

2-934 

2-865

2-8ii3 

2841 

2-858 

2-863

2-912 

2-928 

2-940

2983 

2996 

3-010

3-053 

3-058 

3-077 

3-081

A0

o-oo

0-18 

0-38 1-00

16-98 

20-43 

23-87 

25-53

40-30 

43 '92 

49-02

63-82 

67-88 

73-05

88-87 

91-13 

97-10 

98-73

(0 </>')X103

(*) 

-0-130 

 0-069 

±0-000

+0-042 

0-024 

0-007 

0-002

 0-047 

 0-063 

-0075

 0-118 

 0-131 

-0-145

 0-188 

 0-193 

 0-212 

 0-216

Date.

July 12, 7h 35 

JVX103

3-100

Glass-hard rodreplaced by 

42, annealed, 450°, 1", T, -- +

July 12, 9h 39m 

9 49 

10 54 

5 25

13, 81- 26- 

12 27 

5 06

14, 8" 50" 

12 48 

4 40

15, 10h 45m 

4 25

16, 9h 16m 

1 42 

5 54

(*) 

1-358 

1331 

1-303

1-278 

1-270 

1-270

1-258 

1-258 

1-255

1-245 

1-245

1-237 

1-237 

1-236

ha

111-33

soft steel i 

45°, 2p 0

o-oo

0-17 1-25

7-77

22-78 

26-80 

31-45

47-1.8 

51-15 

55-02

73-10 

78-77

95-62 

100-05 

104-25

(# 4>')X103

 0-235

 od, viz: No.

 082 . .

(*) 

 0-023 

+0-004 

0-032

0-057 

0-065 

0-065

0-077 

0-077 

0-080

0-090 

0-090

0-098 

0-098 

0-099

* Adjusted.
BARU8.J VISCOSITY OF GLASS AND IRON.

The results obtained with glass are given in Fig. 13. The thinner 

glass fiber is uniformly less viscous than steel. The thicker fiber lies 

between hard steel and soft steel in viscosity. But the occurrence of 

the maximum is noteworthy. Glass is here initially more and ultimately less viscous than hard steel.

TableZZ

1.0

QO

1.0

7&i

Steel softy.

FIG. 13. Viscous deformation of steel as compared with glass.

25. Iron, soft and drawn. Tables 24, 25, 26, 27, contain a part of our 

results in which one steel wire is replaced by a wire of wrought iron, 

annealed or drawn as specified. That the amounts of torsion are equal 

in angle (T) is again assumed for convenience of designation only. pa is 

the radius of steel, pt of the iron wire. The applied couple twists soft 

iron beyond the limits of elasticity and the amount of instantaneous 

detorsion is here probably as large as %(Ti+Tz). In case of steel 

instantaneous detorsion is nearly zero.

TABLE 24. APPARATUS I.

223om ; l=Z6cm ; A<0-2«m. Bods: No. 37, steel, annealed at,450°, lb , T= +180°; No. c, wrought iron, 

drawn, T~ 180°. 2p8 =0-082cm ; 2p£=0-083cm.

Date.

July 17, 4b 20m 

4 23 

4 27 

4 51 

5 20 

6 01

JVX10'

1-955 

2-032 

2-113 

2-285 

2-342 

2-362

/» 

0-20 

0-25 

032 

0-72 

1-20 1-88

(0-0') X103

 0-387 

 0-310 

 0-229 

 0057 ±0-000

+0-020

Date.

July 18, 8 "27m 

2 24

19, 9" 37 

12 19 

5 10

20, 8" 29m 

3 45

JVX10*

2-177 

2-122

2-032 

2025 

2-014

1-984 

1-977

ft«

16-32

22-27

41-48 

44-18 

49-03

64-35 

7162

(*-</>') X10*

-0-165 

 0-220

 0-310 

 0317 

 0-328

 0-358 

 0-304

'Adjusted T & /.
32 THE VISCOSITY OF SOLIDS. 

TABLE 25. APPARATUS I.

[BULL. 73.

.E=217<!nl ; Z=27C ">; A<0-2CB1 . Bods: No.49, glass-hard, T= 180°; 2p = 0-082°m ; No. ft, wrought iron,

drawn, r== + ]80°; 2p=0-080<">>.

Date.

Aug. 31, 5h 45m

5 55 

6 30

Sept. 1, 8" 58m 

1 00 

6 12

2, 9" 05m 

5 34

3, 10b 02m

7 55

4, 9h 02'" 

7 40

5, 9" 50m 

6 30

6, 9" 05m

h

o-oo

0-17 0'75

15-22 

19-25 

24-45

39-3J 

47-82

04-28

74-17

87-28 

97-92

112-08

120-75

135-33

A'XIO3

0-967 

0'785

+0-017 

-0-072 

-0-166

 0-376 

 0-470

 0-626

 0-713

 0805 

 0878

-0-970 

 1-032

-1-124

fto

o-oo

0-17 0-75

15-22 

19-25 

24-45

39-33 

47-82

69-23

92-60

116-42

135-33

(<t> tf>')X103

-0-267 

 0-085

+0-683 

0-772 

0-866

1-076 

1-170

i-370

1-542

1-701

1-824

Bemarks.

Untwisted.

TABLE 26. APPARATUS II.

=2W°<»; l±=W» A<0'2cffl . Bods: No. 38, steel, annealed at 450°, lh, T= + 180°; No. d. wrought iron, 

soft, T= 180°. 2p» = 0-082l!m ; 2pi=0-112«n'.

Date.

July 16, 9h 40m 

9 48 

11 14 

1 48 

5 47

17, 8b 47m

ZVXIO'

(*) 

0-714 

0-745 

0-758 

0-750

0731

fto

o-oo

0-13 

1-57 

4-13 8-23

23-12

W.-tf.'JxiO*

 0-026 

+0-005 

0-018 o-oio

 0-009

T hick iron wire replaced by thin w ire. Bod No. 

9, wrought iron, soft ; T- 180°; 2p=0'083cm.

17, 5" 26°> 

5 30 

5 36 

6 00

0-755 

0-745 

0736 

0-718

to-oo

0-07 

0-17 0-57

 0-019 

 0-009 

±0-000 

+0-018

Date.

July 18, 8h 33°>t 

2 35

19, 9h 38m 

12 20 

5 10

20, 8b 28m 

. 3 44

2VX103

0.146 

0-151

0-128 

0-119 o-no

0082 

0064

fto

15-12 

21-15

(40-20) 

(42-90) 

(47-73)

(63 03) 

(70-32)

W>-<£')X103

(0-153) 

(0-148)

(0-171) 

(0-180) 

(0-189)

(0-217) 

(0-235)

* Accident; new adjustment; data otherwise good, but distinguished by parentheses, 

t Adjusted r l f. 

J Adjusted r + l+f, but the time not accurately noted.

TABLE 27. APPARATUS II.

JF2=202cm ; J=26cm ; A<0.2om. Bods: No. 50, annealed at 350°, lh, T= +180°; No. k, wrought iron, drawn, 

T 180°. 2p<=0 084cin ; 2p,=0 -082 .

Date.

Aug. 23, 2"> 00m 

2 13 

2 20 

3 11 

5 37 

7 11

24, 9h 17m 

5 13

25, 9" U5m 

7 00

26, 9h 10m 

4 08

2VX103

(*) 

2-052 

1-914 

1-599 

1-417 

1-392

1-385 

1-411

1-435 

1-448

1-460 

1-469

fto

000 

0-22 

0-33 

1-18 

3-62 5-18

19-28 

27-22

43-08 

53-02

70-65

(4> </>') X 10s

 0-452 

-0-314 

+0-001 

0-183 

0-208

0-215 

0-189

0-J65 

0-152

0-135

Date.

Aug. 27, 9b 10m 

7 36

28, 9" 21m 

6 55

29,10" 11'- 

6 17

30, 9 h llm

31, lb 19m 

6 00

Sept. 1, 9" 19m

2, 9" 05"' 

1 30

2VX103

1-483 

1-490

1-492 

1-494

1-500 

1-501

1-505

1-515 

1-515

1-517

1-524

1-528

fto

96-38

120-13

144-23

163-18

193-66

211-32

237-29

«>-(/)') X103

0-114°

0-107

o-ioo

0-095

0-085

0-074

* Adjusted T+Z+/.
BARU8-1 VISCOSITY OF IRON. 33

Figure 14 contains the results of Tables 24, 25,26 and 27. The signs 

of ordinate and ^wist agree for the wire of greater viscosity. The 

phenomena are here of a complicated kind, showing that viscous motion 

in iron and steel is not similar. The sharp maximum of Table 24 is 

specially noteworthy; as is also the less j^onounced maximum of Table 

27 both of which hold for drawn iron. A maximum is also apparent 

in the thick, soft wire of Table 26; whereas the thin, soft wire of this 

table and the soft wire iron of Table 25 show no retrogression.

O. ^\ Tolls 30.

Time

Table 25

Table

tvz. Jiou, -s.

Z*.

FIG. 14. Viscous deformation of steel compared with iron, soft and drawn.

Other allied data are as follows:

TABLE 28. APPARATUS I.

.R=202om ! l=27om ; Rods: No. 55, steel, annealed at 450°, 2p = 01 082cm ; T positive; No. m wrought 

iron, soft, 2p=0'080 ; T negative.

t Date.

Sept. 6, 9* 30"-

0 42

\j£

1 67 

7 12

7, 9" 11" 

6 11

8, 10 h 4SJ" 

7 42

h

o-oo

0-20

0-37 

4-45 9-70

23.68 

32-68

49-20 

58-20

.ZVX103

0-200

U u£i<j

0-307 

0-333

0-375 

0-397

0-444 

0-478

Ao

o-oo

0'20

U o/ 

4-45 9-70

23-68 

32-68

53-70

(*-*') x

10»

 0-050

 0-027 

+0-057 

H-0'083

0-125 

0-147

0-211

Date.

Sept. 9, IQi" 05m

6 30

10, 8h 32"1 

8 00

11, 9" 03m 

7 55

12, 9" 43- 

5 10

A

70- KQ

81-00

102-03 

106-50

119-55 

130-42

151-67

JVX103

n.coK

0-580

o-ooi

0-C78

0-735

0-751 

0-761

Ao

76*79

104-26

124-99

147-95

(*-*') X 103

0-307

0-421

0-478

0-506

Bull. 73 3
34 THE VISCOSITY OF SOLIDS.

TABLE 29. APPARATUS II.

[BULL. 73.

jB=200cin j Z=27cm, Kods: No. 50, steel, annealed at 450°; 2p = 0-OS2cm ; No.n, iron, soft; 2p = 0-083cn

Ta = + 90°; r»= 90°.

Date.

Sept. 6, 10b 00"

10 12

1 57 

7 12

7, 9h 11«>

e 11

8, 10" 42»> 

7 42

9, 10" 05"> 

6 30

10, 3b 32m 

8 00

11, 9b 031" 

7 65

12, 9h 43°' 

5 10

h

0-00

0-20

3-95 9-20

23-22 

32-22

48-70 

57-70

72-08 

80-50

101-53 

106-00

119-05 

129-92

143-72 

151-17

JVX103

2-072

2-118 

2-128

2-163

2-205

2-307 

2-371

2-477 

2'539

2-085 

2-715

2-807 

2-885

2 '938 

2-980

h0

o-oo

0-20

3-95 9-20

23-22 

32-22

53-20

76-29

103-77

124-48

147-45

(*-<*>') x

* 103

 0-008

+0-038 

+0-048

0-083 

0.125

0-259

0-42U

0-620

0.766

0-879

Date.

13, 10b 20»

9 10

14, 9" 00m 

7 14

15, 9" 00m

7 24

16, 9" 34"> 

7 07

17, 9b 20 

7 00

18, 9k 10°> 

9 08

19, 11" 55" 

20, 9 06

21, 9 22 

28, 2 33

h

168-33

179-17

191-00 

201-23

215-00 

225-40

239-57 

249-12

263-33 

273-00

287-17 

299-13

313-92 

335-10

359-37 

532-55

-ZVX103

3-067

3-116

3-153 

3-184

3-225 

3-244

3-280 

3-307

3-347 

3-379

3-415 

3-451

3-491 

3-541

3-559 

3-767

fto

1 70.7^

196-12

220-20

244-35

268-16

293-15

313-92 

335-10

359-37 

532-55

«>-<*>') X 

103

1-012

1-089

1-155

1-213

1-283

1-353

1-411 

1-461

1-479 

1-687

Permanent set 180° in iron.

TABLE 30. APPARATUS III.

= 370 ; Z=26«m ; A<0-2<"». Bods: No. 51, soft, T= 180°; No. 52, annealed at 450°; T= + 180°.

2p = 0-082<"".

Date.

Aug. 20, 12" 35m 

12 50 

6 44

21, 9b 07» 

5 00

21, 5" 15m 

5 25 

7 08

22, 9h 57"' 

6 54

23, 9" 08 

5 37

24, D" 18"' 

5 13

JVXIO3

(*) 

0-291 

0-306

0-314 

0-311

(t) 

0-546 

0-551

0-556 

0-561

0-561 

0-561

0-581 

0-581

7>o

o-oo

0-25 6-15

20-53 

28-42

o-oo

0-16 1-88

16-70 

25-65

39-88 

48-36

68-00

«>-<£') X 103

(*) 

 0-004

+0-011

0-019 

0-016

(t) 

 0-002 

+0-003

0-008 

0'0]3

0-013 

0-013

0-033

Date.

Aug. 25, 9h 05" 

7 01

26, 9" 10» 

4 08

27, 9" 10»- 

7 36

28, 9 20"' 

6 55

29, 10" Im2 

6 17

30, 9h llm

NX10*

0-581 

0-5G8

0-568 

0-556

0-548 

0-530

0-530 

0-520

0.515 

0-507

0-505

ha

92-80

115-40

144-13

164-87

188'-99

207-93

(<()-0')X10»

0-027

0-014

 0-009

 0-023

 0-037

 0-043

* Adjusted T 6 /. f Eeadjusted T + b +/.

Table 30 shows very clearly, the relatively insignificant difference 

which exists between steel annealed at 450° and soft steel, so far as 

viscosity is concerned. This difference is less than that between steel
BARUS.J VISCOSITY OP NICKEL AND COPPER. 35

aiid iron, as well as different in character. The results of Tables 28, 

29, 30 coutainiug further indication of the behavior of soft metal are 

given in Fig. 15.

ec l.O

z

Tablei

Table 28.

2C07* 3(0

FIG. 15. Viscous deformation of steel compared with iron.

For the purpose of further fixing the ideas I add some data with 

other metals. The results are to be constructed graphically in Figs. 

18,17. These relative results are difficult to interpret because of the 

varying amounts of permanent set incident to the experiments. To 

meet these errors the method must be varied as indicated in Chapters 

11 and III.

Nickel and copper. The data in hand are as follows:

TABLE 31. APPAKATUS III.

,K=370CU1 ; J=27cm. Rods: No. 61, steel, annealed soft; 2p=0-044cm ; No. p nickel, annealed soft, 

2p=0-04Scm ; Ts =

Date.

Sept. 15, llh 30m

11 45 

7 22

1C, 8" 34'" 

7 15

17, 9" 20m 

7 07 

"~187~9h 09^ 

9 09

10,11" 55m 

20, 9 05 

28,11 30

h

o-oo

0-25 7-87

22-07 

31-75

45-83 

55-62 ~~G9'65" 

81-65

96-42 

117-68 

312-00

iVXlO3

0-346 

0'371

0-386 

0-396

0-396 

0-401 0-396" 

0-351

0-346 

0-352 

0-371

Ao

o-oo

0-25 7-87

22-07 

31-75

50-72

""vlTeif

96-42 

117-68 

312-00

($ 0') X103

 -0-004 

-1- 0-021

0-036 

0-046

0-049 

._.....__ _.

 0-004 

+0-002 

+0-021

Remarks.

 -
36 THE VISCOSITY OF SOLIDS. [BULL. 73.

TABLE 32. APPARATUS IV.

314 m ! Z=27cin. Rods: No. 62, steel annealed at450°; 2p=0'082cint1; No. q copper drawn: 2p=0-083cin;

Ts = + 90°; Tc= 90°.

Date.

Sept. 10, 3" 06m

3 30

8 00

11, 9" 00°>

7 55

12, 9h 45">

6 41

13, 10 h 19m

9 12

14, 9" 00m 

7 15

h

'o-oo

0-40

4 '90

17-90

28-82

42-65

51'58

67-22

78-10

89-90 

100-15

.ZVX103

0670

0-850

0-940

0"963

0-995

1-016

1-022

1-034

1-046 

1-058

Ao

o-oo

0-40

4-90

17-90

28-82

47-12

72-66

95-03

(*-*') X 

10»

 0.030

+0-150

0-240

0-263

0-305

0-328

0-352

Date.

Sept. 15, 9h 00»

7 25

16, 9h 35m

7 10

17, 9h 19m

7 07

18, 9" 10m

9 10

19, llb 55m

20, 9 05

h

1 lO.Qft

124-32

138-48

14807

162-22

172-02

186-07

19807

236-82

245-98

JVX103

1 *flfi9

1-094

rioe

1-112

1-118

1-118

1-118

1-106

1-112

1-117

AO

119-11

143-27

167-12

19-207

236-82

245-98

«>-<£') X

103

A.qoo

0-4U9

0-418

0-412

0-412

0-417

Permanent set in copper 180°.

TABLE 33. APPARATUS I.

Kods: No. 63,steel,soft drawn,2p = 0-082cm ; No. r copper, softened; 2p=0-080"; 

T» positive. To negative.

Date.

Sept. 3,1" 55-"

2 06 

9 10

h

o-oo

0-18 7-25

*xu>3

0-468 

0-447

*o

o-oo

0-18 7-25

<*-*') X 

103

-0-008 

+0-013

Date.

Sept. 14, 9" 00°>

1 23

h

19-08

23-47

*X103

0-427

0-426

»,

19-08

23-47

(*-*') X 

103

0-033

0-034

Permanent set in copper nearly 360°.

TABLE 34. APPARATUS I.

JJ=202cnl ; Z=27cm. Kuds: No.64, steel,soft; 2p 0-082 ; 2I=+45°; No.s copper, softened,2p=0-155«!n T- 45°.

Date.

Sept. 14, lh 40m

1 47

1 58 

7 13

15, 9h GO* 

7 22

10,9" 33m 

7 06

h

o-oo

0-12

0-30 5-55

19-33 

29-70

43-88 

53-43

JVX103

0-920

0-942 

1044

1-112 

1-140

1-157 

1-167

7t0

o-oo

012

0-30 5-55

19-33 

29-70

48-65

(*-*') X 

10s

 0-080

-0-058 

+0-044

0-112 

0-140

0163

Date.

Sept. 17, 9" 20«-

7 05

18, 9" 10m 

9 06

19, 11"> 55m 

20, 9 05

21, 9 20

h

67-67

77-42

91-50 

103-43

117-75 

139-42

163-67

tfXIOS

1-170

1-193

1-208 

1-221

1-235 

1-250

-- 1-260

fto

79-fiR

97-47

117-75 

139-42

163-67

(£_<£/) x 

10"

0-186

0-214

0-235 

0-250

0-260

Permanent set of copper 270°.

The viscosity of nickel as compared with soft steel (Fig. 17) is worthy 

of note. The small deformations of copper are the result of the unavoidably small stress intensities which actuate the viscous motion.

JFio. 16. Viscous deformation of copper and nickel compared with steel annealed at 450°.
BARU8.] COMPARISON OF SOFT STEELS. 37

27. Steels annealed at 450° and 1000°. The data in hand are as follows :

TABLE 35. APPARATUS III.

J2=370cm ; Z=27om. Hods: No. 57, steel annealed at 450°; T=+180°; No. 58, steel, commercial, 

softened; T= 180°; 2p = 0'082cm.

Date.

Clant A. Qb Oflra

9 33

7 40

5, 9h 47m

6 3C

6, 9" 05- 

7 10

7, 9" 10m 

6 11

h

o-oo

0-22

10-33

24-45

33-17

47-75 

67-83

il-83 

80-85

2VX103

0-294

0-371

0-411

0-425

0-450 

0-455

0-465 

0-470

Ao

o-oo

0-22

10-33

24-45

33.17

52-79

76-34

(*-*') X 103

 0-006

+0-071

0-111

0125

0153

0-167

Date.

Sept. 8, 10" 42 

7 42

9, 10" 02">

6 30

10, 3" 30m

h

97-37

106-37

120-70

129-17

150-17

tfXlO3

0-485

0-495

0-505

0-515

0-525

fto

101-87

124-93

150-17

(*-*') X 10»

0-190

0-210

0-225

I=27<"

TABLE 36. APPARATUS IV.

Rods: No. 59, steel annealed at 450°, 2p = 0-082, T positive; No. 60, steel softened from hardness, 2p = 0-082, T negative.

Date.

Sept. 4, 9"> 40m

9 55

7 40

5, 9" 47m

6 30

6, 9 05"° 

7 10

h

o-oo

0-25

10-00

24-12

32-83

47-42 

57-50

2VX103

0-105

0-09(5

0-084

0-084

0-078 

0-084

Ao

o-oo

0-25

10-00

24-12

32-83

52-46

(*-*') X 10*

 b-002

+0-007

0-019

0-019

0-022

Date.

Sept. 7, 94 10m

6 11

8, 10" 42">

7 42

9, 10" 02m

6 30

h

71-50

80-50

9703

106-03

120-37

128-83

.yxio3

0-078

0-084

0-090

0-089

0-102

0-102

fto

76-00

101-53

124-60

(!*-*') X 103

0-022

0-013

0

o-ooi

The results for soft steels are constructed in Fig. 17, and corroborate 

Table 30 above, with reference to the small differences between steel 

annealed at 450° and steel annealed at 1000°.

FIQ. 17. Viscous deformation of steel annealed at 450°, compared with soft steel.

28. Quadrifilar arrangement. Table 37 contains results for a quadrifilar as explained below. The small differences of viscosity in question 

are scarcely sufficient to give character to the motion when the stress 

given is applied to such thin wires. Further experiments were not 

made.
38 THE VISCOSITY OF SOLIDS. [BULL. 73.

TABLE 37. APPARATUS III.

Quadrifllar suspension; I=27cm ; R 370 . Eods: No. 58, soft; T, = (+180°) + 90°; No. 57, annealed 

at 450°; r2 = ( 180°)+ 90°; No. 60, soft; T3=(+ 0°) -90°; No. 59, annealed at 450°; T4 = (-0°) 

 90°, p = 0-082c"'.

Date.

Sept 10, y> 45m

4 03

8 00

11, 9" 00m

7 55

12, 9" 45ra 

6 41

h

o-oo

0-30

4-25

17-26

28-17

42-00 

50-93

JVX103

0-906

0-906

0898

0-871

0-860 

0-871

h0

o-oo

0-30

4-25

17-25

28-17

40-46

(*-*') X 103

o-ooo

0-000

O'OOS

0-035

0-038

Date.

Sept.l3,10h 20m

9 12

14, 9>> 00 

7 14

15, 9" 00m

h

6Cv58

77-45

89-25

99-48

113-25

2VX108

0-856

0-848

0-846

0-846

0-866

h0

79'ft9

94-30

113-25

«>-</>') X 

103

0-055

0-060

0-040

29. Tubular apparatus. Table 38 and 39 contain our results with the 

tubular apparatus, pi is the inner radius, p2 the outer radius of the 

tube. Q and q denote the right sections of brass tube and steel wire 

respectively. Of course sections of metallic surface are meant. The 

inclosed wire is twisted alternately in opposite directions as is indicated 

by the sign of T. The result is similarly indicated by the sign of ( q> (p'}. 

Subscripts s and 1) refer to steel and brass respectively. Table 38 contains results for a thick tube, Table 39 for a thin tube. Hard or soft 

rods are inserted, as indicated.

TABLE 38. APPARATUS (tubular) II. 

:22cm. Kods: No. e, brass, 0P1 ^ o'^20<; ' No> 89' 8teel > = 0-127°mj

Date.

July 7, 9h 02ra 

12 15 

5 18

8. 9" 19" 

12 48 

5 50 

9, 8" 30m

9, 8h 50m 

12 12 

5 20

10, 8h 09m 

12 09 

5 18

11, 9" 20" 

11 35 

4 15

11, 4" 15 

4 45 

5 23 

7 00

12, 7" 39 

5 29

13, 8h 30">

NXlO*

0-308 

0-390 

0-420

0-460 

0465 

0-476 

0-500

0-456 

0-337 

0-283

0-222 

0-208 

0-191

0-160 

0-151 

0-142

0-540 

0-575 

0-597 

0-630

0-718 

' 0-743

0-779

Glass-hard rod replaced I 

No. 40, annealed, 450°, lh , 2

13, 10h 04m 

12 30 

5 05

14, 8h 55m

0-876 

0-886 

9-890

0-894

fto

*o-oo

3-22 8-27

' 24-28 

27-77 

32-80 

47-47

to-oo

3-37 8-50

23-32 

27-32 

32-47

48-50 

50-75 

55-42 " *o-oo

0-50 

1-13 2-75

15-40 

25-23

40-25

(</>-4>')X103

+0-002 

 0-080 -0-110

 0-150 

-0-155 

 0-166 

 0-190

-0-056 

+0-063 

+0-117

+0-178 

+0-192 

+0-209

+0-240 

+0-249 

+0-258

+0-060 

+0-025 

+0003

 0-030

 0-118 

 0-143

-0-179

y a soft steel rod, viz :

*0-00 . 

2-43 7-02

22-85

*

+0-004 

 0-004 o-oio

 0-014

Date.

July 14, 8" 57 

10 27 

12 45 

4 45

15, 1011 46m

15, 10" 46"> 

12 35 

4 27

16, 9b 20»

N+iQ3 

0-248 

0-248 

0-248 

0-250

0-250

0-310 

0-306

0-299

fto

*o-oo

1-50 

3-80 7-80

25-82 *o-oo

1-82 5-68

22-57

(£-4>')X103

±0-000 ±0-000

±0-000 

+0-002

+0-002

 0-005 

-0-009

 0-016

Original hard steel rod, No. 39, again inserted.

16, 9" 25 

11 26 

1 45 

5 58

17, 8" 50 

12 55 

6 04

18, 8" 27m 

2 28

19, 9" 4lm 

12 20 

5 15

20, 8'1 28m

20, 10" 50m 

11 18 

11 50 

1 53 

3 44 

6 35

21, 10" 02m 

12- 18

0-948 

1-009 

1-028 

1-052

1-093 

1-102 

1-125

1-151 

1-160

1-185 

1-186 

1-186

1-207

0-458 

0-416 

0-396 

0-354 

0-330 

0-303

0-247 

0-239

 *o-oo

2-02 

4-33 8-55

23-42 

27-50 

32-65

47-03 

53-05

72-27 

74-92 

79-83

95-06

to-oo

0-47 

1 ;00 

3-05 

4-90 7-75

23-20 

25-47

+0-032 

-0-029 

 0-048 

 0-072

 0-113 

 0-122 

 0-145

0-171

-0-180

 0-205 

 0-206 

-0-200

 0-227

 0-OB2

- 0-020

±0-000

+0-042 

+0-066 

+0-093

+0-149 

+0-157

* Total twist T, (-Ti>)=m°, twist of steel Ts, positive, 

t Total twist Ts + ( Tb) = 180°, twist of steel, positive.
BARUS.J INTERPRETATION OP (^> (?'). 

TABLE 39. APPARATUS (tabular) V.

39

12 = 260 ) Z=22cm. Rods: No. /, brass tube, ^2^=0-24 .' No' 41- stee1' annealed at 450°. lh. 

2p = 0-082 . Q =

Date*

Tnlxr 90 Qh Qftm

3 48 

5 39

7 13

23, 7" 64"' 

12 02

23, 12" 57m 

3 37

24, 9h 28m

1 03

4 23

26, 9" 08 

12 17 

3 58

27, 9h 08 

12 38 

4 13

JVX103

3-602 

3-541

3-518

3-465 

3-435

1-026 

1-147

1-289

1-300 

1-307

1-398

1-409 

T417

1-433

1-437 

1-441

7i0

to-oo

0-17 2-02

3'58

J16-27 

20-40 *o-oo

2-67

20-52

24-10 

27-43

68-18

71.33 

75'02

95-71

(<^_^')X103

'-H-0-032 

 0-029

-0-053

 0-105 

-0-135

-0-074 

+0-047

0-189

0-200 

0-207

0-298

0-309 

0-317

0-337

Date.

July 28, 9h 32-

1 18 

4 26

29, 9h 04m

12 48 

4 33

30, 9" 01°> 

1 15

4 16

31, 9h 54"> 

12 44

4 03

An?. 2, 9h 04 

1 27

4 11

6, lh 42m 

5 27

NX103

1-476

1-498 

1-502

1-511

1-518 

1-521

1-651 

1-654

1-660

1-671 

1-672

1-672

1-689 

1-692

1-695

1-727

1-727

fto

120-14

143-86

*1G7'»0

191-94

239-95

338-63

«>-4>')X10s

0-109

0-417

0-533

0-673

0-592

0-627

7

* Adjusted anew. t Total twist fa (Tb) = 180°, twist of steel positive. 

I Total twist Ts+(+ Tb) = 180°, twist of steel negative.

The results of Tables 38, 39 

are given graphically in Fig. 18, 

on a scale ten times as large as 

in the earlier figures. The figure shows the gradual reduction 

of viscous motion in the consecutive alternate twists.

We have not yet made the 

tubular apparatus as sensitive 

in its indications as isthebifilar. 

To obtain the full benefit of this 

adjustment long tubes and wires 

should be used. Theresults are 

nevertheless sufficiently \sharp 

and pronounced and are cited 

here for their important bearing 

in the inferences to be drawn 

for steel. Fine glass tube is to 

be preferred to brass.

DISCUSSION. '*

30. Interpretation of (<p <p'). 

Before proceeding further it is 

necessary to give the quantity ft 

((p (p') a more specific interpretation than appears from a 

persual of the above paragraphs.

Since the Wires are 30cm long FlG. ig.-Besults obtained with the tubular apparatus,,

L
40 THE VISCOSITY OF SOLIDS. [BULL. 73.

A'

L

FIG. 19. Diagram.

and but .08ctn in diameter, the considerations are much simplified by

conceiving the twist helix of each wire to be 

developed, or rolled out on a plane surface. 

Fig. 19 indicates the result in a diagrammatic way. Here db and bd are the developed position of two corresponding fibers 

(helices) of the countertwisted wires A and 

A'j dfanA ag being the lengths, I and ft/and 

bg the cylindrical semicircumferences of the 

two wires, respectively. For in the usual 

cases above bf= T=bg= 180°. Hence dfis 

usually more than 100 times as long as &/, 

and the same ratio holds for ag and gb. 

Hence also the angle dbf expresses the rate 

of twist; and for want of data indicating 

the precise relation between the rigidities 

of steel of different tempers, the angles dbf 

and dbg must throughout the present volume be regarded equal. 

Suppose now that at any section of the wires, and at a distance x and 

x' respectively above the lower end, viscous sliding takes place, on 

both the plane surfaces of an elementary cylinder, of the length dx and 

dx' respectively. Now it is clear from the equality of couples, that the 

sliding on the two plane faces of the cylinder dx will be equal, and opposite in direction. The same is true of the sliding on the two ends of 

dx'. It is also clear that throughout this sliding the elastic equilibrium 

of the system of two wires is continually being disturbed. Therefore 

the viscous motion must be accompanied by purely elastic motion of 

the whole system, such that throughout every stage of viscous deformation the rate of twist is kept constant. From these conditions it 

follows that after a very short time dt, the originally straight fibers db 

and ba will make up a broken line dnmh and hm'n'a; that furthermore 

dn and km must be parallel, lim' and n'a be also parallel, and that the 

angles mhf and m'hg are equal. Clearly lib corresponds to the motion 

observed at the movable mirror of the bifilar suspension (Fig. 1), and 

may therefore easily be interpreted.

Prolong <the lines db and mli till they meet at Jc. The triangles pWi 

and JibJc are equal in all their parts. Hence pb=bJc=y.

Let 2<p be the amount of viscous angular motion of any section of the 

wire A, relative to another section at a unit distance from it, under the 

given conditions of adjustment. Let 2q>' have the same signification for 

A'. Then since the same couple acts throughout the length of either 

wire, mn=2(pdx and m'n'=2(p'doc', no matter what be the value of a? or a/.
BABUS.] MEAN RESULTS TABULATED. 41

Let dtf) be the angular motion at the mirror, so that d(f}=Kb. Then for 

* an inspection of the figure it follows that

2g)dx I 2g>'dx' I1 ,

 ~ -4-1 and 1.

dip y dib y

whence by elimination, since

l=l't y=yf, dx dx', dijj=((p--(p')dx', .... (1)

and by integration

cp-cp'-^/l ......... (2)

31. The quantity q> ^/ defined by equation (2) is clearly identical 

with the (<p g)') of the above tables. The signification of the symbol 

is therefore evident. In case of any stated twist stored between the 

two bifilar wires, the two end sections of the unit of length of one wire 

K slide viscously 2tp radians relative to each other, whereas the end sections of the other wire slide 2<p' radians relative to each other.

VISCOSITY AND TEMPER.

32. Graphic digest. The results of Tables 1 to 21 may be discussed 

in two ways: We may either accept some definite and applicable law 

like that of Weber or that of Kohlrausch, and calculate the mean constants for each set of results, or we may construct them graphically 

and then calculate the coordinates of the mean curve for each set. The 

latter is decidedly the better way, because it is less arbitrary and more 

convenient. In Table 40 the mean results in question are thus summarized. The first two columns indicate the tables from which in each 

case the selections are made, and the tempers of the rods selected. 

The remaining columns contain the differences of viscous detorsion, 

(93 93'), in radians per centimeter of length of .the bifilar, one of the 

wires of which is invariably glass-hard, the other annealed as stated. 

(99 93') is arbitrarily fixed at zero, for one hour after a twist of T+ISO0 

and T 180° has been imparted to the soft and hard wire, respectively.

Instead of making all references to glass-hard wires, it would have 

been more in keeping with the purposes of the work to make such references to soft wire; but at the outset of the work, the high viscosity 

of annealed steel, as compared with hard steel, was not known, nor 

even conjectured.

In the tables and figures the data are positive in the direction of increasing viscosity.
42 TflE VISCOSITY OF SOLIDS. 

TABLE 40. A digest of mean results, Tables 1 to 26.

[BUM,. 73.

Table 

No.

1..... 

2.....

Mean .

6..... 

8 ....

7.....

4..... 

Mean.

9..... 

12...,. 

10..... 

11.....

Mean .

13..... 

14.....

Mean.

16..... 

15.....

Mean .

19..... 

21..... 

18.....

20.....

Mean.

Annealed

at

20° 

20°

100°, 10 1" 

...do....

...do ....

...do.... 

...do....

190°, lh 

...do.... 

...do.... 

...do....

...do....

360°, 1" 

...do ....

...do....

450°, lb 

...do ...

...do....

lOOOc- 

...do.... 

...do....

...do....

...do ....

Angular motion ($ <£') in radians.

SO*

013 0-02

0-08

0-50 

0-44 

0-62 0-81

0-59

1-07 

1-34 

1-55 1-56

1-38

1-70 1-90

1-80

2-03, 1-98

2'01

1-36 

1-78 

1-94 1-95

1-76

100"

0-19 0-03

0-11

0-81 

0-75 

1-00 1-28

0-96

1-52 

1-79 

2-18 2-06

1-89

2-54 2-68

2'61

2-74 2-78

2-76

2-06 

2-50 

2-74 2-76

2-51

150"

0-26 0-03

0-15

1-06 

1-08 

1-85 1-66

1-41

1-88 

2-16 

2-55 2-50

2-27

3-12 3-15

3-13

3-20 3-42

3-31

2-64 

3-10 

3-32 3'36

3'10

200b

0-34 0-04

0'19

1-26 

1-41 

1-70 1-95

1-58

2-20 

2'51 

2-89 

2 '91

2-63

3-56 3-51

3-53

3-57 3-92

3'75

3-12 

3-62 

3-81 3-90

3-61

250>>

1.42 

1-24 

1-99 2-18

1-71

2-50 

2'81 

3-17 3-32

2.95

3-86 3-82

3-84

3-91 4-37

4-14

3-55 

4-07 

4-20 4-35

4-04

300k

4-15 4-14

4-14

4-23 4'75

4-49

3 '93 

4-45 

4-47 4-74

4-40

350"

4-42 4-42

4-42

4-52 5-08

4-80

4-20 

4-72 

4-69 5-05

4-67

400h

4-70 4-70

4-70

4-80 5-34

5-07

All radii identically 2p = 0-082 . Like signs of (<#> <£') and of JV refer to the same angular direction.

The results of Table 40 are graphically constructed in Fig. 20, time 

in hours as abscissa, difference of angular detorsiou (<p <£/), in radians, 

as ordinate.

33. Immediate results. Table 40 and Fig. 20 lead to this curiously remarkable result : If we abstract for the moment from the states of 

temper extreme hard and extreme soft, the viscosity of steel decreases in 

proportion as the hardness of the metal increases. We call to mind here 

that the torsion imparted was not sufficiently large to produce marked 

permanent set (cf. Chapter III). If we express its intensity by

- T, and introduce the constants of the apparatus 

T=TT, J=?0cm, 2p=0"-082cm,

we find that the moment of the applied torsion couple did not exceed 

0-5 kg. on centimeter of arm. (Of. remark on stress value, p. 48.) If, 

following Sir William Thomson, 1 we agree that "the molecular friction

'Thomson: loc. cit., or Thomson and Tait, Natural Philos., 1883, vol. 2, p. 303. Our present conception of tbe viscosity of liquids, as well as the hypotheticated proportionality of frictional resistance 

and velocity were introduced by Newton (Principia, Liber 2, sect. 9, "resistentia quse oritur ex 

defectu lubricitatis").
BARU8.] VISCOSITY AND HARDNESS. 43

in elastic solids may properly be called viscosity of solids," then our deduction may be stated, the molecular friction in case of steel is greater in 

proportion as the metal is softer. 1 Examples of such relations in divers 

substances are not unknown. Hard steel as regards viscosity and hardness may be typified by sealing-wax; soft steel by tallow.2 Nevertheless the continuous variations of these properties exhibited by steel is 

as unique as it is striking. Indeed we felt diffidence in reporting this 

result and have taken pains to substantiate it.

FIG. 20. Viscous deformation of steol, as related to temper.

1 Degrees of thermo-electric hardness are here specially in place. Cf. Bull. U. S. Geol. Survey, No. 14, 

p. 65. 

* These examples (tallow, sealing wax) are given by Maxwell: Heat, Apploton, New Tork, 1883, p. 29&
44 THE VISCOSITY OF SOLIDS. tBvu.13.

34. The motion ot the bifilar body of the above apparatus can be interpreted from two standpoints: Either it is due to the torsional couple 

and the result of viscous yielding of the harder wire relatively to the 

softer; or it may be due to the bifllar and flexural couple and is then 

the result of viscous yielding of the softer wire relatively to the harder 

(page 29). But the bifilar and flexural couples have been proved to 

be zero and to produce a zero effect. Hence the inference above italicized is alone admissible. Again, in the bifllar apparatus where steel 

is twisted against glass (Table 23) the soft steel is demonstrably more 

viscous than glass. Hard steel, as shown by its behavior with the same 

fiber, is less viscous than soft steel. We do not wish to say that it is 

less viscous than glass because the sectional area of the latter fiber is 

larger. Again, in Table 38, which contains the data obtained with the 

tubular apparatus, soft steel yields viscously at about the same rate as 

the brass tube of more than four times the sectional area of the steel 

wire. Hard steel under the same circumstances yields at a very much 

greater rate than brass.

35. Our results for degrees of hardness higher than "Annealed at 

100°, 1010' are to be regarded incomplete because of the magnetic importance of those degrees. As steel passes in hardness from "Annealed 

at 450°" to "Annealed at 1000°" (soft), it probably marches through 

maximum viscosity. This result is pretty clearly indicated by Table 40 

and Fig. 20. Here also the results are to be regarded incomplete because of the magnetic importance of the (soft) degrees of hardness in 

question. Our methods of annealing between 500° and 1000° are not 

as yet satisfactory. It will be shown below that all remarks here made 

refer to intensities of stress less than the value (0-5 kg., cm.) given at 

the outset of this section. (Of. Chapter II.)

36. Viscosity and electrics of steel If we compare the results of Table 

40 or of Fig. 20 with the known thermo-electric behavior1 of steel wires, 

we detect a very striking similarity in contour and position of corresponding members of the viscous and thermo-electric families of 

curves. Both phenomena practically subside in the first phase of 

annealing; the effect of temperature becomes rapidly less as higher 

degrees are approached. The same relations hold between viscosity 

and electrical resistance of steel.

37. Viscosity and hardness. The relations between hardness and viscosity here encountered may perhaps be conceived somewhat as follows: 

Suppose stress to be so distributed in a solid that its application at any 

interface is nowhere sufficient to produce rupture. Then that property 

of a solid in virtue of which it resists very small forces (zero-forces) 

acting through very great intervals of time ( oo-times) may be termed 

the viscosity of the solid. That property in virtue of which it resists 

the action of very large forces ( oo-forces relatively) acting through zerotime may be termed the hardness of the solid. Since the application of

1 U. S. Geol. Survey, Bull. 14, pp. 54, 55.
BAHU8.] RESIDUAL PHENOMENON. 45

forces in such a way as accurately to meet either of these cases is rare, 

we have in most practical instances mixtures of viscous resistances and 

hardness to encounter. We may reasonably conceive that in the case 

of viscous motion the molecules slide into each other or even partially 

through each other by interchange of atoms, so that the molecular configuration is being continually reconstructed; that in the other case 

(hardness) the molecules are urged over and across each other and that 

therefore the intensity of cohesion is in this case more or less thoroughly 

impaired. In most cases of scratching, the action is indeed accompanied 

by physical discontinuity of the parts tangentially strained. The interpenetration of the molecules of a viscous substance is necessarily favored 

by temperature. Hence we infer the experimental result that the viscous influence of temperature is marked. If Clausius's theory of electrolysis be correct, then a certain instability or imperfect uniformity in 

the molecular structure of solids follows at once from the fact that many 

solids, notably glass,1 may be electrolyzed even at moderately high temperatures (300°). The important bearing of all these remarks on Maxwell's theory of viscosity of solids will be given in Chapter III.

38. Residual phenomenon. The stored torsional stress imparts a strain 

to the solid. Viscous detorsion therefore is accompained by a residual 

phenomenon. The observed deformation will continue until the applied 

tendency to change of form is reduced in value to the evoked and increasing tendency against change of form. If the applied stress be removed, 

the reciprocating stress becomes apparent and produces viscous effects 

of its own kind, as Kohlrausch has shown. The result has many magnetic and electrical analogies, among which the phenomenon of residual 

static charge is most obvious. In the tubular apparatus (Table 38), the 

residual deformation of the preceding twist may be superimposed on the 

deformation immediately in progress. Whether the two residual phenomena here annul each other so that the primary detorsion only is 

exhibited remains to be seen.

In liquids there is no such reaction unless it be the reciprocating 

force of galvanic polarization. In polarization, however, the mechanism 

is of an obviously chemical kind. In solids it is believed to be not 

chemical.

SECTIONAL AREAS OF BIFILAR WIRES.

39. The essential peculiarity of the bifilar apparatus is this, that the 

two wires are twisted by identical couples.2 The absolute value of these 

couples during the experiment remains constant to 2 or 3 per cent. If 

the sectional areas of the wires be identical our apparatus leads to re1 Warburg: Wied. Ann., vol. 21, 1884, p. 622. Literary notes are there given. Warburg is able to 

replace ? of thn sodium of glass by sodium of the anode.

2 Many years ago we compared the longitudinal resilience of hard and soft steel by fastening one 

end of thin wires in a vise and bending them with a weight applied at the other. We found but 

insignificant differences. Hence the stored torsions of two steel wires, hard and soft, produced by 

equal couples are cseteris paribus of equal angular value.
46 THE VISCOSITY OF SOLIDS. [BULL. 73.

suits which come very close to Newton's definition of viscosity. Newton suggested that the iuterual friction of liquids is cseteris paribus 

directly proportional to the difference of velocity between nearly contiguous surfaces. In the bifilar apparatus the torsional viscosities of 

two substances are equal if for identical strains and equal sectional 

areas torsioual change of form occurs at like rates per unit of lengthThis is the condition of rest or zero-motion of the suspended body. 

Such inferences as are here given must, however, be drawn with extreme caution. There are certain cardinal differences between solid 

and fluid viscosity, which will .be indicated in Chapter III and which 

must first be decided upon as prerequisites to conclusions like the 

present. It is doubtful whether Thomson and Tait's definition of solid 

viscosity can be at once accepted.

We do not at present wish to do more than advert to an important 

deduction here 5 it is obvious that if the sections of the wires be so 

chosen that the motion of the bifilar body is zero, the viscosity of the 

wires must be inversely related to those sections. This principle apparently enables us to arrange solids in a scale of viscosity. We may 

formulate it approximately thus :

Consider an elementary ring of either wire, whose height is dz and 

whose right sectional area is 2nrdr. Let df be the amount of tangential force uniformly distributed over this area. At the time t let the 

velocity of the upper surface relatively to the lower be cr, where c is a 

time-function and cteteris paribus a characteristic of the viscosity of 

the wire. Then if jjit be the coenicient of viscosity at the time t we have

Jf cr27crdr 2 df=J = t ^- 

dz dz

If we multiply by r and then integrate between zero and p (thickness =2p), the numerical result is the part of the impressed torsional 

couple which corresponds to the length dz. A similar integral holds 

for the other wire, to distinguish which it is merely necessary to accentuate/, // c, r, p. The sum of the two integrals is zero. If, moreover, 

we put c=c' in view of the state of rest of the bifilar body, we find that 

the viscosities (/* /*'*) OI> *ne two substances (wires) are to each other 

inversely as the squares of the respective sectional areas by which the 

motion of the bifilar suspension is annulled.

40. Unfortunately the problem is much more complex than it here 

appears. The dependence of torsional deformation on time in case of a 

single wire is obviously related to the character of the molecule. When 

two different substances in wire form are twisted bifilarly against each 

other, the effect will rarely be such that the torsional yieldings continually equalize each other, no matter what relations of section may 

be chosen. The motion-curve of the bifilar-suspension will show maxima 

or even points of circuin flexion, such as have been actually encountered 

in Tables 23, 24, 25, etc., and the definition, of relative viscosities of the 

two wires will become correspondingly involved. Apart from these
BARU8.1 VISCOSITY AND STRAIN. 47

complications which are inherent in solid structure, a modification of the 

apparatus such as is given in Chapter II, or the present tubular apparatus, may easily subserve the purpose of classification by initial tangents.

41. Again, /*, for solids is not merely a function of time but very essentially a function of stress. Above we show (page 12) how by simply 

adjusting the lengths of the bifilar wires, viscosities may be compared 

at a given temperature, as time-functions with identical values of the 

parameters stress, strain (sectional area). We do not believe that viscous detorsion in this full relation has ever been rigidly investigated. 

The results would lead to families of curves.

Given a quadrifilar arrangement of four viscously identical wires. 

Let the twist T& be stored between any two of them and then let the 

twist T12 , 34 be additionally stored between these two as one, and the 

third and fourth wire as one. Such a device enables us in the above 

way to study viscosity in its simple dependence on strain, for all values 

of stress.

VISCOSITY AND STRAIN.

42. Steel and glass. When we commenced the present research a 

comparison of the viscosity of glass and steel appeared desirable. In 

Tables 22, 23, such comparisons have been attempted, though we regret 

that the limitations of our available time have restricted our pursuit of 

them. In Table 22, the sectional area of glass fiber is less than that of 

steel wire; nevertheless the viscous yielding of the fiber is so much 

more rapid than that of the wire, that we may reasonably infer degrees 

of viscosity of the same order in the two substances. In Table 23, the 

sectional area of glass exceeds that of steel. Hence these data prove 

that the torsional viscosity of annealed steel is greater than that of 

glass. The viscosity of hard steel during the first ten hours of detorsion is certainly very much greater than that of glass. During the 

remainder of the time it is decidedly less. The curve passes through 

a maximum for which point the rates of viscous detorsion of glass and 

of glass-hard steel exactly coincide. Since the sectional area of glass is 

greater, we safely infer that the viscosity of glass is not uniformly 

greater than that of glasshard steel. It is well to call to caiud, however, that the sum of the torsions is here only T.-f Tff =90°. Moreover, 

since for equal couples and dimensions JHg Tg=]l]s Ts, where JK is Young's 

modulus1 of resilience for glass and for steel respectively and Tthe corresponding torsion 5 and since Eg /Ee=l /3 approximately, it appears 

that Tg=3Tt nearly. Hence for equal stresses, strains are thoroughly 

unequal, and in the same measure are these comparisons not thoroughly 

just.

43. Steel and iron. A similarly important desideratum is the comparison of the viscosities of steel and of iron. In Tables 24, 25, 26,

1 To obtain an estimate it is sufficient to accept the same ratio of modulus of torsion to modulus of 

longitudinal resilience for each case. Poisson's ratios for glass and steel are about as 26 to 30.
48 THE VISCOSITY OF SOLIDS. [BULL. 73.

etc., such comparisons are made, though further results are not superfluous. It appears distinctly that during the first five or ten hours of 

detorsion the viscosity of iron is in a strikingly pronounced manner 

less than that of steel. As detorsion continues the viscosity of soft iron 

continually remains below that of steel, whereas the viscosity of drawn 

iron grows temporarily greater than steel but finally reaches the same 

value. In this case the motion-curve passes through an exceedingly 

sharp maximum, at which the viscous yielding of iron and of steel occurs at like rates. Having exhibited greater viscosity in drawn iron 

it finally, by circumflexion, merges into a horizontal asymptote, which 

probably indicates subsidence of motion in each wire. These unexpected results show that the viscosity of steel is not uniformly greater 

than that of iron. Obviously glass-hard steel for the given stress is 

very much less viscous than iron.

The sum of the twists is here nominally Tt ( T^SGO0. Particularly in the case of soft iron its efficient value is very decidedly less, 

however. The applied torsion carries the iron wire much beyond the 

limits of elasticity; and so much of the stress vanishes instanter that 

the "after-action" subsides within relatively small limits. The viscosity of (soft) iron is either less or greater than that of hard steel 

according as the applied torsional stress surpasses or falls below a certain critical value. This result again shows the importance of stressmeasurement, as a means of coordinating the lingering of purely viscous 

deformation and the instantaneous (?) deformation.

In the above results the curvature of the (absolute) motion curve for 

a single wire increases uniformly from hard steel to soft steel; increases, 

moreover, from soft steel to iron. Curvature is greater in the glass 

curve than in hard steel curves. So far as we have observed (steel, 

iron, glass) viscous deformation occurs more nearly at uniform rates 

(linearly) in proportion as hardness is greater. Of. Chapter III, where 

similar results are given under "accommodation." Curvatures for 

early time are meant, the later parts of curves being asymptotes.

44. Effect of quenching. The remarks just made on the viscosities of 

glass and iron suggest this plausible inference: if glass and steel be 

alike subjected to a stated process of quenching, and if after the operation has been performed glass be found to have retained a very high 

intensity of strain (Eupert's drop), then, a fortiori, steel, the substance 

of greater viscosity, must have retained a similarly high intensity of 

strain. This reasoning, however, is incomplete and must be approached 

with caution. We pointed out1 that the low degrees of thermal conductivity possessed by glass were favorable to the retention of strain. 

We also remarked2 that the occurrence of Gore's phenomenon of sudden 

expansion at red heat distinguished iron and steel from all other metals, 

and that in spite of relatively good thermal conductivity, iron and steel

» Am. Jour. Sci. (HI), 1886, vol. 31, p. 451. 

» BulL TJ. S. Geol. Survey, No. 14, p. 99.
BARUB.] STRESS STOKED IN QUENCHED SOLIDS. 49

possessed virtually all the favorable conditions of glass for retaining 

strain. Whether differences of viscosity are sufficient to account for 

the unlikeness of behavior during quenching we are unable to say. It 

will be necessary to compare iron and steel at higher than ordinary 

temperature and also under greater values of applied stress than was 

easily feasible in the above experiments. In other words, iron and soft 

steel are nearly equally viscous for small values of stress. After stress 

exceeds a certain intensity, the permanent set suddenly imparted to 

iron is enormously great as compared with steel. Similar relations are 

true for soft steel when compared with hard steel. It is this class of 

"sudden"-phenomena which come into play during quenching. The 

primary effect of quenching steel is chemical hardness. Strains are 

retained in the steel so modified, just as they are in glass; whereas in 

soft steel or soft iron the result would be permanent set. In Chapters 

II and III, a more complete explanation than is here possible will be 

given, so that further consideration may be waived for the present.

The occurrence of sudden and gradual deformation in a single substance suggests that ordinary static friction is probably a viscous phenomenon.

45. We add in passing that the observed inefficiency of temperatures 

less than 200° in producing marked viscous deformation in a Eupert's 

drop proves that mere interference of thermal expansion with the conditions of strain cannot be the primary cause of its variations; that 

strain variations essentially depend on diminished viscosity.

46. Steel and cast-iron. We also add in passing that the importance 

of strain as associated with glasshardness is emphasized by the massconstants of the cast-irons. The densities of these metals1 range between the maximum of ca. 7-6 for white cast-iron and the minimum of 

ca. 6-9 for gray cast-iron. Hence density increases in marked degree 

in proportion as total carbon is more and more nearly combined. Quite 

the reverse of this is true for steel where density decidedly decreases as 

total carbon is more and more nearly combined. This discrepancy we 

interpreted as a strain of dilitation and carefully compared it with the 

analogous behavior of glass in our earlier papers.

47. Stress intensity estimated. We add finally the following data from 

.the elastics of glass and of steel. The seolotropic expansion produced 

by quenching glass or steel we showed elsewhere2 to amount to 0.005. 

The volume resilience of glass and of steel, according to Professor Everett's measurements,3 is 4xlOu and 2xl012 respectively. Hence if per 

square centimeter ^> be the stress-value for the given expansion, we find 

approximately j?=10xl09 dynes for steel and 2xl09 dynes for glass. 

Now per square centimeter the tenacity of steel is 8x 109 dynes; the 

tenacity of glass 0-6 x 109 dynes. The approximate ratio of stress to

» Cf. Bloxham'a Chemistry, Lea, Philad., 1873, p. 342. Bull. IT. S. Geol. Survey, No. 14, pp. 76,77. 

* Am. Jour. Sci.(III), 18C6, vol. 32, pp. 190, 191. By ajlootropic expansion we refer to the part of the 

total expansion which produces explosiveiiess and the polariscopic phenomenon. 

1 JEverett: Phil. Trans., 1866, p. 369. The above numbers'are rounded from Everett's values.

Bull. 73 4
50 ' THE VISCOSITY OF SOLIDS.

tenacity is therefore estimated at 1-3 for steel and 3-3 for glass. This 

shows that in both cases stress and tenacity are of the same order; that 

stress is in excess; that but for the peculiarly favorable, symmetrically 

arched structure of the quenched globule, rupture would ensue in glass 

certainly; probably also in steel. This accords with the explosive 

tendency of a Prince Rupert's drop and with the less pronounced liability of steel to crack on quenching.1 If therefore quenched glass and 

quenched steel are under mean stress intensities of several thousand 

atmospheres, then in discussing the corresponding viscous properties 

they must be brought into relation with these high values of peculiar 

stress.

MAGNETIC RELATIONS.

48. Viscosity and magnetic intensity. If again we abstract from the 

extreme states of hardness, we find that both the viscosity and the moment of linear magnetization per unit of mass, of a permanently saturated steel rod, increase in marked degree from hard to soft. This is a 

singularly striking result, inasmuch as the conditions of magnetic stability (following Hopkinson we shall call them coercive force), conditions 

which at first sight we would be inclined to associate with viscosity, 

decrease as viscosity increases. Hence permanently saturated linear 

magnetic intensity and viscosity on the one hand, magnetic stability or 

coercive force and hardness on the other, seem to belong together.

49. Magnetic and viscous maxima in steel. The minimum of permanent 

linear intensity of saturated steel rods has no viscous equivalent; but 

we have not yet studied the viscosity of \extremes of hard steel minutely, nor have we as yet sufficiently sharp data for the magnetization 

of very long rods (length /diameter >100) in its relation to temper. In 

the extreme soft region, on the other hand, the occurrence of a unique 

maximum of magnetization seems to be coincident with the occurrence

of maximum viscosity. The magnetic maximum so far as our results 

go is apparently much more clearly pronounced than the viscous maximum. We remark in general that as the ratio of length to diameter 

increases, the minimum of permanent magnetization shows a tendency 

to move from soft to hard. Furthermore, it is proved that the permanent magnetization of soft rods is greater in proportion as they are 

more and more nearly linear.3 Hence as our march approaches the 

linear limit we observe an unmistakable tendency toward more detailed 

similarity between the variations of-the magnetic and the viscous properties of steel.

Mr. Hopkinson3 in his memoir on the magnetization of iron introduces 

a definition of coercive force, defining it as "that reversed magnetic 

force which just suffices to reduce the induction to nothing after the

1 Mr. .T. M. Batchelder has just communicated to us his interesting results (Jour. Franklin In*t. (3), 

1844, vol. 8, p. 133). in which of twelve massive pieces of quenched steel, eight subsequently cracked 

and one actually exploded.

2 Bull. 14, U. S. Geol. Survey, pp. 140 to 143.

3 Hopkinson: Phil. Trans., 1885, vol. 2, p. 463.
BABUS.] MOLECULAR CHANGE IN HOT IRON, 51

material has been subjected temporarily to very great magnetizing 

force." There is a slight objection to this definition, inasmuch as it 

introduces a somewhat vaguely complex state of zero-magnetization.1 

Wiedeniann2 in comparing magnetization to and fro with viscous torsional accommodation has been most explicit on these points. But the 

feature in question is hard to improve and the definition is valuable. 

Mr. Hopldnson's extensive experiments show that coercive force isv iuvariably increased by hardness. Together with others we have proved 

that hard steel is alike well adapted to withstand the influence of percussion.

50. Steel and iron. These general relations between viscosity and 

maximum permanent linear intensity observed for steel are sustained 

by iron. According to data contained in a paper of the lamented Dr. 

L. M. Cheesman3 the permanent magnetization of drawn iron exceeds 

that of soft iron. The magnetic intensity of permanently saturated 

drawn iron is comparable with that of soft steel and quite equal to that 

of hard steel. More recently and even more elaborately Ewing has discussed the subject. He finds " in the absence of mechanical or other 

disturbance, soft iron is far more retentive than either hard iron or 

steel," an exceedingly remarkable result.4 Our experiments show that 

the intensity of applied stress is an important factor in determining the 

viscous behavior of iron ; that for moderate stress values it ultimately 

approaches very closely or even exceeds the maximum viscosity of steel j 

that it is much greater than the viscosity of hard steel.

REMARKS.

51. Among the results of this paper is the light thrown on the crucial 

importance of the physical changes which steel undergoes during annealing at high temperatures, i. e., when subjected to the action of temperatures between 500° and 1000°. Prof. W. F. Barrett,5 who made valuable researches on this subject, pointed out the more important coincidences (elongation, crepitation and ticking, recalescence, magnetic and 

thermo-electric anomalies). In our our earlier work we unfortunately 

overlooked these papers. Tait, however, had before this connected his 

peculiar iron line (thermo-electrics) with Gore's phenomena. The occurrences in question may now be sum marked as follows: Gore's6 sudden

1 The unmagnetic state, though dependent on the details of the process of tempering, is a distinct 

magnetic state. Similarly we may regard the saturated magnetic state, though allowance must here 

be made for the occurrence of cyclic magnetization, a phenomenon suggested by Fromme (Wied. Ann., 

1878, vol. 4, p. 89) and (Wied. Ann., 1881, vol. 14, p. 308), concisely, interpreted by "Wnrburg (Wied. Ann., 

1881, vol. 13, p. 141) and which Ewing (PhiL Trans., 1885, vol. 2, p. 545) has recently discussed generically 

under the name of "hysteresis."

2 Wiedemann: Wied. Ann., 1879, vi, p. 512.

8 Cheesman: Am. Jour. Sci. (Ill), 1882, vol. 24, p. 183. Lengths 100 diameters and less.

* Ewing: op.cit.,p. 541.

6 W. F. Barrett: Journal London Inst., July, 1873; Rept. Brit. Assoo., 1875, vol. 45, pp. 259-60; PhiL 

Mag. (5), December, 1873; ibid, January, 1874; Proc. Royal Dub. Soc., 1886; Am. Jour. Sci. (Ill), 1887, 

vol. 33, p. 308. For recent work on recalescence see Hopkiuson: Proc. Hoy. Soo., 1889, voL 45, p. 453.

6 Gore: Proc. Roy. Sue., 1869, vol. 17, p. 260.
52 THE VISCOSITY OF SOLIDS. [BULL. 73.

volume expansion; Tait's1 sinuously broken thermo-electric diagramline; Barrett/'s (loc. cit.) recalescence, crepitation, and elongation phenomena; Barrett's behavior of manganese steel; Gore-Baur's2 sudden 

disappearance of magnetic quality; the passage of carbon from uncombined to combined; Jeans's3 critical cementation temperature. Further, 

Chernoff-Barus's4 sudden appearance of hardness in quenched steel, 

Fromine's5 maximum density, Chwolson's6 minimum resistance, our own 

unique maximum of magnetization7 and probable maximum of viscosity, 

Eowe's8 sudden decrease of rigidity, are all referred to this interval, 

approximately to the same temperature. To determine the interdependence of these phenomena it is obviously first necessary to devise 

methods of operating on steel adapted to the interval in question. In 

other words, our introductory problem is the annealing of steel without 

oxidation and without carburation, at measured (high) temperatures, 

during stated times. It is in this direction that our investigation will 

ultimately proceed. In the present work, however, the thermal relations of viscosity still command paramount attention; and their importance gains much when it is called to mind that before a satisfactory 

physical theory of viscosity has been formulated, the light which data 

like the above throw on ulterior electrical phenomena will not be 

searching.

1 Tait: Trans. Koy. Soc., Edinburgh, 1872-73, vol. 27, p. 125.

2 Gore: Phil. Mag., IV., 1869, vol. 33, p. 59; Baur.Wied. Ann., 1880, vol. 11,p. 408; Ibid., 1870, vol.40, 

p. 170.

3 Jeans: "Steel, its history, etc." London, Spon, 1880.

* Chernoff: Vortrag. geb. in der Euss. techn. Ges., April und May, 1878. Barns: Wied. Ann., 1879, 

vol. 7, p. 405.

6 Fromine: Wied. Ann., 1879, vol. 8, p. 354. We were unable to find Eromme's maximum: but we will 

search again. All these results are crucially dependent on the method of annealing,' as stated, in the 

text,

6 Chwolson: Carl's Kepertorium, 1878, vol. 14, p. 26.

»Barus and Strouhal: Bull. U. S. Geol. Survey, No. 14, pp. 145,198.

8 H. M. Ho we: Scientific American Supplement, April, 1889, p. 11055.
OHAPTEE II.

THE VISCOSITY OF STEEL AND ITS RELATIONS TO TEMPERATURE.

INTRODUCTION.

52. This chapter is to be restricted to a discussion of the relation between torsional viscosity and temperature, as observed with steel in 

different states of hardness. Some mention of the effect of stress on 

the amount of viscous motions in solids is, however, unavoidable; and 

the experiments lead naturally to the investigation of a more general 

method, by which the instantaneous deformation and the gradual deformation produced by stress may be coordinated. The data already 

show that imperceptible gradations lead from the purely viscous deformation which follows strains within the elastic limits, to the sudden, 

permanent set which follows strains beyond the elastic limits. As £ 

whole the data bear directly on the truth of Maxwell's theory of viscosity. (Of. Chapter III.)

METHOD OF MEASUREMENT.

53. Apparatus. Instead of countertwisting two wires suspended bifllarly, as was done in Chapter I, it is for many purposes preferable to 

suspend and twist them unifilarly. In this case they may be kept at 

different temperatures throughout different parts of their lengths, and 

the adjustment therefore has special advantages for the class of experiments indicated in the present chapter.

In the actual work it is expedient to compare two identical wires, 

one of which is kept hot, the other cold. These wires are shown in the 

annexed diagram (PI. I) at ab and cd. The ends, having been bent 

loop-shaped, are screwed near the middle of the apparatus to a crosspiece of iron parrying the adjustable mirror M. This is the index referred to in the preceding paragraph, and angular deviations are read 

off by Gauss's method. To deaden lateral vibrations the mirror is also 

provided with a cross-vane, mm, dipping appropriately into a fixed dish 

of water. In later experiments this dish was replaced by an annular 

vessel surrounding the wire. The upper end of the system of wires is 

screwed to a round steel rod, a/, which fits snugly in the perforation of 

the massive fixed piece of brass gli. A steel pin, p, passing through 

both brass and steel rod, secures the latter to the former. The lower 

end of the wires is similarly fastened to the steel rod dh and the fixed

63
54 THE VISCOSITY OF SOLIDS. [BULL. 73.

piece of brass Tel. To keep the wires tense they are stretched by a 

weight, EQ ; and a part of the lower fixed brass Id has therefore been 

cut away in such a manner that the lower pin q may slide along a plane. 

The system of wires is therefore free to expand.

To heat the upper wire, a given part of it was surrounded by a special 

form of vapor bath, without being necessarily in contact with it. This 

has been described elsewhere.1 Steam (100°), aniline vapor (190°), aud 

mercury vapor (360°) were consecutively introduced, and errors due to 

radiation were carefully avoided by appropriate screens.

The vapor bath mentioned is seen in the figure at ttt, being a boiling 

tube containing the liquid whose boiling point is to be utilized and 

surrounded at its lower end by the ring burner rr. The asbestus screen 

as protects the upper end of the tube from direct radiation. It is desirable to bring as much of the wire within the central tube uu as 

possible. If necessary the upper end of this tube may be loosely closed 

with asbestus to obviate currents of air. By carefully regulating the 

ring burner there is no difficulty in maintaining ebullition for hours.

By removing and then re-inserting the pin q, the wires may be twisted 

in multiples of 90° for each length, or in multiples of rate of twist (T) 

of 3° for each wire. For the given dimensions this is the effect of a 

couple of 250 g. on one centimeter, for each 3° of rate of twist. In later 

forms of this apparatus a divided circle was attached to the lower piece 

dh, thus enabling the observer to vary the value of r aud to measure the 

amount of permanent set at the end of the experiment.

54. A few critical remarks on the efficiency of the apparatus are in 

place. In most of the experiments made the torsioual deformation is so 

great that special fiducial marks to register the possible motion of the 

fixed pieces gh and Id are superfluous. Indeed, for angles as large as 

those observed, Gauss's method of angular measurement is no longer 

conveniently applicable, because of the number of corrections which become essential, and in future measurements it will be expedient to use 

other methods. The large deflections, however, made it possible to use 

the Gauss method even when the apparatus is thrown into unavoidable vibration; for instance, when the upper wire is surrounded by boiling mercury. In the present work it did not seem necessary to take 

special precautions for jacketing the lower wire. Its temperature is 

that of the surrounding air, very nearly, and it is not heated by radiation. In the case of steam and of aniline vapor, the length of the hot 

part of the upper wire is sharply measurable, but in the present work 

this could not be so satisfactorily done for mercury vapor. Eegarding 

the mode of heating, there are two methods available: the wire may 

either be heated and the twist then applied, orthe wire may be twisted to 

the desired amount before heating. The former of these methods eliminates the time error, but it is difficult to obtain an accurate reading 

for the zero-point, i. e., the scale reading for the twisted system before

1 Bull. U. S. Geol. Survey No. 54, p. 86 et esq., where the form of boiling tube used is fully given.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 73 PL.

, /i|i?T[

if ^

1 1

\\ $

\lllfr

KV*Pg3*;

'-%&?,

- --Sm>tt

\\^<\^\\

 ro^

fxx/ ^ 

<s

«- 1 i ff /^ ' ( / i i I

V-J.MJ , ! - -f \\lUfl : : 

8/ V : ! 1

(^ 1 i v>

6^ \^/ ^

^\

. *\

UNIFILAR APPARATUS.
BARUS.] TEMPERING AND ANNEALING DISTINGUISHED. 55

heat is applied. Hence the other method was adopted, in which the 

invariability of the zero referred to can be satisfactorily tested before 

each experiment. The error is the time consumed in heating the wire, 

and in the second part of the observation, the time consumed in cooling 

the wire after heating. Special means for cooling were not applied. 

When the motion is great, it is desirable to have the index-mirror adjustment light, though the device used was not perhaps objectionably 

heavy.

The immediate effect of heating the upper wire is an expansion of the 

system. Hence if the part of the lower fixed brass cylinder U, along 

which the pin q is free to slide, be not plane and true, there will be a 

tendency to rotate the system. If, however, the twist be alternately 

applied positively and negatively, this expansion error is eliminated by 

commutation. This safeguard was invariably applied. When the twist 

stored amounts to 180° for each wire, its sign may often be reversed and 

readings may be made without necessarily readjusting the mirror. 

For smaller twists the mirror must be readjusted. Larger twists were 

not applied because of liability to permanent set of the wire so twisted.

55. The wires used are Stubs's best steel, hardened and tempered 

electrically, as described elsewhere.1

A few words relative to the technical terms used to designate the 

temper of steel may here find place. Prof. Roberts-Austen2 has endeavored to give defiriiteness to the notation by proposing that the operation by which steel is made as soft as possible (heating to redness with 

very slow cooling) be termed "annealing"; whereas operations by 

which any other degree of hardness between extreme hard and extreme 

soft is imparted to steel, be termed "tempering". From a physical 

point of view I see little importance in such a distinction, except perhaps that under annealing exceptionally slow cooling is implied i. e., to 

anneal steel, it is essential to cool the hot metal much ir.ore slowly, 

than is usually necessary in tempering. Otherwise an extreme of soft 

state will not be obtained. In general, however, since in any case of 

tempering it is necessary to act on a rod of a higher degree of hardness 

than the one to be produced, it makes little difference whether the rod 

be described as having been tempered at a temperature a?, during a 

time #, or annealed at a temperature a?, during a time y. Sufficiently 

slow cooling after the heating is evidently and always understood. In 

short the whole process is continuous in character, and a rod tempered 

at red heat is virtually annealed. Hence in the present work I have 

not thought it needful to discriminate between annealing and tempering, and I use the words interchangeably.

.56. Theory of the apparatus. In a general way the theory of this ap. 

paratus is similar to that given in Chapter I, § 31. There are special 

points however to which it is necessary to call attention specifically. In

1 Of. above, Chapter I, § 8 et seq. Also Bull. U. S. Geol. Survey, No. 14,1885, p. 29. 

* Nature, vol. 41,1889, pp. 11,42.
56 THE VISCOSITY OF SOLIDS. [BULL. 73.

the bifllar suspension the twist helices of the two wires were right handed 

and left handed respectively. In the present instance the sign of the 

twist is the same throughout its length. Given a continuous straight 

steel wire of length L, to which a convenient rate, of twist, r^ has been 

imparted. Consider two right sections whose distance apart is the unit 

of length, and let 2q> be the amount of viscous angular motion of the 

first relative to the second, during the'given small time t, for the stated 

rate of twist T. To fix the ideas, let the wire be adjusted vertically, and 

provided with an index to register angular motion at a distance I' above 

the lower end. At every section the viscous motion is such, that if the 

contiguous parts immediately below the section slide in a given direc: 

tion, the parts immediately above it slide, in equal amount, in the opposite direction. Again, of the two equal and opposite viscous motions 

which take place on any section, only the part nearest the index will 

influence it. Finally throughout the whole viscous detorsion the twist 

is kept constant throughout the wire in virtue of its elasticity.

In Pig. 2i I have developed the conditions which here obtain, on a 

plan similar to that described in § 31. The length of the tWo wires A

and A', is shown at fd=l' and da I, respectively, so that af=l+l'=L. Again 

gf Tp, where T is the twist for the length 

L and p the common radius of the wires. 

Hence gf is small as compared with a/. 

The developed position of the twisted fiber 

is shown at ag, so that tan gaf is the twist 

T Lr. Virtually of and ag are equal in 

length and the position of the index is at 

d or the corresponding point of junction b. 

Consider the viscous sliding which takes 

place on the two end faces of the elementary cylinders dx and dx', distant x and x' 

respectively from the lower end of the 

system. Then in a very short time, the 

originally straight fiber abg is changed to 

a broken line amnh, hm'n'g. Here wn= 

2<pdx, m'n'=2(pldx', and Wi=d$. If Tc be 

the point of intersection of the broken line amnm'n'g and the straight 

line ag, let l)k=y. Then an inspection of the diagram shows

ti.

Fig. 21.

2<pdx l+y 

--

2(p'dx' I' y -^-- y (1)

If for y its geometrical value in terms of L, I, x, x', etc., be inserted, 

and if for brevity 2<pdx=a and 2g}'dx'=a', the following relation results:

a a1 2(L+x x') L(a+a')/a 

difj ~~ L+x x' l(a-\-a')/a (2)
BABU8.] THEORY OP THE APPARATUS. 57

Unfortunately this is too complicated for use except where L=2l=2l', 

or where the two wires of the system are of equal length with an index 

at the point of junction. In this case (pdx q)'dx' d^ ..... (3)

57. This premised, the conditions of experiment may at once be introduced. Let the parts of the wire below the index, the parts whose 

position is 0 to I1 be kept at a given constant temperature, and be of 

the same temper throughout. Also let those parts of the system above 

the index be of the same, or any other uniform temper ; but suppose 

them heated to different constant temperatures. Thus let the viscous 

detorsion between #=0 and x=l' be2<p'j between x=l' and x=fi be 

2^3 ; between #=/? and x=a be 2<p; between x=a and x=L be 2^. 

The differences q>i, cp, <p3 are evoked by differences of temperature of 

the parts of the wire to which these data refer, whereas y' may differ 

from all of these by an increment of temper as well as of temperature, 

Then the influence of the viscous detorsion in each of the parts in question on the index whose position is x=l' will be in the aggregate

^^(p-l^+^a-ft+cp^L-o^-cp'l' .... (4)

Equation (4) results at once from a suitable integration of (3).

In the present chapter <p3=(pi=(p', since the tempers and temperatures of these parts are alike. Hence

$=(<p- 9')(a-p) ........ (5)

It will usually be convenient to put a fi=a.

58. If a series of detorsions cp be observed at 6°, and another series, 

#, at @°; if <p=(p0F(6) and ty=n /2R (Gauss's method of angular measurement), then (p0(F(®) F(d))=(N n) / RL, where R is the distance 

between mirror and scale in cm and where N and n are the scale parts 

(cm) corresponding to @° and 0°, respectively. Hence the distance of 

the individual curves for @° and 6° apart varies directly as cp0 . This 

result, though simple enough, has special bearing on the text below.

59. Digression. In the interest of certain correction to be applied to 

some of rny early results, I will inquire what correction is to be applied 

when the elastic restitution which accompanies viscous motion, is disregarded. In this case the differential equation corresponding, to (3) is

......... (3') I *''

and equation (4) is replaced by

Equation (5) finally by

1 ........ (5)

Thus to reduce such data as are given in tables 42 to 51, if calculated 

by (5') to data calculated by (5), the factor would be 0-66 ; for tables 62 

to 54, the factor would be 0-78, etc., or in general Ina //?.
58 THE VISCOSITY OF SOLIDS. [BULL. 73.

EXPERIMENTAL RESULTS.

60. Residual twist. The following experiments have an introductory 

and suggestive character. Two glass-hard wires with their ends bent 

loop-shaped are fastened firmly together at one end of each. The other 

ends are twisted T° against each other and also fastened. This twisted 

system of glass-hard wires, or system in which a rate of twist of 3° or 6° 

has been stored, are then annealed at divers temperatures during stated 

times as shown in the tables. The amount of twist lost during annealing is measured by determining the angle between the planes of the 

upper and lower loops of each wire before and after annealing. A gallows arrangement by which a needle is suspended over a divided circle 

by the steel wire itself is used for measurement.

The tables contain the number, length (L) and diameter (2/>) of the 

glass-hard wires used for each couple j also the temperature and the 

time (h) in hours, during which the couples are annealed. They contain, furthermore, the amount of viscous detorsion (d^ A^ or twist lost 

during annealing, for each of the times specified, and each of the wires j 

finally, the amount of twist stored in each wire of the system. This 

amount is equal to the twist nominally applied, minus the angle between the plane of the loops. Allowance is made for the amount of 

permanent set produced by mere manipulatory twisting of the cold 

wires. When this exceeds 10°, the A is discarded. The error of angular measurement is probably not greater than a few degrees.

In the second part of the table the wires 8 and T are soft.

TABLE 41. RESIDUAL TWIST. RODS GLASS-HARD.

No.

AandB 

i=31"» 

2p=0-082OT

C andD JD=31cm 

2p = 0082«n

EandF £=31 

2p = 0-82cnl

G/andH L=W 

2p=0-082CID

I and J

£=31 

2p=0'082cm

K and L £=31cm 

2p=0-082CI»

Maud N i = 31cm 

2p = 0 > 082CID

OandP L Blcm 

2p = 0'082HB

QandK L=3l 

2p =0-043 

S and T i = 31 

2p = 0-043 

Annealed 

at

100°

100° .

190'

190°

190°

360°

360°

360°

300°

300°

A

o-oo

1-08 

2-08 3'58

o-oo

0-17 

0-67 2-00

o-oo o-io

0-80

o-oo o-io

1-00

o-oo

0-08 1-20

o-oo

0-30

o-oo

0-30

o-oo

0-30

o-oov 0-30

o-oo

0-30

A,

o-o

57° 

64 

70

-

-

-

0 

. 39° 

57

0 

166°

0 180°

0

770

0 156°

U

48°

A2

-

 o-o

 36° 

-64 

-70

 o-oo

 123° 

 153

-0.0 -104° 

 130

0 52° 

69

0 148°

0 166°

0 71°

0 165°

0 54°

Twist.

 l80°-7°

180°-10°

180° 25°

180° 2°

90° 10°

180° 20°

1SO°-10°

90° 8»

180° 8°

180° 2°
TWISTED SYSTEMS ANNEALED. 59

61. This table contains results which may be expressed as follows: 

the viscous detorsion produced by the action of any temperature on a 

twisted system of glass-hard steel wires, increases at a rate gradually 

diminishing through infinite time, diminishing slowly in case of low 

temperatures (<100°), rapidly at first and then again slowly at high temperatures (>20G°); so that the residual twist corresponding to any given 

temperature is reached asymptotically. Moreover, the strain carried 

by the glass-hard twisted system is almost completely annulled when 

the temperature at which annealing takes place exceeds 350°. These 

results are strikingly similar to the thermoelectric effect1 produced by 

annealing glass-hard steel, that the present purely mechanical result 

may safely be used to interpret the electrical result: in both experiments we observe strains disappearing under like conditions. 

The table contains another important result: by comparing the second 

part of the table with the first, it appears that the effect of temperature 

in decreasing the viscosity of steel is greater in proportion as steel is 

harder. For where the twist is stored between *two glass-hard wires 

it is found to have almost completely vanished after annealing; but 

where the same twisb is stored between two soft wires less than onethird of it has vanished after annealing. The curious inference that in 

so far as its viscous properties are concerned, steel is much more susceptible to temperature when it is hard than when it is soft, will be 

carefully discussed in the following pages by aid of the apparatus 

already described.

In Fig. 22 I have shown graphically the results reached by annealing 

twisted systems of glass-hard wires at 360°. The form of the wire before annealing is given at (7, the shape being that of an 

elongated 0. This same wire is then twisted to the form of 

an elongated 8 and then annealed in this twisted condition. 

After annealing, the cold wire will be found to be permanently S-shaped, all temporarily stored twist having 

vanished during the exposure. This shows that hard steel 

during the period of occurrence of the annealing in question, is almost a viscous fluid.

0

TORSIONAL VISCOSITY AND TEMPERATURE.

D

0*0

62. Notation. The data of the following thirteen tables 

give a clear description of the viscosity of steel for temperatures between 0° and 400°, and for all degrees of hard 

ness. These data are readily intelligible. 6 denotes the 

temperature of the hot part, 6' the temperature of the cold ri&- 22- 

part of the wires in the apparatus (PI. I). The distance between mirror 

and scale was 360cra throughout. L, Z, /?, a, have the signi ficatiou already 

given, beingthe total length of system of two wires, the distance of mirror

> Bull. U. S. Geol. Survey Xo. 14,18S5, pp. 55,95.
THE VISCOSITY OF SOLIDS. [BULL. 73.

above their lower end, the length of their cold and of their hot parts, respectively, in centimeters. Hence a=a fi. The tempers of the rods 

(diameter 2p) are expressed by the temperature at which the originally 

glass-hard rod was annealed. Soft rods are annealed at red heat. The 

tabular arrangement contains the date and the time (h0 )in hours and fractions of an hour, of each of the angular detorsions (cp q)1 }, in radians. 2q> 

has been denned, §§ 31,56. It denotes the angular viscous motion between two right sections of the hot wire, whose distance apart is the unit 

of length, when the temperature of the included wire is 6° and the original rate of twist is r for the given diameter 2/o. 2<p' has the same meaning 

for the cold^wire. Identical signs of T and ((p qt1 } refer to angular motions in the same sense, and since r and ((p cp'} agree for the cold rod 

this is invariably of greater viscosity. 

63. Viscosity at 100°. The data in hand are given in Tables 42 to 47.

TABLE 42.

fl_inno. si sno I/=60 . J=30em. *o nA!,. No. 1, soft ? « n. nfi9cm B ] 00"; 8 200. ^ _ 26cm p _ 34cm jjods. -^ 2, soft J 2p ~ ° °82 '

Date.

Feb. 18, Ob 53m

0 56

1 00

15 

45

2 45

3 50

4 30

4 33

44 

54

19, 9 30

19, 1" 17 

1 25

56 

2 14

40

»o

O'OO

0-05

0-12

0-37 0-87

1-87

2-95

3-63

3-67

3-85 4-02

20-67

o-oo

0'13

0-65 0-95

1-38

(*-*') x

103

o-oo

 1-04

 1-10

 1-22 

 1-43

 1-61

 1-81

 1-97

 1-85

 1-50 

 1-46

-1-24

 o-oo

 1-14

 1-29 

-1-35

-1-40

*

Steam on.

> Steam off.

J

t

> Steam on.

'

Bate.

Feb. 19, 2" 44">

3 00

25

4 55

24, 10h 42m

10 45

59

11 12

27 

59

12 23 

1 15

1 22

30

50

2 12 

3 30

fto

1-45

1-72 2-13

3-63

o-oo

0-05

0-29

0-50

0-75 1-30

1-66 2-50

2-65

2-80

303

3-50 4-80

(*-*') X 103

 1-30

 1-16 

 -69

 -63

+0-00

 75

1-06

1-16

1-20 1-26

1-28 1-30

1-08

 89

 76

 67 

 63

> Steam off.

)

J

)> Steam on.

1

1

i> Steam off.

j

* r (cold rod) 6°, imparted after heating. 

1 1 (cold rod) 6°, imparted before heating. 

t T (cold rod) + 6°, imparted before heating.
BARU6.J HARD STEEL TESTED AT 100°. 61

_inno. 0' sno a = -100°; 9 -20°. -

TABLE 43.

= 26<!m . 1 = 30 . 

(3-340 .

No. 3, ann'ld, 100° 9'' > NO. 4, ann'ld, 100°9i>5 ..,, -° °82

Date.

Feb. 24, 4»> 36°>

4 43

45 

55

5 10

5 15 

25, 9 40

25, 10" 00m

10 06

10

20 

25

30

34

45

11 00

28

1 40

28, 9 37

%o

0.00

0.12

0.15 

0.32

0.57

0.65 

17.07

0.00

0.10

0.18

0.32 

0.42

0.50

0.56

0.75

1.00

1.47

3.67

23.62

(*-*') X 10s

 o-oo

 3-05

 3-75 

 8-81

 10-61

 8'2l 

 6-95

o-oo

5-91

9-40

12-09 

13-06

13-41

13-80

]3'21

12-71

12-47

12-27

12-03

*

> Steam on.

J

£ Steam off.

t

S Steam on.

J

Steam off.

Date.

Feb. 26, 10" 02 

10 10

15

20

25

30 '44 

55

11 04

16

43

57

12 55

1 09

30 

55

8 12

fto

o-oo

0-13

0-21 0-30

0-39

. 0-46

0-70 0-89

1-03

1-22

1-70

1-92

2-87

3-10

3-41 3-88

5-10

(*-*') X 103

O'OO

 7-97

 884 

 9-80

 10-42

 10-95

 12-15 

-12-86

 13-31

 13-89

 14-89

 15-38

-16-80

 16-08

 15-64 

- 15-56

-15-16

t

 Steam on.

.)

Steam off.

* r (cold rod) 6° imparted before heating.

t T (cold rod) +6° imparted before heating, immediately after*.

j r (cold rod) 6° imparted before heating, immediately after t.

TABLE 44.

100°; e' = 20°; a=26cm ; Z=30cm ; £ = 60 ; /3 = 34cm. Rods: No. 5, annealed, 190", 2"; 

nealed, 190°, 2b ; 2p = 0-082cm.

o. 6, anDate.

Feb. 26, 3h 57m

4 15

4 20

25

34 

40 

51 

5 10

5 17

28, 9 52

28, 9" 68°

10 20

10 27

34 

41

51 

11 02 

33

54

12 17

50

1 04

15 

26 

42

12, l"49m 

2 05

2 15 

20 

30

35 

51 

8 13 

20 

45

fto

.... "b-66

0-09

0-17

0-32 

0-42 

0-60 0-92

1-03 

41-62

...... o-oo

0-12

0-23 0-35

0-52 

0-70 1-22

1-57

1-95

2-50

2-73

2-92 

3-10 3-37

"o'-bo"

0-17 

0-25 0-42

0-50 

0-77 

1-12 

1-25 1-67

(*-*') *

103

o-oo

o-oo

3-22

 3-86

 4-50 

 4-79 

 5-10 

 5-50

 5-02 

 3-84

o-oo

o-oo

2-41

5'34 6-02

6-55 

6-96 7-59

7-87

8-13

8-42

7-52

7-21 

7-07 6-97

o-oo o-oo

-4-04 

-4-86 

-5-74

 6-03 

 6-57 

 6-96 

 7-20 

 7-53

*

> Steam on.

| Steam off.

t

> Steam on.

^

> Steam off.

t

 Steam on. 

J

Date.

Feb. 28, 3h 55-»

4 05

54

Mar. 5, 10" 20m

10 26 

30 

35

44

56 

11 01

06

13

23

31

5, 11" 33m

11 35 

54 

12 03

11

12 15

24 

35

45

6, 1M61"

1 52 

2 03

08 

15 

24

2 31 

41 

51 

3 11

fto

1-83

2-00

2-82

o-oo

o-io

0-16 

0-25 0-40

0-60 

0-68

0-76

0-88

0-05

1-18

o-oo

0-08 

0-36 0-50

0-63

0-70

0-85 1-03

1-20

o-oo

o-io

0-28

0-37 

0-48 0-63

0-75 

0-92 

1-08 1-41

(*-*') X 103

-6-86

 6-48

 C'12

o-oo

 1-59 

 1-95 

 2-05 

-2-16

 2-30 

. 1-93

 1-59

 1-27

 1-04

 -93

o-oo

2-04 

5-12 6-63

6-74

6-52

6-01 4-74

4-58

-o-oo

 2-84 

 4-97

-5'27 

 5-51 

-5-75

 5-32 

 4-75 

 4-51 

-4-33

j

> Steam off.

>

*

}> Steam on.

1

J

) '

; Steam off.

j

. t

! Steam on.

> Steam off.

j

t

> Steam on.

J- Steam off.

* T (cold rod) 6°, imparted before heating.

t T (cold rod) +6°, imparted before heating, immediately after*.

J T (cold rod) 6°, imparted before heating, immediately after t.
62 THE VISCOSITY OF SOLIDS. [BULL. 73.

TABLE 45.

2I=100°; ^=20°! a = 26cm ; & = 30cm ; L~6Qcm ; k=Ucm. Eode: Mo. 7, annealed, 360°; No. 8, an.

nealed, 360° j 2p = 0-083cm.

Date.

Mar. 1, 10" 30-

10 35 

47 

59 

11 12 

22 

45 

12 00

12 15 

57 

1 17 

37

1, lh 40*-

47 

51 

58

ho

o-oo

0-08 

0-28 

0-48 

0-70 

0-87 

1-25 1-50

1-75 

2-45 

2-78 3-12

o-oo

0-12 

0-18 0-30

(*-*') X 10s

o-oo

1-44 

1-79 

1-91 

1-99 

2-03 

2-11 2-15

1-52 

1-20 

1-17 1-16

o-oo

-1-42 

 2-27 

^2-70

(*)

 Steam on. 

) 

> Steam off.

W 

> Steam on.

Date.

Mar. 1, 2h 09 

35 

3 04 

24 

43

4 55 

5 03 

25

1, 4" 40°>

4 47 

55 

5 05 

15

5 22 

2, 9" 42m

ho

0-48 

0-92 

1-33 

1-73 2-05

2-25 

2-40 2-75

o-oo

0-10 

0-25 

0-42 0-58

0-70 

17-03

f*-*')X 

10s

-2-95 

 3-22 

,-3-36 

-3-43 

-3-49

-2-97

-2.77 

-2-58

o-oo

1-55 

2-31 

2-63 2-75

2-45 1-65

} Steam on.

1

> Steam off.

(» 

> Steam on.

> Steam off.

* T (cold rod) +6°, imparted before heating,

t T (cold rod) 6°, imparted before heating, immediately after *.

J T (cold rod) + 6°, imparted before heating, immediately after t.

TABLE 46.

= 100°; 0'=20°; i=60am ; Z=30cn>: a=26<"»; j8 = 34«m. Bods: No. 9, annealed, 480°; No. 10, annealed

480°; 2p = 0-083 .

Date.

Mar. 2, 10" 53m

11 00

10

21

31

40

58

12 15

55

1 00

07

1 24 

.34

43

2 00

2, 2h 05m

2 14

19 

24

32 

45

3 00

08

15

3 23

32 

38 

47

58

4 11

3, 10" 02-n

ha

o-oo

0-07

0-17

0-28

0-38 0-47

1-05

1-22

2-02

2-07

2-14

2-31 2-41

2-50

3-07

o-oo

0-15

0-23 0-31

0-45 0-66

0-92

1-05

1-16

1-30

1-45 

1-55 1-70

. 1-88 2-10

o-oo

(<j> <J>')X 103

o-oo

 90

1-42

1-53

1-60 1-64

1-68

. 1-71 1-44

1-55

1-26

 96 

 89

 85

 81

o-oo

-1-26

 1-66 

 1-86

 1-99 

-2-08

 2-ir>

 2-18

 2-21

 1-85

 1-54 

 1-41 

 1-31

 1-25

 1-21

o-oo

(*)

 Steam on.

,

j

[> Steam off.

|

}

(t)

f Steam on.

Steam on.

tt)

Date.

Mar. 3,10b 05 

10

15

25

31

43 

11 02

11 07

15

25 

37

55

12 02

3, 12>" 12m

12 17

22

28

33

44 

55

1 08 

19

30

56

2 00

06

12 

22 

33

49

ho

0-05

0-13

0-21

0-38

0-48

0-68 1-00

1-08

1-21

1-38 1-55

1-88

2-00

o-oo

0-08

0-16

0-26

0-35

0-53 0-72

0-90 1-10

1-30

1-74

1'80

1-90

- 2-00 

2-16 2-35

2-61

(*-*') X 103

 94

1-C3

1-85

1-94

1-97

2-00 

 2-07

1-81

1-50

1-26 1-13

1-05

1-03

o-oo

-1-23

 1-61

 1-45

-l-8t

 1-92 

 1-97

 2-02 

 2-05

 2-07

 2-10

 1-92

 1-65

 1-46 

-1-30 

 1-20

 1-15

1 

( Steam on.

J

Steam off.

(§)

 Steam on.

1

> Steam off.

j

* T (cold rod) + 6°, imparted before heating.

t T (cold rod) 6°, imparted before heating, immediately after *.

t T (cold rod) + 6°, imparted before heating.

§ T (cold rod) 6°, imparted before heating, immediately after J.
U. 8. GEOLOGICAL SURVEY BULLETIN NO. 73 PL. II

I h. 2A.

VISCOUS DEFORMATION AT 100° FOR DIFFERENT STATES OF TEMPER.
BAIIUS.] VISCOUS DEFORMATION AT 100°. 63

= 100°; 0'=20°; a = 26cm ; Z=30om ;

TABLE 47.

= 60cm ; /3 = 34CID . Kods: No. 11, soft; No. 12, soft; 2p=0'082cm.

Date.

Mar. 4, 10h 08m

10 13

18

24

33

47 

57

11 12

20

40

11 45

11 55 

12 05

15

29

fto

o-oo

0-08

0-16

0-28

0-41

0-65 0-83

1-06

1-20

1-53

1-62

1-78 1-95

2-11

2'35

(</>-*') X

103

o-oo

1-05

1-45

1-56

-1-61

1-68 1-73

1-79

1-83

1-91

1-76

1-34 1'2G

1-19

1-13

(*)

> Steam on.

Steam off.

'

Date.

Mar. 4, 12» 59m 

1 40

4, lh 57m

° 2 04

09

19

28

40

3 06

3 10

16

24 

33

44

fco

2-85 3-53

o-oo

o-n

0-20

0-30 0-51

0-71

1-15

1-21

1-31

1-45 1-60

1-78

(*-<*>') x

103

1-08 1-05

O'OO

-1-69

 1-03

 2-11 

 2-13

-217

-2'24

-2-14

-1-85

 1-68 

-1-58

 1-52

| Steam off.

(t)

 Steam on.

Steam off.

* r (cold rod) + 6°, imparted before beating.

t T (cold rod) 6°, imparted before heating, immediately after *.

In PL II I have represented the results of these Tables 42 to 47 

graphically, (cp <pt}\W as a function of time. The plate therefore shows 

the amount of viscous deformation, at 100°, for each of the states of 

temper in question. The numerals in brackets indicate the number of 

twists applied, alternately in opposite directions. It is significant that 

in proportion as harder wires are operated upon, the (2) twist is in advance of the first, the third being usually intermediate as regards 

viscous deformation. Even in case of 190°, the oscillatory effect of 

counter-twisting is marked. It is obscure in soft rods. All this has an 

important bearing on the discussion in Chapter III, where the phenomenon of "accommodation" is discussed. It may be noted that the 

two parts of Table 44 are not immediately continuous; hence the difference of behavior of parts (1), (2), (3), and parts (4)', (5)', (6)' of the 

table.
64 THE VISCOSITY OP SOLIDS. [BULL. 73.

61 Viscosity at 190°. The data in hand are as follows:

TABLE 48.

0=190°; 0'=20° ; a=2Ccm j l = 30cm ; £ = 60 ; (3 = 34 . Bods: No. 5, annealed, 190°; No. 6, annealed, 190°; 2p = 0-082 . 

Date.

Mar. 7, 9 h 55m

10 00

04 

10

19

7, 12" 27m

12 33

36 

40

42

12 55 

1 40

7 2h 35m

2 45

47

53 

8 10

19

43

3 53

4 07

45

8, 9' 00

8, 9h 35m

9 43

45

48

fto

o-oo

0-03

0-15 0-25

0-40

o-oo

0-10

0-15 0-22

0-25

0'47 1-22

o-oo

0-17

0-20

0-30 0-58

0-73

1-13

1-30

1-53 2-17

18-42

o-oo

0-13 0-17

0-22

(*-*') x

10'

o-oo

 4-97

 14-80 

 12-39

-15-81

o-oo

14-61

22-98 

26-83

28-36

27-01 

26-23

o-oo

-11-42

-12-26

-13-48 

-15-40

 15-71

 14-28

-16-99

 16-68 

 16-58

 16-58

<*to

4-14 6-54

8-85

ft

> Vapor on.

J

(t)

Vapor on.

| Vapor off.

tt)

!

.

Vapor on.

Vapor off.

(§)

> Vapor on.

'

Bate.

Mar. 8, 9h 50»

53

56

10 00 

0815"

27

40

47

11 00

20

55

8,12" 00m

08

10

12

15

18 

21

25

30

35

40

45

50

1 00

1 12

30 

. 45

fto

0-25

0-30

0-35

0-42 0-58

0-67

0-87

1-08

1-20

1-42

1-75

2-33

o-oo

0-13

0-17

0-20

0-25

0-30 0-35

0-42

0-50

0-58

0-67

0-75 0-83

1-00

1-20

1-50 1-75

(*-*') X 103

9-81

10-70

11-09

12-26 

13-52

14-48

15-84

17-11

17-89

17-11

16-73

16'63

000

 7-23

 8-34

 9-12

 9'99

 10-71 

-11-28

 11-95

 12-68

 13-34

 13-85

 14-29 

 14-69

 15-36

 14-80

 14-49 

 14-45

 Vapor on.

> Vapor off.

)

(II)

 Vapor on.

j

> Vapor off.

' " * T (cold rod) 6°, imparted before heating.

t T (cold rod) + 6°, imparted before heating, immediately after *. 

J T (cold rod) 3°, imparted before heating, immediately after t. 

§ T (cold rod) + 3°, imparted before heating, immediately after J. 

|| T (cold rod) 3°, imparted before heating, after §.

TABLE 49.

0=190°; 9'=20°;a=26l!m ; Z=30cm ; L=60 ; /3=34cm. Rods: No.7,annealed,360°; No.8,annealed, 

, 360°; 2p = 0-082 .'

Date.

Mar. 8,2* llm

2 20

25 

36

3 05

3 12 

35

8,3h 41m

3 50

57

4 08

26

52

fto

o-oo

0-15

0-23 0-42

0-90

1-02 1-40

o-oo

0-15

0-27

0-45

0-75

1-18

(*-*') X

10»

o-oo

2-09

2-47 2-63

2-77

2-26 1-86

o-oo

-2-25

^2-99

-3-21

-3-25

 3-32

(*)

Vapor on.

? Vapor off.

(t)

|

> Vapor on.

I

j

Date.

Mar. 8, 5" 01 

10

9, 9" 27m

9 32

40 

10 35

48

11 02

07 

17

26

Ao

1-33 1-48

o-oo

0-08

0-21 1-13

1-35

1-58

1-66 1-83

1-98

(*-*') X 10»

-2.57 

 2-34.

o-oo

 84

2-01 3-01

3-04

2-29

2-19 2-09

2-05

J Vapor off.

(1)

> Vapor on.

J

i

> Vapor off.

J

* r (cold rod) + 3°, imparted before heating.

t T (cold rod) 3°, imparted before heating, immediately after *.

J T (cold rod) + 3°, imparted before heating, immediately after t.
U. 8. GEOLOGICAL SURVEY BULLETIN NO. 73 PL. Ill

I Vft fi 2h

VISCOUS DEFORMATION AT 190° FOR DIFFERENT STATES OF TEMPER AND STRAIN.
66 THE VISCOSITY OF SOLIDS. [HULL. 73.

stress r=3° ((1), (2), (3), in PI. II); whereas, its behavior toward stress 

T=6° ((4)', (5)'), is just like a viscous fluid. This is one of the most 

noteworthy results of these tables. It will be specially referred to iu 

Chapter III.

It is also to be observed that viscous oscillation does not occur in the 

case of soft rods (Table 51, parts (1), (2), (3)). -

65. Viscosity at 360°. The data in hand are as follows:

TABLE 52.

0 = 3GO°; 0'=20°; rt=9cra ; Z = 30cm ; L G0cra ; /3 = 34cm. Rods: No. 11, Soft; No.l2,80ft; 2p = 0'082cm.

Date.

Mar ll,llh 25'"

11 34

3(5

39 

44

47

53

11 59

, 12 05

JO 

18

27 

1 J3

11, 2h 03m

2 06

(19

11 

]2 

15

18

AO

o-oo

0-15

0-18

0-23 0-32

0-37

0-47

0-57

0-07

0-75 0-88

1-03 1-80

o-oo

0-05

0-10

0-13 

0-15 0-20

0'25

<*lJ? x

o-o

- 7.8 -lo-i

 11 -6 

 12 9 '

 14-0

 14-9

 13-1

 12-4

 12-0 

 11-8

 11-5 

 11-1

O'O

7-7

20'0

27-7 

35-0 41-7

44-5

*

1

1

' S Vapor on.

1

J

1

> Vapor off.

J

t

1

1> Vapor on.

1

J

Date.

Mar. 11, 2h 21m

25

35

2 54 

3 01

2K

11, 4" 25 

4 32

34

36 

39

41 

45

51

57

5 10

5 17 

26 

12, 9h 25 

*.

0-30

0-37

0-53

085 0'97

1-42

o-oo

0-10

0-15

018 0-23

027 0-33

0-43

053 0-75

0-87 

1-02 

17-00

103

46-8

48-0

49-1

46-6 46-4

46-2

o-o

 17-4

 24-9

 28-1 

 31-5

 32-7 

 34-4

 35-6

 36-9

-38-8

 36-1 

 35-0 

 33-8

> Vapor on.

)

> Vapor off.

)

t

1 '

} Vapor on.

J

> Vapor off.

* T (cold rod)- 3°, imparted before heating.

t T (cold rod) + 3°, imparted before heating, immediately after *.

I T (cold rod) 3°, imparted before heating, immediately after 1.

TABLE 53.

6=360°; 0'=20°; a O1""; Z = 30 ; £=60 ; 0 = 34<"". Hods: No. 9, annealed, 450°; No. 10 annealed, 450°. 2p = 0-082 .

Date.

Mar. 12, 10h 04m

10 10 

31 

49

57

11 15

27

59

12, I2h 15m

12 25

27 

30 

36

45

55

V

o-oo

o-io

0-45 0-75

0-83

1-18

1-38

1-92

o-oo

0-17

0-20 

0-25 0-35

0-50

0-67

« <*>') X 10'

o-o

 4-7 

 19-2 

 23-1

-24-8

 20-1 

 19-6

 19-3

o-o

28-6

32-2 

35-3 39-0

42-1

43-3

*

> Vapor on.

J

[ Vapor off.

)

t

 Vapor on.

Date.

Mar. 12, lh 10 

2 00

12, 2 h 15'" 

2 19

20

25

27 

28

36

47

3 13

3 20 

32 

48

h0

0-92 1-75

D-00

o-oo

0-08 o-io

0-20 0-22

0-35

0-63

0-96

1-08 

1-28 1-55

(*-*') X 

103

39'4 38-2

o-o

 9-9

-26-3

 30-3

 33-0 

 39-0

 43-3

 47-6

-44-8

 42-9 

 42-5

> Vapor off.

J 

)

-Vapor on.

> Vapor off.

* T (cold rod) 3°, imparted before heating.

t r (cold rod) + 3°, imparted before heating, immediately after *..

t T (cold rprl^ 3°, imparted before beating, immediately after t^
U. S. GEOLOGICAL SURVEY BULLETIN NO. 73 PL. IV

VISCOUS DEFORMATION AT 360° FOR DIFFERENT STATES OF TEMPER.
BAKU6.] TEMPERED STEEL AT 360°. 67

TABLE 54.

= 300°; 0' = 20°; a=9cm , l SO"n ; L = 6<y>m ; 0 = Mcm. Kods: No. 7, annealed, 300°; No. 8, an

nealed, 360°.

Date.

Mar. 14,10h OO'"

10 03

05

00

07 

09

10 

13

15

10 1!)

31 

40

11 04

14, 1"32"'

1 38

40

43

40 

51

59

2 02

11

2 20 

50

/'o

000

0-07

UOO

Ovl2

0-13 0-17

0-18 0-23

0-27

0'33

0-53 0-08

1-08

o-oo

0-10

0-13

0-18

' 0-23 

032 0-45

0-50

0-05

0-90 1-27

(0-<>')X 

LU3

o-o

 19-0

-20-7

 32-0

 30-8 

 41-3

 148 

 49 5

 51-9

 511

 495 

 49-3

-49-1

o-o

1G-9

25-2

32-2

37-0 42'7

47-0

48-9

51-9

47-0 40-8

+

I

> Vapor on.

J

1

> Vapor off.

J

1

 Va.por on.

£ Vapor off.

Date.

Mar. 14, 3 h 19'"

3 22

23

24

25 

27

28 

29

32

33

J 35

37 

40

3 55

4 12

20

14, 4h 45'"

4 49

50

52

54

50

57

5 05

5 24

ft.

o-oo

0-05

0-07

0-08

0-10 0-12

0-15 0-17

0'22

0-23

0-27

0-30 0-35

0-GO

0-88

1-12

o-oo

0-07 0-08

012 0'15

0-18

0-20

0-33

0-05

<*-0') X lo3

o-o

4-0

8-9

14-0

19'3 20-4

30-1 34-7

41-1

43'9

4G'0

49-1 51-5

47'2 46-4

46-4

o-o

 C'4

- 98

-24-4

-31-5

 30-8

 40-2

 45-0

-41-7

t

1

[> Vapor on.

> Vapor off.

J

§

1

J- Vapor on.

J

Vapor off.

* T (.cold rod) 3°, imparted before heating.

t r (cold rod) 3°, imparted before heating, after *,

J T (cold rod) + 3°, imparted before heating, immediately after t.

§ T (cold rod) 3°, imparted before heating, immediately after |.

In the twist (2) and (3) (PI. IV.), the latest torsion favorable to motion 

stored up in the wires during the period of twist (1), asserts itself. 

Hence the actual stress for the former case is very decidedly greater 

than in twist (1). The chart again shows, that viscosity is dependent 

on the stress-intensity producing viscous motion, in very marked degree.

In PI. IV the results of Tables 52, 53, 54 are graphically given, on a 

plan symmetrical with the above. A larger time-scale would perhaps 

have been preferable.

This plate preserves the character of the preceding charts. Steel 

annealed at 360° here shows maximum rate of viscous deformation. 

Indeed, the rapidity of motion for this case is extreme, so that the rod 

must be considered a viscous fluid. The four alternations of twist [(1), 

(2), (3), (4)], as before, give indications of gradually increasing viscosity; 

and the march toward the limit is a^jain oscillatory.

The chart is also instructive when the behavior of steel annealed 

at 450° and of soft steel is considered. During twist (1) the former 

shows less viscosity than the latter; and both are enormously less viscous than steel annealed at 360°. But in twist (2) and twist (3) this 

character changes in very large degree. The reasons have already 

been adverted to, in considering Fig. 22 B; where stress as well as temper varies.
68 THE VISCOSITY OF SOLIDS. [BULL. 73.

66. Remarks on the tables. A few remarks on the tables are here in 

place. Large angles ?/>, for the measurement of which Gauss's method 

is inconvenient, were calculated directly from the tangents. The error 

is everywhere within 1 per cent. In Table 44 and more particularly in 

special experiments, the observations on the constancy of the scale 

reading when the temperatures of both upper and lower wires are identical, prove that errors due to differences of viscosity in the cold wires 

are negligible. No motion is perceptible until heat has been applied. 

The difficulty encountered .in fixing the zero of time has already been 

mentioned. The curves are therefore correct in their vertical dimensions, but may have been shifted laterally as much as is indicated in 

each table by the interval between the parts marked "vapor on" and 

"vapor off1." It has also been stated that the results for mercury are 

too large because of the difficulty in accurately defining the length of 

the hot part a. Finally two sets of experiments were made with soft 

wire (Kods, Nos. 1, 2, 11, 12) because tfte viscous properties of soft 

wire are not sharply definable. The curves lie sometimes above, sometimes below the mean zone for steel annealed at 450°. This vagueness 

of the soft state is largely due to strains incidentally impressed. When

a positive twist immediately follows a 

negative twist, or vice versa, the values 

of (<p <p'), caeteris paribus, are larger 

than for the case of an untwisted wire. 

It is therefore to be noted that in the 

arrangement of apparatus employed the 

permanent set of any prolonged torsion 

is added to the following torsion, particularly in the case of high 6.

DEDUCTIONS.

67. Viscosity and temperature. The 

behavior of a given steel wire varies 

with the character and with the amount 

of twist it has received. These variations are not insignificant. Of. Figs. 

22 A, 22 B, 22 C. Hence it is expedient to construct a diagram of the mean 

viscous motion for each degree of hardness and then to discuss the secondary variations with reference to this 

diagram. In Figs. 23 A, 23 B, 23 0,

FIG. 23. Viscous deformation increasing 

with tirae, for different states of temper 

and of temperature. Mean values.

23 D (<p (p'), the angular torsion in radians is exhibited as a function of time in hours, when wires in all degrees of hardness are exposed to degrees of temperature (6) of 100°, 190° and 360° respectively. 

The series is made complete when the rate of twist (T) is 3°, the values 

of ((p cp1 } corresponding to 0=100° (Tables 42 to 47) where r=6° having
BAUUS.J ACCOMMODATION Itf HARD STEEL. 69

been divided by 2 to effect this reduction. This operation is probably 

not always rigorous1 ; bat it is sufficiently correct for the present purposes. In the case of #=190° experiments were made both for r=3° 

(Fig. 23 B), and for r=6° (Fig. 23 C). Each curve consists of two 

distinct parts, an anterior ascending branch showing the motion at the 

high temperature' 0, and a descending branch showing the (elastic) 

effect of cooling from 6 to room temperature (6'}. Figures 23 A to 23 D 

and Tables 41, and 42 to 54 clearly show that the viscous detorsion 

(cp cp1 ) exhibited by steel is very much more influenced by temperature 

when the steel is hard than when it is soft. In other words, viscosity 

decreases with temperature (cteteris paribus) at much greater rates 

in hard steel than in soft steel. Again, at the same temperature (9, the 

differences of viscosity are very large when the temper of steel lies 

between glass-hard and annealed at 350°. Intermediate differences

within this interval are larger in proportion as mean hardness is greater. 

When temper lies between annealed at 350° and soft, differences of viscosity at the same 6 are relatively small. In general therefore the 

variations of viscosity due to temper are marked occurrences during 

the first phase2 of annealing, and nearly vanish during the second 

phase, a result which corroborates the close analogy between the viscous effects of temper, the thermoelectric effect and the electric resistance effect of temper already pointed out.

68. For the same degree of hardness viscosity increases at an accelerated rate with temperature 6. In Fig. 23, where #=100°, the largo 

viscous interval between Annealed at 100° and Annealed at 300° is in 

striking contrast with the smaller viscous interval Annealed at 3GO° to 

Annealed at 1000°, notwithstanding the fact that to avoid erroneous 

comparisons the latter interval has rather been chosen too large than 

too small. Indeed, the values for Annealed at 1000° in Table 47 would 

place the locus for soft wire even above the curve Annealed at 450° in 

Fig. 23, suggesting the occurrence of a maximum viscosity for #=100°. 

Passing from Fig. 23 to Fig. 23 B ((9=190°), the interval between Annealed at 190° and Annealed at 360° is phenomenally increased. The 

interval Annealed at 360° to Annealed at 1000° is also increased, but 

only slightly. Again, passing from Fig. 23 0 to 23 D (0=360°), 

the interval of the second phase of annealing (Annealed at 360° to Annealed at 1000°) is largely increased.3 The marked tendency of a steel 

wire annealed from hardness at 6° to suffer viscous deformation when 

exposed to 0°, is the chief result of the present paper. This tendency 

decreases with great rapidity in proportion as the temperature of exposure falls below 6.

1 Of. Weidmanu: Wied. Ann., .1886, vol. 22, pp. 220,222. He believes proportionality between stress 

and deformation to obtain.

2 Am. Jour. Sci. (HI), 1886, vol.31, p. 443.

8 Of course the degree of hardest temper to be exposed to 6 for viscous comparisons is Annealed at 

0. Harder wires would be annealed at this temperature and the concomitant effects due to changes 

of temper erroneously confounded with simple viscous motion.
70 THE VISCOSITY OF SOLIDS. [BOLL.73.

As temperature increases, glass seems to lose rigidity much less 

rapidly than hard steel, but probably not less rapidly than soft steel. 

The magnetic instability of glass-hard steel is probably due to its extreme susceptibility of temperature, since every change of temper is 

the cause of loss of magnetic moment. This close relation between 

hardness and magnetism is good evidence in favor of the essentially 

strained character of hard steel. The full bearing of all these points is 

made the subject of Chapter III.

69. Behavior of other metals. Kohlrausch, 1 Streintz,2 Schmidt,3 and 

Pisati4 have discussed the effect of temperature on viscosity. More 

minute investigations on the relation between viscosity and temperature 

have recently been made with silver, platinum, iron, and germau silver, 

and for temperatures within 100°, by Schroeder.5 It is in place to advert in passing to certain important accordances between Schroeder's 

results and the present results. In the data above, one or more alternations of the sign of twist are applied to the steel wires (Tables 42 to 

54, particularly Table 44), and the amount of deformation decreases 

(cceteris paribus) with the number of torsions applied gradually toward 

a limit. This fact has been studied by Wiedemanu6 and at even an 

earlier date though in a somewhat less relevant way, by Streintz7 under 

the term "accommodation." Schroeder has apparently enlarged the 

importance of these observations by showing that, repeated alternations 

of temperature from low to high values have the same effect.8 It remains to be seen, however, whether this is not an immediate result of 

the fact that Schroeder's hard-drawn wires are annealed by exposure 

to 100°. Indeed the results of Chapter III make this altogether probable. A second result of Schroeder's,9 viz: that the amount of " afteraction," as well as the amount of change of after-action due to stated 

increments of temperature is greatest in silver, of intermediate value

in iron, and smallest in german silver, has an important bearing on 

the present experiments. The present results taken together with 

the earlier paper of Barus and Strouhal10 show conclusively that the 

viscosity of steel and the variation of viscosity due to temperature 

increase in like order, and in ways which throughout the course of 

the phenomena are thoroughly analogous. A final result of Schroeder's bearing on the present paper, viz: that the viscous detorsion 

occurring at 100° is arrested by suddenly lowering the temperature

1 Kohlrausch : Pogg. Ann., 1866, vol. 128, p. 216; 1876, vol. 158, p. 371.

2 Streiutz : Wien. Berichte, 1874, vol. 69, p. 337.

3 Schmidt: Wied. Ann., 1877, vol. 2, p. 264.

4 Pisati: Wien. Berichce, 1870, vol. 80, p. 427. 

0 Schroeder: Wied. Ann., 1886, vol. 28, p. 369.

6 Wiedemanu: Wied. Ann., 1879, vol. 6, p. 512.

7 Streiutz : Pogg. Ann., 1874, vol. 153, p. 406.

8"Ebensowie das log. Decrement bei Torsionschwingnngen zeigt auch die Nacliwirkung unter 

dem Einttusse wiederholter Temperaturanderuugen eine Accommodation."

9 "Sowohl die Nachwirkung wie die Anderung derselben mit der Temperatur ist ani griissteu beiui 

Silberdraht, geringer beim Eison, am kleinsten beim Neusilberdraht."

»» Am. Jour. Sci. (HI), 1887, vol. 33, pp. 25,26.
BARUS.I STEEL COMPARED WITH OTHER METALS. 71

as far as 20° is again fully corroborated by the behavior of steel; but 

the character of the viscous motion while the temperature either rises 

or falls does not so fully appear, because a large part of the retrograde 

movement observed during cooling is here to be ascribed to concomitant changes of the modulus of elasticity produced by temperature. In 

other words, relatively large variations of elasticity are superposed 

upon and obscure the nature of the viscous detorsion during the interval 

of transition from high to low temperature, or from low to high temperature.

70. It is because of the mixed character of the retrograde movement 

that I refrain from using the data for the construction of the temperature relations of the rigidity of steel. If a device for cooling with 

sufficient rapidity to annul the viscous movement be applied, then the 

present method may be used at once for investigating tho effect of 

temperature on rigidity.

71. Viscosity and pressure. In view of the great importance of viscous deformations in questions of dynamic geology, I will insert a few 

remarks relative to the effect of pressure on viscosity, such as follow at 

once from the above experiments.

At a depth.^ of ten miles below the surface, the temperature of the 

stratum of earth is certainly as high as 450° C. 1 At this temperature 

glass is practically a viscous fluid as appears at once from experiments 

by Dr. Strouhal and myself, on the strain effect of quenching exhibited 

by the Prince Rupert drop.3 We found all strain to have vanished 

when the temperature of annealing reached this limit. Special experiments on the torsion viscosity of glass made with the above apparatus 

shows a similarly marked effect at 370°, so that glass which is less viscous 

than soft steel at mean atmospheric temperatures maintains this state 

of inferiority when temperature is raised. It is not necessary to tabulate the experiments with glass here. They are difficult of reduction, 

because glass-fiber can not easily be drawn to have the same uniform 

section throughout its length. Again, at these temperatures glass 

easily devitrifies, a phenomenon which decreases its viscosity enormously. The omission is easily justified since Warburg and others 

have proved that even at 300° glass behaves like an electrolyte (cf. 

Chapter I).

It follows that if the earth were of glass, and if the viscous effect of 

pressure were nil, the behavior of strata at even ten miles below the 

surface would be that of a viscous fluid. Indeed the strata there and 

to some extent above this level, would yield to the application of even 

small intensities of shear.

Again, if the earth were made of steel in the state of maximum viscosity, the rigidity ten miles below the surface would be nil, so far 

at least as the action of continuous shearing stress is concerned.3

1 Cf. Thomson and Tait Nat. Philosophy, I, part 2,1883, pp. 476 to 477. 

2 Bull. U.S.Geol. Survey,'No.42,1888, p. 109.

8Considerations of this kind have been made specifically and carried out in detail by Mr. Clarence 

King.
72 THE VISCOSITY OF SOLIDS. [BULL. 73.

*.

It follows finally that, if the earth, throughout depths of this insignificant vf.lue, behaves like an elastic solid, the effect of pressure on 

viscosity must be of importance.

72. Sudden and gradual deformation. In the experiments for 0=100° 

the rate of twist r=6° was uniformly applied. The results were then 

approximately reduced to r=3° by merely halving the values of (q> <£>') 

PI. Ill shows that the same strain, r=6°, applied for (9=190°, is too large 

for convenient measurement by Gauss's method. On applying r=3° 

directly, the completed series of results is obtained. Comparing the 

loci of PI. Ill and Fig. 23 0, it appears clearly that (cp cp'} increases 

very much more rapidly than r. Moreover, if the rate of increase of r 

be 2, the rate of increase of (<p <p'} is certainly as much as 3 in case of 

steel annealed at 190°, and even more than 10 in case of soft steel 

(annealed at 1000°). It follows therefore very probably that the viscous 

relations of soft steel to hard steel vary enormously and even change 

sign as the stress producing viscous motion passes from low to high 

values. This is an important deduction. For rates of twist less than 

r=3° for the diameter 2/>=0-082cm, steel is less viscous, and as regards 

viscosity much more susceptible to the influence of temperature, in proportion as it is harder. For rates of twist greater than r=6° steel is 

less viscous and more susceptible to the influence of temperature in 

proportion as it is softer.1 The complete coordination of these facts, 

in other words the full expression of the viscosity of steel as a function 

of hardness for all degrees of temperature 6 and all values of stress T, 

will be the key for the explanation of the mechanical behavior of steel 

and its important bearing on magnetic, electrical and other properties 

of the metal. To elucidate these remarks I will complete the description of the apparatus with which the present results were obtained, 

leaving theoretical inferences for discussion in Chapter III.

73. In the apparatus, PI. I, suppose the lower (cold) wire to be iu 

connection with clockwork, in such a way that it may be twisted uniformly, at any given velocity, variable at pleasure. Suppose the method 

of adjusting the index to be such as is suitable for the measurement 

of angles of any magnitude. If the clock be set in motion from 

r=0, the strain will increase at some determinate arbitrary rate. For 

a given value of #, therefore, a family of curves may be obtained in 

which the angular motion of the index ^i for a given wire must be expressible as a function of the time during which twisting has taken 

place and the rate at which the strain is increased. In other words, if 

c be the rate of rotation of the lower end of the lower wire, the experimental results may be symbolized by

'Ui. Cams VVilsuii: Phil. Mag., 1890, vol. 2'J, p. iuu.
Junes.] SUDDEN AND GRADUAL DEFORMATION. 73

where t is the symbol of time. It follows that the strain per centimeter of the total length L, at any time £, will be et)L diminished by 

the amount of viscous motion.1 Hence it is experimentally possible and 

fuliy feasible to pass from the family of curves ^j, y;2 ,.. - .^>n to a similar 

family,

(9-9>}=F(t, r),

by an appropriate method of graphic solution. (cp <p') thus expressed 

as a function of time and strain, for all degrees of hardness and all degrees of temperature 6, is the complete solution of the problem in hand. 

I take pleasure in acknowledging that the greater number of experiments in this paper are due to Mrs. Anna H. Barus.

'If c' be the rate of the index for perfectly elastic wires, then ^ c't, and 2 c't ty correpond respectively to the viscous motion and the strain intensity at the time t. The curves ^ will in general he circumflex, passing from an initial tangent c' to an asymptote which is the rate of rotation of the lower 

end of the wires.
CHAPTEE III.

MAXWELL'S THEORY OF THE VISCOSITY OF SOLIDS AND ITS 

PHYSICAL VERIFICATION.

INTRODUCTION.

74. The viscosity of solids has been theoretically discussed in the 

memoirs of O. E. Meyer, Boltzinaun, Seesen, Warburg, Maxwell, and 

Butcher. Views of a distinctly theoretical kind have also been given 

by Weber and Kohlrausch, and more recently by Nissen. In almost 

all cases, excepting alone Butcher's1 work, which formulates the theory 

of Maxwell,2 the problem has been approached from distinct points of 

view.

Despite the diversity of methods of discussion and the elaboration of 

evidence, the results do not in any case so fully represent the phenomenon as to lead to general acquiescence in one elementary physical hypothesis. Boltzmann's theory is perhaps the most powerful and is elegantly worked out; but it is purely mathematical in character. Maxwell's theory has the broadest physical basis, although left by its author 

in shape merely of a terse verbal sketch.

Now it seems to me, if indeed I may venture any assertion, that Maxwell's theory is a version of Williamson's3 theory of etheriticatiou, and 

of Clausius's4 theory of electrolysis. The transition made is from unstable groupings of atoms to unstable groupings of molecules. But 

preserving minutely all the essentials of Maxwell's argument, the experiments Of this paper justify the assumption that viscosity is a phenomenon evoked by certain changes of molecular structure, the inherent 

nature of which is ultimately chemical. I say chemical because if molecular break up occur, cardinal questions at once arise as to the manner 

of removal of the debris; and the phenomenon thus depends not only 

on the past history, but on the immediate future history of the typical 

mean configuration. The analogy of the three theories is very close, 

so that they admit of generic classification. They are examples of the 

invasion of statistical method into liquid and solid molecular kinetics.

The behavior of steel when regarded as a viscous solid and in the light 

of known facts,5 is convincingly in favor of the view to be advocated;

1 Butcher: Proc. Lond. Math. Soc., 1878, vol. 3.

2 Maxwell: " Constitution of Bodies," Ency. Brit., 9th ed., 1876, vol. 6, p. 310.

3 Williamson: Ariu. d. Chem. u. Pharm., 1851, vol. 77, p. 37.

4 Clausius: Pogg. Ann., 1857, vol. 100, p. 353; ibid., 1857, vol. 101, p. 338.

* I refer in particular to the work of Dr. Strouhal and my.-elf. These papers, systematically discussed and enlarged, are embodied with much new matter in the bulletins of the U. S. Geological 

Survey, viz: Bull. No. 14,1885, pp. 1-226; Bull. No. 27,1886, pp. 30, 61; Bull. No. 35,1886, pp. 11-60; Bull. 

No. 42,1887, pp. 98-131. Other references are given in the text. 

74
THEOKIES OF VISCOSITY. 75

and it was the direct bearing of some of the results on Clausius's theory 

of electrolysis, that led nie to suspect a chemical explanation, 1 before

1 became aware of the existence of Maxwell's article. To show hosv 

clearly Maxwell's theory interprets the complex and almost anomalous 

phenomena of viscosity exhibited by steel, is the chief endeavor of the 

present paper; but I shall also add other matter.

HISTORICAL SKETCH OF THE THEORIES OF SOLID VISCOSITY.

75. It is desirable to pass in brief review the divers hypotheses on 

the nature of solid viscosity to which I have referred.

0. E. Meyer's2 theory is the earliest and most direct. It discusses 

the action of elastic forces in a medium of imperfect elasticity, and develops formulas to express the diminution of stress in virtue of the 

occurrence of internal friction.3 The results to which Meyer's formula 

eventually leads are incomplete and were uot fully verified by subsequent experiment. The theory is therefore sharply antagonized by 

Boltzmaun,4 by Streintz,5 and by Kohlrausch.6 In later paper Meyer7 

partially assents to these adverse views, acknowledging that the theory 

does not reproduce the phenomenon actually observed. It also fails, 

as Kohlrausch (loc. cit.) pointed out, in predicting an insufficiently 

slow time of occurrence. After giving reasons for dissenting from 

Boltzmann's and from Neesen's hypotheses, Meyer proceeds to partially 

develop an older idea of Weber's.8 This physicist referred viscosity in 

solids, to partial molecular rotation, a view adopted by Kohlrausch,9 

by whom it has been more clearly interpreted. The rotations underlying Weber's phenomenon are considered identical with the rotations 

of molecule postulated by Clausius10 in discussing shear. Following 

Meyer and others, "elastische Nachwirkung" is a possible occurrence 

in liquids.

 76. Boltemanitfs11 theory, amplifying deductions of Lamy and of 

Clebsch, is based on the assumption that the elastic forces are dependent 

not only ou the present but on the preceding deformations of the body. 

The effect of earlier states of stress on the existing stress diminishes 

with the intervening time bat is independent of intervening states of

I Am. Jour. Soi. (Ill), 1887, vol. 33, p. 28. It is much to be regretted that Maxwell's theory was publisho.d out of the lino of a physicist's usual routine reading.

2 Moyer: Pogg. Ann., 1874, vol. 151, p. 108.

3 Following the usage of the term hy Navier, Cauehy, Polsson, St. Venant, Stokos, Stcfan. Cf. 

Moyor, loc. cit.

4 Boltzmann : Pogg. Ann., Ergiinzb., 1870, vol. 7, p. 624.

 Streintz: Pogg. Ann., 1875, vol. 155, p. 588; ihid., 1874, vol. 153, p. 405.

0 Kohlrausch: Pogg. Ann., 1877, vol. 160, p. 225.

i Meyer: Wiecl. Ann., 1878, vol. 4, p. 249.

» Weber: Pogg. Ann., 1835, vol. 34, p. 247 ; ibid., 1841, vol. 54, p. 1.

9 Kohlrausch : Pogg. Ann., 1860, vol. 128, u. 413; cf. also ibid., 1863, vol. 119, p. 337.

lo "Weuu eiu soldier Korper fremtlen Kriiften unterworfeu wird, die vou verschiedenen Soiten 

iingleich auf ihu \virken, also z. B. iiach einer Dimension gedehnt wird, wahrend er nach anderen 

Dimensioiiou frei hleibt odor gar zusatnmengedruckt wird, dann die Molekille neben ihrer Verechiebung sich auch etwas dreheu konnen, indeiu sie in Bezug auf ihre Kraftrichtung den ungleichen 

Spannungen etwas folgen. ..." Pogg. Ann., 1849, vol.76, p. 66.

II Boltzmann: Pogg. Ann., Ergiinzb., 1876, vol. 7, p. 624.
76 THE VISCOSITY OF SOLIDS. [BULL. 73.

stress. Different viscous deformations are superposable. Boltzmann's 

theory, therefore, presupposes the phenomenon1 and brings the laws of 

viscosity tersely into formulae. If K> is an interval of time reckoned 

back from t &?, when the strain ^_u existed, then Boltzmann's law 

may be clearly exhibited in its application to the problem of vibration 

of a viscous solid. Given a wire of the solid of length I and radius R. 

Let the upper end be fixed, and the. lower end be attached to a heavy 

bob, whose moment of inertia for the given conditions is IL Then the 

equation of motion is (slow oscillation presupposed)

v ~-/L ,1, » 21

where T> is the moment of the applied couple, JJL Lamy's constant, and 

i/j some function of GO. Eeplying to Meyer's critique that a theory of 

this kind is at variance with the present state of knowledge in atomistics, Boltzmann2 disclaims all present purpose to connect his theory 

with definite physical hypotheses. He points out, however, that the 

assumed dependence of the existing strain on foregoing deformations 

is easily justified when the simultaneous changes of molecular, configuration are taken into account; for it is not necessary to suppose that the 

elastic forces as such have any dependence on the preexisting stress. 

The changes of configuration in question are closely similar to Maxwell's, so that in this respect Boltzraann's theory may be looked upon 

as one form of mathematical development of Maxwell's physical hypothesis. I may add that Boltzmann tested his theory with data of 

Kohlrausch, Neesen, and Streiutz. A special series of experiments 

subsequently undertaken by Kohlrausch3 give additional strength to 

Boltzmaun's deductions. The theory does not, however, predict permanent set.

77. Neesen's theory. A. theory similar to Boltzmaun's, but atomistic 

in character, is due to Neesen.4 It also assumes the occurrence of solid 

viscosity. ISTeesen distinguishes the forces producing and retarding 

motion and the final purely elastic forces which obtain when viscous 

motion has subsided. Neesen practically postulates a change in the 

constants of elasticity. Warburg 5 objects to Neesen's deductions because they contain no reference to the form of the molecule. Meyer 

(loc. cit.) fails to find in it definite causal relations to the observed viscous motion.

Braun's 6 research,though largely experimental in character, deserves 

mention here, because of special light which it throws on the superposition of different viscous deformations. Excepting in glass,7 he finds

' Kohlrausch: Pogg. Ann., 1877, vol 160, p. 227. 

* Boltzmann: Wied. Ann., 1878, vol. 5, p. 430.

3 Kohlrausch: Pogg. Ann., 1877, vol. 160, p. 225.

4 Neeaen : Pogg. Ann., vol. 1876,157, p. 579. 

8 Warburg: Wied. Ann.. 1878, vol. 4, p. 233.

6 Braun: Pogg. Ann., 1876, vol. 159, p. 337; cf. Kohlrausch: Pogg. Ann., 1877, vol. ICO, p. 227. 

7 I do not believe that glass is an exception. The occurrence of devitrification, for instance, decreases 

the viscosity of glass enormously, as I found. Other points of view will be adduced in another paper.
BAKUB.J MAXWELL'S THEORY OF VISCOSITY. 77

that these molecular raotious do not take place independently of each 

other. He concludes that elastic and viscous deformations owe their 

occurrence to forces of different origin, and he refers viscous motion to 

the partial rotations postulated by Weber and Kohlrausch.

Warburg's theory. Wartmrg, 1 following out the suggestions contained 

in Braun's results, formulates a new theory, in which viscosity is the 

result of partial rotations of molecules of a form other than spherical.

78. Nissen's* theory is unique. He considers the ether in the space 

surrounding the body, in its relations to the ether within the intermolecular spaces of the body; and he bases his theory on the conditions under which the external ether enters the said intermolecular 

spaces when the body is deformed by stress. He thus obtains both a 

time and a thermal effect. In many respects this curious theory seems 

to anticipate Osborne Reynolds 3 in recognizing the importance of the

"dilitaucy" of a granular medium.

79. MaxweWs* theory would require more extended comment; but the

'Warlnirg: "Wied. Ann.. J878 vol. 4, p. 232.

2 Nisseu : Inaug. Dissert., Bonn. 1880. (Not accessible to me.)

3 Keyuolds: Pbil. Mag., V, 1885, vol. 20, p. 4G9.

4 Maxwell: Eucyclop.Brit., 9th eel., 1870, vol. 0,p. 311.

The theory is here subjoined in full:

The molecules of all bodies are in motion. In gases and liquids the motion is such that there is 

nothing to prevent any molecule from passing from .any part of the mass to any other part; but iu 

solids we must suppose that some, at least, of the molecules merely oscillate about a certain mean podition, so that, if we consider a certain group of molecules, its configuration is never very different from 

a certain stable configuration about which it oscillates.

This will be the case even when the solid is in a state of strain, provided the amplitude of the oscillations does not exceed a certain limit, but if it exceeds this limit, the group does not tend to return to 

its former configuration, but begins to oscillate abont a new configuration of stability, the strain in 

which is either zero, or at least less than in the original configuration.

The condition of this breaking up of a configuration must depend partly on the amplitude of the 

oscillations, and partly on the amount of strain in the original configuration j and we may suppose 

that different groups of molecules even in a homogeneous solid are not in similar circumstances in this 

respect.

Thus we may suppose that in a certain number of groups the ordinary agitation of the molecules is 

liable to accumulate so much that every now and then the configuration of one of the groups breaks 

up, and this whether it is in a state of strain or not. Wo may oven in this case assume that in every 

second a certain proportion of those groups break up, and assume configurations corresponding to a 

strain uni form in all directions.

If all the groups were of this kind, the medium would be a viscous fluid.

But wo may suppose that there are other groups the configuration of winch is so stable tha.t they 

will not break up under the ordinary agitation of the molecules unless the average strain exceed a 

certain limit, and this limit may be different for different systems of these groups.

Now if such groups of greater stability are disseminated through the substance in such abundance 

ns to build lip a solid framework, the substance will bo a solid, which will not be permanently deformed except by a stress greater than a certain given stress.

But if the solid also contains groups of smaller stability and also groups of the first kind which break 

up of themselves, then when a strain is applied the pesistonce to it will gradually diminish as the 

groups of the first kind break up, and this will go on till the stress is reduced to that due to the more 

permanent groups. If the body is now left to itself, it will not at once return to its original form but 

will do so only when the groups of the first kind have broken up so often as to get back to their oniginal state of strain.

This view of the constitution of a solid, as consisting of groups of molecules some of which are in 

different circumstances from others, also helps to explain the state of the solid after a permanent doformation has been given to it. In this case some of the less stable groups have broken up and assumed new configurations, but it is quite possible that others, more stable, may still retain their 

original configuration, so that the form of the body is determined by the equilibrium between these 

two set of groups j but if, on account of rise of temperature, increase of moisture, violent vibration, or 

any other cause, the breaking up of the less stable groups is facilitated, the more stable groups may 

again assert their sway, and tend to restore the body to the shape it had before its deformation
78 THE VISCOSITY OF SOLIDS. inuu,73, i

terms in which bis views are expressed are so precise, that it is impossible to abbreviate them, cf. §99. Aside from the remarks of the next 

paragraph, the ideas underlying Maxwell's theory have been given by 

many others, indeed by almost all the chief writers on solid viscosit}7 ; 

but Maxwell carries them through consistently to a complete theory.

I have stated that Maxwell's theory is the analogue of Clausius's 

theory of electrolysis. Where the latter uses "Theil molecule" and 

electromotive force to effect chemical decomposition, Maxwell has unstable configurations and stress available to produce permanent deformation. In Clausius's case the number of decomposable molecules (i. e. 

unstable configurations as regards the action of electromotive force), in 

any given case of actual electrolysis, is practically infinite. This corresponds to Maxwell's viscous fluid, hard or soft. In a viscous solid, 

molecular configurations are present in all degrees of stability, with a 

sufficient preponderance of stable configuration to constitute a solid 

framework. The relative number of unstable configurations varies 

with the viscosity of the material. If, therefore, I conceive the case of 

an electrolyte exhausting itself with respect to electrical conductivity, 

by the chemical decomposition induced by current, until conduction 

cease, I have the analogue of a solid which is reaching the limit of viscous deformation, cf. §107.

80. From this analogy it follows that a solid (?) electrolyte is necessarily viscous; whereas a viscous solid is only an electrolyte when the 

molecules break up into parts oppositely charged. Again, a viscous 

solid (?) is probably more viscous when undergoing electrolytic decomposition than when no current passes through it.1 Experiments to the 

same effect can, however, be made with greater facility, if the solid 

operated on is such that special instability of molecular configuration is

superinduced by heat, instead of electrical action, Such a solid is hard

steel, in which, in addition to the ordinary thermal instability, what 

may be called a carburation instability of molecular configuration 

asserts itself, even at mean atmospheric temperatures, and in the homogeneous metal. Inasmuch therefore as the gist of Maxwell's theory is 

instability of configuration, it follows that the evidence which can be 

derived with reference to it, from hard steel, must be unique in character: for despite the extreme hardness and elasticity of tempered steel, 

instability of molecular configuration demonstrably exists,2 and is distributed uniformly throughout the metal; moreover the number of unstable groups can be made to vary over an enormous range, at pleasure.

I must distinctly state, however, at the outset, that Maxwell limits 

his considerations to configurations of molecules. The responsibility 

of fusing Clausius's and Maxwell's theories rests with me. The step is

I I have since been at some pains to verify this surmise, working with glass at 360°. But the experiments thus far are not decisive, because the amount of current passing through glass is not only 

very small, but soon ceases entirely even in the case of thin-walled tubes (Warburg, Wied. Ann., vol. 

21, p. 622). On the other hand, if the current passes the electrolyte in strict accordance with Ohms 

law, it will produce no special decomposition, and will not therefore affect the viscosity of the 

electrolyte.

8 B»F»a a»d StronUal; Aqj. ,jour. Sgi. (Hi) vol. 32,1886, p. 270,
1MRU8.1 DATA FOB STEEL. 79

dictated by the behavior of steel, in which the integrity of the molecule 

is certainly invaded without producing essential differences in the 

character or history of the viscous phenomena (§ 93). I may note that 

the occurrence of chemical change makes the hypothesis verifiable.

EXPERIMENTAL RESULTS.

\ APPARATUS.

81. The remarks made in the preceding sections clearly show, that 

notwithstanding the abundance of experimental data in hand, further 

researches tending to throw light on the ultimate nature of viscosity 

are urgently called for. To obtain such I made a new set of experiments on the plan indicated in Chapter II, modifying the apparatus 

there described in the following respects. The lower wire of the system 

is provided with a torsion circle of large radius, by aid of which the 

amount of permanent set of the wires can be accurately registered. In 

this way also any amount of twist can be permanently stored, at the 

operator's pleasure. Again the basin X in PI. I was replaced by a ringshaped basin surrounding the wires so that the wire could be twisted 

without removing the vane. In other respects the present experiments 

are like the above, except that the individual viscous detorsions were 

not watched for so long a period as occurs in Chapter II. 

I 82. Theory of the apparatus. This has been fully given in Chapter 

/ II, §§ 56 to 59.

83. Measurements with steel. The following tables exhibit the new 

results for steel. About twenty rods were examined. Table 55, after 

enumerating the rod ("No."), and stating the temperature at which it 

was annealed (abbreviated "An.") from glasshardness, gives the amount 

of twist, r (radians), temporarily imparted per unit of length, and 

2(99+99'), the mean amount of viscous detorsion, in radians per unit of 

length, observed immediately after the end of the experiment. 2(<p+ q>') 

is therefore the mean viscous effect of r impressed on the system of two 

vertical wires. Hence r+2(cp-{- (p')=27rlL. Furthermore, 6' is the temperature of the lower wire, 6 that of the upper wire, and (<p (p')lr 

(radians) is the amount of viscous detorsion, as observed at the index 

between the wires, at the time specified, per unit of T. Eegarding this 

differential quantity, which is the chief datum of the tables, it is merely 

necessary to call to mind that 293 is the viscous detorsion, per unit of 

length of the upper wire, for the rate of twist r; and 299' has the same 

signification relatively to the lower (normal) wire. The reference to the 

unit of r is a convenience permissible when r, as in the present work, 

has nearly the same value throughout.1

The normal wire, No. 7, with which all the other steel wires are compared, is annealed from hardness at 450°, and has been twisted back

i > In how far suob reductions are generally permissible, cf. Weidmanu: Wiod. Ann., 1886, vol. 19, pp. 

220,222.
80 THE VISCOSITY OF SOLIDS. [BULL. 73.

and forth till viscosity is practically unchanged by further twisting 

within the same limits. It is therefore in a state of extreme viscosity, 

and at the same time less liable to permanent set than a soft steel wire. 

Its dimensions are Z'=30cm, radius =p=0-0405em, so that l'=l. The 

wire of unknown viscosity is examined at 20° (nearly), and immediately 

after at 100°. Two experiments are made at each temperature with r 

alternately positive and negative. When r and ((p (p')/T have the 

same signs (the usual case), the lower wire, No. 1, is of greater viscosity. In case of 0=100°, only a part of the upppr wire, length a=a /?, 

could be heated; the remainder being kept at the lower temperature 6'. 

Time is conveniently given in minutes, reckoned after twisting. 

84. Viscous behavior of the rods. This is given in the following table:

TABLE 55. Viscous DETORSIONS OF HARD STEEL.

J=30cm. p=0-0405cm. a=28-5 . jS = 31-5£m.

No.

An.

2 450°

3

450°

4 

36QC

5 360°

6

190°

2(0+*')

-1045 

 0003

+ 1027 

+ 0020

 1033 

- 0014

+ 1030 

+ 0017

-1033 

 0014

+ 1007 

+ 0041

- 1027 

 0020

+ 1021 

+ 0026

 1035 

 0012

+ 1035 

+ 0012

6

8'

20 

20

20 

20

20 

20

22 

22

22 

22

23 

23

23 

23

19 

19

19 

19

3 

17 

50 

60

I 

8 

28 

52

2 

C 

19 

28 

44

a

8 

20 

30

2 

17 

42 

54

33 

44 

64

2 

15 

21 

34

2 

12 

19 

27

2 

5 

17 

35

2 

19 

31

A A'

+0-00 03 

 05 

 06

 o-oo

 -06 

 -12 

 -12

+0-00 17 

 34 

 43 

 49

 o-oo

 -03 

- -63 

- '03

-O'OO 

 -19 

 -24 

- '24

"+0-00 

1-47 

1-61 1-77

 o-oo

 -19

- -25 

- -28

+0-00 25 

 29 

 31

 o-oo

- -12 

 -28 

- -18

+0-00 00 

 06

No.

An.

2 450°

3

450°

4 360°

5 360°

6

190°

2(A+A')

 1027 

 0020

+ 1027 

+ 0020

 1027 

 0020

+ 1027 

+ 0020

- 1007 

- 0041

+ 0998 

+ 0049

 1019 

- 0029

+ 1015 

+ 0032

 1023 

- 0024

+ 1003 

+ 0044

0

0'

100 

20

100 

20

100 

20

100 

20

100 

22

' 100 

22

100 

23

100 

23

100 

19

100 

19

Time.

2 

6 

18 

29 

45 

58

2 

20 

33 

47

2 

11 

20 

34 

48

2 

10 

18 

24

 3 

15 

28 

46

2

12 

22 

37 

49

3 

22 

32

2

7 

20 

27

1

4 

12 

20 

29 

36

1 

5 

10 

15 

20 

26 

32 

38

A A'

 o-oo

 -92 

 1-97 

 2-49 

 3-08 

 3-47

+ o-oo

1-71 

2-56 3'2l

 o-oo

 -88 

- 1-21 

 1-51 

 1-97

+ o-oo

3-11 

4.65 5-50

 o-oo

 1-74 

 2-48 

- 3-05

+ o-oo

5-32 

7'62 

9-86 

11.07

 o-oo

- 2-24 

 2-94

+ O'OO 

212 

4-04 4-74

 o-ou

 3-69 

- 8-02 

 10-39 

 12-95 

 13-35

+ o-oo

8-18 

13-29 

16-98 

19-53 

22-14 

24-10 

25-87
[liARUS. MEAN VALUES FOR STEEL. 

TABLE 55. Continued.

1=30 . p=0-0405cm . a=28-5 . /3 = 3l'5cl

81

No. 

An.

7 190°

8 190°

9

100°

10 100°

11 100°

2(<frr*')

 1027 

 0020

+ -J009 

+ 0038

 -1035 

- 0012

+ -1U30 

+.0017

 IAQO"

- 0014

+-10J3 

+ 0023

 -1041 

 0006

+ 1023 

+ 0023

 1033 

. --0014

+ 1027 

+ 0020

0 6'

20 

20

20 

20

20 

20

20 

20

~19 

19

19 

19

20 

20

20 

20

21 

21

21 

21

Time.

2

8 

' 18

1 

9

20 

30 

50

2 

12 

19 

27

2 

9 

17 

33 

44~2~ 

8 

27

3 

10 

31 

42

1

12 

25 

38

2 

21 

45

1

8 

32 48-

2 

12 

26 

37 

60

0 "fr'vins

T

 o-oo

 -64 

- 1-02

+ O'l.O 

1-17 

1-77 

2-08 2-58

 o-oo

 '24 

 '37 

 '37

+ o-oo 43 

 71 

 99 

1-15

 '55 

- 1-48

 »- 0 00 

l-0:t 

2-33 2-74

 o-oo

- -92 

- 1-34 

 1-65

+ o-oo

1-74 2'48

- o-oo

- -46 

 -80 

- '89

+ o-oo

1-18 

1-83 

2-17 2-46

No. 

An.

7 100°

8 190°

~~9 

100°

10 100°

11 100°

r 

2(<f>+</>')

 1007 

. 0041

+ 1003 

+ 0044

 1007 

- 0041

+ 0995 

+ 0052

 

 

0 9'

100 

20

100 

20

100 

19

100 

19

100 

19

Time.

1 

3 

8 

19 

33 

40

2 

9 

16

20 

40

3 

11 

20 

32 

55

2 

11 

22 

28 

41

2

5 

8

*-*'xio»

r

 o-oo

 3-88 

 11-10 

 19 47 

 25-02 

 26'95

+ 000 

10-81 

1603 

20 '07 

24-75

 000 

 902 

 14-51 

 18-07 

 23-88

+ O'OO 

17-05 

20-59 

2930 

34-59

 o-oo

 17-50 

 20-9:3

Accident.

 0974 

+ 0073

+ -0!HW 

+ 0078

+.1007 

 -0041

+ 0900 

+ 0081

100 

20

100 

20

100 

20

100 

20

1 

3 

. 7 

16 

19 

21

2 

5 

8 

12 

18 

22 

25 

32 

35 

42

2 

5 

10 

16 

22 

26

3 

5 

16 

23 

31 

37 

45

 o-oo

 20-38 

 32-33 

 50-23 

 62-31 

 65-03

+ o-oo

15-08 

24-41 

33-30 

42-1)6 

48-14 

5V79 

59-43 

61-23 

67-76

 o-oo

 8-56 

 16-18 

 22 06 26-49 

 2903

+ o-oo

5-79 

30-88 

4079 

49-84 

55-57 

62-39

Bull. 73 G
82 THE VISCOSITY OP SOLIDS.

TABLE 55 Continued.

J=30cm. p=0'0405c'°. a = 28.5cra . 0 = SI'S .

[BULL. 73.

No.

An.

12 

25°

13

25°

T

2(0+*')

+ 1007 

+ 0041

 -O'JOa 

 0053

 1007

 0041

+ 1001

+ 0047

- 1019

 0029

e

6'

22 

22

22

22

20

20

20 

20

20

20

2 

.5 

11 

29 

36

2 

13 

20 

25

0

12

22 

30

2 

6 

14

26 

31

41

4 

9 

17

23 

36 

45 

59

^~^'vin»

T

+ o-oo '

2'2rf 

4-24 

688 7-57

 (i-CO | 

 5-11 

 C'32 

- 7-08

 2-43 

 3'63 

 4-74

+ o-oo

2-00 

3-91 !

5'46 

5-94 I

6'6t 1

 O'OO 

 -75 

 1-56

 2-75 

 3-13 

 3'75

No.

An.

14 2u°

17 100°

r

2(0+0')

 1003 

 0014

+ 0969

+ 0057

 10^1

 0026

+ 1019 

+ 0029

+ 1041

+ 0006

 -11)33 

 0014

+ 1038 

+ 0009

e

20 

20

20 

20

20 

20

22

22

22 

22

22 

22

Time.

2 

10 

21 

31 

42

2 

7 

14 

18

23

5

15 

37

o/ 

63 

82

1 

111

2

12

22 

34

1 

15

28 

40

2 

9 

19

27

* "P'vios

T

 o-oo

 399 

 5-95 

 703 

 7-23

+ 000 

2-89 

475 

5^9 6-18

 o-oo

 1 37

 2-PA

 3 -SO 

 4-40

+ 0 00 7-74

- + o-oo

1-04 

1-52 1-89

 o-oo

 1-66 

 2-21 

 2-59

+ O'OO 79 

. 1-32 1-50

85. Mean values deduced. The following Table 56 is interpolated from 

the preceding, and contains mean values of ((p (p'}/r^ as derived from 

the two twists, r, alternately positive and negative. The justification 

of this mode of obtaining data for a chart is given below. Besides 

these data Table 56 contains the number and temper, and the electrical 

constant1 (specific resistance, *0> microhms, cc, 0° 6'.), as well as the 

differences s0 s0' and sm s20', in which the subscripts are the temperatures at which s is taken, and s' is the constant of the normal rod, JSo. 1. 

Hence these electrical differences correspond to (<p (p'J/r, when #=0° 

C. and when #=100° 0., respectively. For No. 1, V=18-6, s0 -V=0 

and (cp (p')/t=0. The values (<p <p'}/r are in the same horizontal 

row with the temperatures, 6, to which they belong. It is not necessary 

to distinguish s0 s'0 and s20 s'2o, "here.

1 For definition of thermo-electric hardness, cf Bull. TL S. Geol. Survey, No. 14, p. 65.
BAKU8.] VISCOSITY OF PLATINUM ALLOYS. 83

TABLE 56. Values of <P <P X103 for consecutive times.

Temper.

Annealed at 4 50° J

Annealed at 360° <

I

f

|

[

No.

S0 -

2 

19-4 

3 19-2

4 

19-0 

5

201

6

28-8

7

30-9

8

31'3

!) 37'2

1034'2

1133-5

1239-2

1337-0

.14 40-0

S0 80' 

8100 s'ao-

 8 

5-9

 o

5-6

 4 

5-5 

1-5

0-5

10-2

15-8

12'3

17-7

12-7

17-8

18-6

24-2

15'C

21'0

14-9 20-5

20-8

18-4

22-1

6.

20 

100 

20 

100

22 

100 

23

100

19

100

20

100

20

100

19

100

20

100

21 

100

20

20

20

2 .

 00 

+ 00 

 00 

+ 00

+ 00 00 

 00

 00

 00

 00

 00

 00

 00

 00

 00

 oo

 00

 oo

 00 

 00

 00

 oo

 00

5m.

 03 

+ 50 

 00 

+1-15

+ 14 

 1-58 

 08

1-12

 06

2-99

 40

5-10

 14

6-1.2 30

17-48 43

13-94

 32 

8-84

2-41

1-15

2-14

10m.

 05 

+1-12 

 12 

+1-97

+ 34 

3-20 17

1-97

 12

7'48

 88

11-08 34

12-92 68

32-98 80

27-88 69 

19-38 4-24

2-27

4-00

20'".

 07 

+ 1-88 

 19 

+3'05

+ 57 

4-79 26

3-13

 16

12-72 1-31

1802 57

20-54 1-20

1-38

47-20

1-08 

32-04 6-09

3-55

5-80

30 .

- 08 

+ 2-47 

- 23 

+3-91

+ 69 

5-92 30

4-00

 16

15-84

21-90 68

24-96 1-56

1-71

1-31

41-82 7-42

4-38

7-00

40'".

- 10 

+2-90 '26

+ 75 6-66

17-95

24-82

28-08

1-96

1-48

7-91

50'".

 10 

+3-29 28

+ 81 7-34

1-01

86. Data of the measurements with platinum alloys. Before proceeding 

to a discussion of these results, I will insert the following set of similar 

data which I found with alloys of platinum. The normals here are 

wires of pure platinum, and with these the alloys are to be compared. 

The plan of comparison and tabulation is the same as explained for 

steel except that in the present case the temperature, 100°, is made to 

act on the upper wire without untwisting. The experiment at 100° 

therefore joins on to the experiment at ordinary temperature in such a 

way that no adjustment of apparatus is made, further than the change 

of temperature specified.

The wires w, n1 and A are of commercial platinum, purified by long 

continued fusion on a lime hearth before the oxyhydrogen flame. The 

other compositions are given. In all cases S0 is the specific resistance, 

a the temperature coefficient of the alloy.

As before, like signs of T and <p <p' show that the lower wire (pure 

platinum, normal) is of greater viscosity.
84 THE VISCOSITY OF SOLIDS. 

TABLE 57. VISCOSITY OF PLATINUM ALLOYS.

C jt _on.Ocm )

Fixed Normal, n', j /~ "5.0215 J0 = 25°.

[BULL. 73.

No. of wire: 

1, P.

J 06.2cm .......

p 0.0215 ...

^

j 26-0 .....

p 0-0215cm ...

1. .............

Z 26-1 ......

p 0-0215 ...

2.............. I 26-lc"'......

**

1 2G'Ocm

4..............

I 26-1 ......

p 0-0215 ...

**

7 OVQcm

p. 0-0217 ...

Alloy.

Ft............

Pt.... ........

Pt.Ag.......

Pt.Ag........

>%

aX103

13-3

2-50

12-0

2-90

18-5

1'84

22-1

1-49

24-7

1 *33

19-1

1-87

1-5

(</>+</>)

0-0829

 0-0378

 0-0748

i

0-0043

 0-0805

o-onos

0-0303

 0-0547

 0-0660

 0-0923

0-0285

6'

25

100

25

100

25

100

25

100

OK

100

24

100

25

100

Time.

0

2

14

34

54 

68 

73 

85 

91 

107 

120

0

2

17

29 

50 

75 

80 

102 

119 

129

0

19

34,

47 

54 

69 

91 

104

0

16

39 

55 

65 

75 

80

0

6

21 

45 

67 

63 

74 

85 

117

0

19

22 

36 

56 

60 

70

0

6

15 

30 

42 

48 

55 

60 

75 

81

<fc <f>' 

 ^XIO3

T

+ -oo 2-26

3-54

4-16 

 3-54 

 4-24 

 4-86 

 5-13 

 5-49 

 5-71

o-oo

+3-97

+5-00 

+5-98 

+6-71 

+5-20 

+5-29 

+5-49 

 iS-78

 00

 -26

 -54 

 '54 

 5-21 

 5-46 

 5-60 

 5-73

 00

 QO

 -69

- '82

 -oo

 1-18 

 1-55

+ -00

+2-43

rt-5'67

+7 '87 

+8-56 

+2-19 

+2-55 

+2-63 

+2-75

 00

1-06

 1-49 

 1-86 

 2-17

 -oo

 7-38

 -00

,2'30

 4-85 

 7-11 

 8-07 

 8-56 

 2-75 

 3-02 

 3-20 

-3-24

** Scale readjusted.
BARtTS.] VISCOSITY OF PLATINUM ALLOYS. 

TABLE 57. VISCOSITY OF PLATINUM ALLOYS Continued.

Fixed Normal,»', { * = ^j^. } fl = 25°.

85

No. of wire: 

I, PC. .............

J 25-3c»> .....

p 0-0220cra ...

7..............

7 9fVdcm

p-0-021Ccn'...

**

8.............. Z--26-4""......

. _ ft-flOl r»cin

71.

*

I 2G-2<"»......

p 0-0215CU> ...

n.

t. ..........

thoroughly 

red hot.

th oroughly 

red hot.

After heating

thoroughly 

red hot.

thoroughly 

red hot. 

1 26-3 .....

p 0-0212cm ...

Alloy.

Pt A IT

Pt.Pd. .......

20-4. ..........

Pt. ...........

Pt...... ......

l> .............

Pt...... ......

Pt ............

d .............

Pt. ...........

Pt. ...........

/..............

00

aXlO3

34'0

. i-o

19-4

1-70

1-67

..........

(*+*)

-0-1003

-0-04G8

 0-0796

 0-0413

-00867

 0-0344

 0-0052

 0-0443

 0-07C6

 0 0383

 0 0826

 0 0390

 0-0813

6'

25

100

25

100

25

100

25

25

22

22

22

22

Time.

0

1

C

30 

42 

52 

59 

64 

75 

80 

100 

100

2

23

38 

47 

54 

59 

74 

87 

105 

119

0

1

6

21 

30 

41 

52 

C2 

79 

84

0

2

9

15

27 

33

0

17

44

0

1

4

14

28 

44

0

17 

25 

43 

64

0

3

7

26 

47 

55

0

3

8

13

90

37

46

</> </>' 

v - V-X103

T

' + -oo

+ 3-G8

+G-68 

+7-18 

+7-H8 

+08 

 1-04 

 2-i3 

 299 

 401 

-4-20

 -oo

- 8-07

 14-01 

 14-90 

 15 40

- -oo

- 2-47 

 427 

- 4.87 

- 5-27

 -00

- 1.84

 3-18 

 3.51 

 3-83 

 15-U2 

 16-15 

 16-70 

 J6-70

 -oo

O.OO

 3-90 

 4-06

O./lo

 3-38

+ -oo

+ 14-21

+32-29 

+42-71 

+4R-61

 nil

1K.no

-28-57 

 34-64 

 42-37 

 45-40

+ -oo

+ 3-84

+13-52 

+ 19-18 

+20-70

 -oo

7. to

-12-07 

20-] 5

-22-77

 25-39

* "Without anueaiing. t After careful annealing (both wires) at rod heat. ** Scale readjusted.
86 THE VISCOSITY OF SOLIDS. [tuu,. 73. 

DEDUCTIONS PROM PLATINUM ALLOYS.

87. Viscous effect of alloying. The results just communicated for 

platinum alloys were made first in chronological order, and led to the 

results already communicated for steel. It will therefore be in place to 

discuss the purposes of the alloy work and the difficulties encountered in 

endeavoring to arrive at intelligible results. In Chapter II I inferred 

from certain results obtained by Dr. Schroeder and by myself independently that wires of small viscosity were proportionately more susceptible to the influence of temperature. It is this proposition which the alloy 

work was primarily intended to elucidate. Moreover the resistances and 

temperature coefficients of the alloys were known from earlier investigations,1 in which the same alloys had been operated upon. Hence I 

hoped also to see whether any relation between viscosity and electrical 

resistance would be discernible, a result which in a general way obtains 

for tempered steel. In other words, if the temperature coefficient of 

viscous deformation should hold similar generic relations to the amount 

of deformation that the temperature coefficient of electrical conductivity holds to conductivity, then an investigation like the present 

might reasonably be expected to lead to results bearing directly on the 

mechanism of electrical resistance. This is the chief point of view from 

which the work is undertaken.

The normal wires .IV and N' were originally identical. After heating 

both to redness, however, I was surprised to find that the large difference registered at the beginning of Table 57 obtained. The upper 

wire is more viscous than the lower at 25°, but decidedly less viscous 

than the lower when 100° is applied to the upper wire, the temperature 

of the lower as in all these experiments being fixed. Yet these results are not sustained by the platinum wire A.

The gold alloys form a series in. which mean viscosity tends to increase 

with electrical resistance; but the behavior in the divers cases is obscure. Again, the silver alloys form a series in which the increase of 

viscosity with resistance is very decidedly marked. Moreover, the effect 

of temperature to accelerate viscous deformatian decreases as the viscosity decreases.

Finally these deductions hold for the two palladium alloys.

88. These results are encouraging, notwithstanding the element of 

vagueness which it is almost impossible to eliminate. The general result is in favor of high electrical conductivity associated with small 

viscosity and small temperature coefficients. Platinum itself, however, 

is a marked exception to this observation. Hence to determine the 

amount of variation of the normals, as well as to enter more closely into 

the nature of the discrepancy, I made the investigation comprehended in 

the second part of Table 57. The results obtained show, in the first 

place, that in consequence of the twisting incident to the examinations

i Bulletin U. S. Geol. Survey, "NTo. 54,1889, p. 143.
BARU6.1 ACCOMMODATION IN STEEL. 87

of the wires Nos. 1 to 8, the lower wire has gained in viscosity sufficiently 

to exceed the upper (unused) wire in this respect. This relation is maintained even after both wires are similarly annealed. I then made the 

experiment of annealing only one of these wires in the way the table indicates. The results are striking. It appears that in every case the freshly 

annealed wire is enormously less viscous than the unannealed wire; 

and that this difference of viscosity produced by these mere mechanical 

means is so large as would wholly mask and obscure the effects of alloying investigated in the earlier part of Table 57. Having thus found 

how large an error in the observed viscosity may be introduced by even 

trifling differences of mechanical treatment, I concluded that an investigation into the true effect of alloying would necessarily be of an exceedingly refined character, and would therefore not fall properly within 

the scope of the present bulletin. Further attempts to study the viscosity of alloys were therefore for the present abandoned.

Whatever may be the effect of alloying on viscosity, it is clear that 

the enormous electrical effect produced by alloying platinum (resistance 

increased) and the relatively small electrical effect produced by imparting a strain are quite out of proportion and symmetry with the corresponding viscous effects in the two cases. Again, the effect of temperature in changing viscosity is much too marked to conform with the 

resistance effect of temperature. These results appear more clearly in 

the data for steel.

89. Effect of annealing and hardening platinum. In this place, however, the effect of annealing at red heat is of special interest. The two 

wires N and N' being chemically identical, the effect of annealing on 

the molecular configuration must be the same in each case. If a thin 

wire be heated red hot and cooled in air, tlfe result is a strain of dilatation imparted to the wire on cooling. Hence, for this reason alone, 

the molecular stability of the wire is of a lower order than obtains, 

cseteris paribus, when cooling takes place with extreme slowness. 

This is the case of the freshly annealed wire. Again, it is probable, if 

such a wire is twisted, even over small arcs, that the greater number 

of the more unstable configurations will be mechanically broken up; 

for it is clear that the prevailing tendency must be such as to cause the 

unstable configurations continually to fall to positions of minimum potential energy. If twisting be indefinitely repeated, therefore, the 

result is very perceptible hardness and elasticity. It is not necessary 

to recite here the many experiments I made to elucidate these questions. I will confine myself to a statement of results.

In the first place, when two wires as nearly as possible identical 

(chemically and physically) are compared, the question arises in how 

far viscosity may vary with the time which elapses after annealing. 

The experiments made showed a slight increase of viscosity with the 

time given to. the molecules to subside after annealing in air. Two 

identical wires of platinum were annealed, for instance, and then al-
88 THE VISCOSITY OF SOLIDS. (BULL. 73.

lowed to rest for several hours; after which only one of the wires was 

again annealed, and the two were at once compared after cooling. This 

and similar tests indicated small decrease of viscosity of the freshly 

annealed wire; results, however, by no means comparable with the data 

of the above table and often obscure.1

The sign of the twist of the wires JT, N', of pure platinum, compared 

in the table is the same throughout. The question therefore arises in 

how far an earlier stage of viscous subsidence simply overtakes a later 

stage. To determine this it is sufficient to reverse the sign of the twist 

alternately without fresh annealing; or to reverse it with each of the 

alternate annealings of the upper and lower wire. Experiments made 

in some number showed that even in this case the results of the second 

part of Table 57 hold good, the diminution produced being in degree, 

not in sign. The viscous deformation of freshly annealed wire takes 

place at a decidedly greater rate even when the viscous motion of the 

other wire is intensified by an impressed latent strain.

SUMMARY.

All these results are such as follow at once from Maxwell's theory. 

They show that the effect of twisting is to be referred to the motion of 

molecules which accompanies it. The molecules, together with their 

component atoms, are thus placed in new relative positions; therefore 

unstable configurations during the course of such motion are continually broken up into configurations of smaller potential energy and 

greater stability. Hence, finally, the observed decrease of viscosity. 

By reversing the sign of the twist the original configurations can be 

only partially restored, even for small permanent set, such as is here in 

question; and the effect of prolonged and repeated twisting is stiffness 

and constant viscosity, because all the molecules have collapsed into

configurations of minimum stability, and the intrinsic molecular energy 

is the potential minimum compatible with the given conditions.

DEDUCTIONS FOR STEEL. 

"ACCOMMODATION" IN GLASS-HARD STEEL.

01. Tlie phenomena proper. Steel wires were used in our earlier work,2 

free from torsion strain. The hard steel wires of the present paper, employed in other researches, may contain twists stored up like residual 

magnetism. This produces a kind of unilateral symmetry, so far as 

torsions are concerned; but it is not otherwise objectionable. In critical cases wires free from latent torsion are selected.

1 The thermal effect without annealing is ?o nearly negligible as to prove that in Dr. Schroeder's 

 work (Wied. Ann., vol. 28,1886, p. 309) the observed result is to be ascribed to annealing of hard-drawn 

wire. Regarding my own work I may say that I am not sure that both wires were kept quite free 

from tensile stress, the importance of which I did not at the time fully appreciate. In a later research 

I made a detailed study of the viscous effects of traction and other mechanical stress. (Of. Phil. Mag. 

Feb., 1889, p, 155.)

*Barus and Strouhal: Am. Jour. Sci., (HI), 886, vol. 32, Ip. 448; 1887, vol. 34, p. 4.
BAKU8.1 ACCOMMODATION IN STEEL. 89

Turning to Table 55, the individual wires are found to show wide differences of viscous behavior. In No. 2 the viscous subsidence takes 

place at nearly the same rate for T and for + T, both at 0=20° and 

at #=100°. In No. 3 the effect of r and -fr is of different magnitude 

at 20°, and enormously different at 100°. In No. 4 the effect of +T 

following r is even more phenomenally pronounced at 20° and particularly at 100°. In No. 5 the wires nearly identical at 20° show 

differences at 100°. In No. 6 this is true in even much greater degree, 

whereas in No. 7 wires differing considerably at 20° show relatively 

small differences at 100°. And so I might go through the series. Nos. 

13 and 14 are wires originally free from strain (shear) j but vagueness 

also appears in these.

Careful inspection of the tables reveals the law that viscous deformation takes place at numerically greater rates during the even twists 

than during the odd twists which immediately precede them respectively. Aside from these oscillations, the effect of twisting here (§ 90) 

is again pronounced increase of viscosity.

Maxwell's theory accounts for the stated vagueness of behavior at 

once. In two samples of a complex substance like steel the distributions and relations of the unstable molecular configurations will only in 

very rare instances be physically and chemically identical. The foregoing paragraph shows that such identity is rare even in pure homogeae'ous metal. (§ 94.)

The effect of twisting alternately in opposite directions is of so great 

importance in its bearing on Maxwell's theory that I made further 

special experiments. From these I select the following example, tabulating it as in case of Table 55. The normal No. 1, annealed at 450°, 

has been described. No. 18, annealed at 25°, or glass-hard, is carefully 

selected free from latent torsion, having experienced no other strain 

prior to the examination in Table 58 than that incident to tempering 

(quenching). There are twelve alternations of twist, indicated by subscripts, and the current time.in hours and minutes of each is given. I 

also give under m the time in minutes which refers specially to the 

.duration of each twist. No. 1 being of greater viscosity, r and (<p (p')/r 

are alike in sign, by agreement.

 Experiments made by counter-twisting two glass-hard wires gave results like this, but on a smaller scale. To compare the results of Table 

58 perspicuously it is sufficient to construct the differences, d((p <p')/T, 

of the respective value of ((p-±-(p')/T, at two and four minutes after 

twist is imparted. These are then to be compared in their dependence 

on current time, as has been done in Fig. 24. Phenomena of this kind 

were called "accommodation" by Streintz, 1 their discoverer, by Wiedemann,2 Kohlrausch,3 and others. The fact that Boltzmann's law contains them is among its chief excellencies.

1 Streintz: PogR. Ann., 1874, vol. 153, p. 400.

* Wiedemann: Wied. Ann., 1879, vol. 0, p. 512. This work is tlio most comprehensive of the relevant 

researches. 

8 Kohlrausch: Pogg. Ann., 1876, vol. 158, p. 371. Cf. Schmidt: Wied. Ann., vol. 2,1877, p. 48.
90 THE VISCOSITY OF SOLIDS.

TABLK 58. Viscous effects of twisting glass-hard steel alternately in opposite directions. 

Normal wire No. 1; I=30 p = -040'5cm.

Remarks.

No. 18, 

Annealed at 250.

No. 18j.......

No. 18,...-...

No. 184 .......

No. 18S .......

No. 18«. ......

No. 187.......

r

 102

+ 102

 102

+ 102

- 102

+ 102

. --102

Time.

9" l:»» 

15 

17 

28 

35

9h 37,,, 

39 

41 

52 

60

10" 2m 

4 

8 

19 

25

10h 28m 

30 

36 

41 

48

10" 50m 

52 

59 

70 ii" ilia

15 

25 

S3

11" 35'" 

37 

39 

56 

57

TO

0 

2 

4 

15

22

0 

2 

4 

15 

23

0 

2 

6 

17 

23

0 

2 

8 

13 

20

0 

2

7 

20

0 

2 

4 

14 

2i

0 

2 

4 

21 

22

*-*'xl03

T

 -00 

 1-31 

 4-07 

-5-04

+ -oo

1-59 

5-17 6-45

- -oo

 1-45 

 3'28 

 3-93

"+" 00 

2-04 

3-04 

3.86

 00 

-1-59 

 2 '73

+ -00 76 

2-59 3-42

" " 00 

 -52

 2-38 

 2-45

Remarks.

No. 18g .......

No. 18........

No. 18, 0 ......

No. 18a ......

No. 1812 ......

No. 1813 ......

No. 18,4 ......

No. 1816 ......

T

+ -J02

 102

+ 102

- 102

+ 102

Alter se 

- 102

+ 102

 102

Time.

12" Om 

2 

4 

20

I2b 24'" 

26 

28 

40

12" 42m 

44 

46 

54 

63

1" 5"' 

7 

9 

21

1" 23m 

25 

27 

36

veral days 

9 b 47 

40 

51 

60

IQh 2'"

4 

6 

15

10h 17"' 

19 

21 

30

m

0 

2 

4 

20

0 

2 

4 

16

0 

2 

4 

12 

21

0 

2 

4 

16

0 

2 

4 

13

. 

0 

2 

4 

13 

0 

2 

4 

13

</> <£' V1()C

T

+ -00 59 

2-62

 -00 

 -41

 2-38

+ -oo 55 

1-70 2-55

 -00

 '45 

 1-76

 00 

 48 

1-09

 00

 -62 

-2-07

+ '00 09 

442

0 ......

2 -00 

4 -02 

13 2-21

TABLE 59. Viscous accommodation of glass-hard steel. Digest of Table 58.

Twist 

No.

1 ......

2 ......

3 ......

4 ......

Time.

flm

24

49

75

A *~*' X 10'

T

 1-31

+ 1-59

- '83

+ -97

Twist 

No.

6......

6 ......

7 ......

8 ......

Timf.

97 

118

142

167

A *-*' X 10'

T

 -69

+ '76

- -52

+ -59

Twist 

No.

9 .....

10....

11 .....

12 .....

Time.

191m

209

23:!

250

A 0~*'X103

T

 -41

+ -53

 -45

+ '48

If the numerics of A ((p (p')/r in Table 59 be regarded in their dependence on time, the results are seen to oscillate around a mean line of 

equilibrium. The ordiuates of this mean line decrease with time at a 

gradually retarded rate, until a definite inferior limit is eventually 

reached. This is very clearly shown by the diagram, Fig. 24. It is 

curious to note that the largest observed ordiuate (time = 0, nearly), is at 

least three times the limiting ordinate (time = so). After 12 twists oscillation has considerably subsided, but it has not ceased j in the same 

degree the viscosity of the glass-hard rod has reached a fixed maximum.

This complicated phenonomen is at once elucidated by Maxwell's 

theory. The ordinates of the line around which oscillation takes place, 

are an index of the degree of instability of molecular configuration, at 

the time given by the abscissae. The oscillations are the result of strain
fiAKUS.l ACCOMMODATION IN HARD STEEL. 91

(latent shear, I may call it) imparted to the configurations by the successive twists to which the wire is subjected. Thus if t be the impressed twist, and Ar the mean strain left in the configurations at the

IS

1.0

.5

.0

2

/'\

\

'" \

\

* \

X \

P ' 

-v^

1

^

5

^.-^

.>''''

i

\

Ttr

O"1' H

6 -"X

\2-

i&.

k/TZi ii

.---Ifx

V

e

»

^ ff -Tz

Q»t

FIG. 24. Viscous accommodation of glass-hard steel.

instant when r is removed; and if n be the original relative number of 

unstable configurations, and An the number broken up during the period 

of the strain T; then (apart from subsidiary considerations) Maxwell's 

theory analyzes the effects of alternate twisting in accordance with the 

following scheme:

Strain.

First twist.... T 

Second twist.. -f- T + AT 

Tbirdtwist ... T-\-A\r A1 r 

Fourth twist.. +r + J.2 r A\ r-{- A" T 

Fifth twist.... T + J3 r J'a T + J", T A"

Molecular instability.

-f- n A n

-{-« A in An

-\-n A3 n A'\ n A"' n

The variation which A undergoes in passing from one twist to the 

next is indicated by subscripts. Thus Ar, A\t, z/2 r,.... is probably 

a decreasing series; whereas An, A^Atfi, .... is an increasing series 

because reversal of the sign of the twist must be supposed to reconstruct some of the configurations broken up by the preceding twist. 

The first part of the scheme indicates that the strain in the 2d, 4th, 6th 

.. . twists is necessarily greater than the strain in the immediately preceding 1st, 3d, 5th ... twists respectively, at least at the outset of the 

experiments. Hence the observed oscillation. Again, the number of 

unstable configurations must continually decrease, according to the 

second half of the scheme. Hence the mean line about which the observed viscous deformations oscillate. Finally, experiment shows that
92 THE VISCOSITY OF SOLIDS. [BULL. ?a

the accelerating effect of AT on viscous deformation is greater than 

the retarding effect of An. After this, however, the accelerating 

effect of A^t A\r -\-A"r, and the succeeding r-quautitles, is always 

less than the retarding effect of A^n A\ n A"n, and the succeeding 

%-quantities, respectively.

The scheme admits of simplification; but inasmuch as the period of 

oscillation is arbitrary, the phenomenon remains indefinitely complex.

92. Motional effects estimated. The second part of Table 58 shows 

that the viscosity gained in virtue of consecutive alternate twisting of 

glass-hard steel is permanently gained. The results indicate some recuperation; but the amount is small in comparison with the havoc of 

configurations made by twisting. Mere molecular motion has therefore 

permanently broken the more unstable configurations. I will note that 

the viscous effect of prolonged twisting to and fro in case of glass-hard 

steel, is of the same order of magnitude as the effect of prolonged annealing at 100°. This indicates the importance of the motional effect 

in question.

If, following the analogy of steel, I consider annealing a process by 

which unstable configurations are broken up, I may designate the phenomenon here in question as motional annealing. Experiments for 

which there is no room here showed that motional annealing is relatively without electrical effect. For increasing rates of twist thick 

wires show viscous deformation sooner than thin wires. Hence motional break up commences at the external surface where stress is most 

intense, and proceeds thence toward the axis where stress is least. 

Thus there appears an essential dependence on the dimensions of the 

twisted rod. Elsewhere1 1 pointed out that the limits of torsional resilience of soft iron are reached when the obliquity of the external fiber 

(shear) somewhat exceeds -003 radians. Begarding the laws of motional annealing, cf. § 101. It follows from the absence of electrical 

effect, that motional annealing probably presents a pure case of Maxwell's "break up" of configurations of molecules.

93. "Accommodation" and hysteresis. Streintz and Wiedemanii's 

phenomenon "accommodation" admits of representation from a different point of view. Eeturning to the data of Tables 58 and 59, suppose 

the experiment so conducted that the twelve twists are immediately 

consecutive. Suppose, furthermores that time, m, instead of being reckoned positively onward from the beginning of each of the said twists, 

were reckoned alternately positive and negative, conformably with the 

sign of the deformations (<p <p'}/T. In this oscillatory march (time as 

abscissa), since each deformation (ordinate) now begins where the preceding deformation ceased, a continuous series of open cycles is necessarily generated. The positions of these cycles shift at a gradually 

retarded rate, toward a final very flat cycle, which for the constant 

values of time and stress-is fixed in position and closed.

1 Am. Jour. Sci. (TIT), 1887, vol. 34, p. 183.
BABUB.] VISCOSITY AND ELECTEICS OF STEEL. 93

Cycles here, fixed or not, are expressions of the fact that the "past 

histories" (in Maxwell's words) of the molecular configurations in the 

"stress positive" and "stress negative" phase of each cycle are not 

the same. Shifting is brought about by permanent molecular break up, 

the amount of which gradually vanishes. In the ultimate and fixed 

cycle as many configurations are broken during the "stress positive" 

as are reconstructed in the " stress negative" phase, though they need 

not be the same configurations.

These considerations suggest a comparison between "accommodation" and Prof. E wing's 1 " hysteresis," for the purpose of detecting the 

extent to which like causes are discernible in each phenomenon. Both 

exhibit a static character. But such comparison would not be fruitful 

without special and direct experiments; for the instantaneous values of 

stress and of viscosity must be coordinated.

94. Viscous and electrical behavior compared. Having thus discussed 

one phase of the results in Table 55,1 pass to Table 56, which is a 

digest of the mean values of Table 55, in so far as such a digest can be 

made. Following the scheme at the end of the preceding paragraph, 

this comparison should be made after an infinite number of twists have 

been imparted to each wire. In such a case, however, the original 

number of unstable configurations has been seriously reduced; so that 

apart from the annoyance of so time consuming a method as this, the 

original properties of the wire are not clearly present in the results. 

In wires perfectly free from strain, at the outset, the first twist leads 

to the best indications of the viscous quality. As this condition could 

not always be guaranteed for the wires of this chapter, I have accepted 

the mean viscous behavior during the first and second twists as the 

best available index for comparison. It is sufficient, at least for the 

present purposes. Again taking the mean for rods of the same nominal 

temper, I obtain data from which a chart is easily constructed, by representing mean viscous deformation ((p cp^/r^ varying with time, for 

each of the divers degrees of hardness annealed at 25°, 100°, 190°, 360°, 

450°, respectively. It so happens that the normal rod, No. 1, is less 

viscous than the other rods, No. 2 and No. 3, of like temper. Hence 

the negative numbers in Table 56, which may be eliminated by increasing the other data.

Keturning to Table 56, it is clear, inasmuch as viscous deformations 

are measured differentially, that ((p cp'}r and s0 s'0 are to be compared. It appears that these quantities increase and decrease together. 

This is more easily discernible when rods free from strain are compared.2 The exceptions of Table 56 are due to the fact that the latent 

strains influence ((p cp')/? to a relatively much greater extent than 

SO S'Q. Again, if sm s'2o and (<p cp')/r be compared at 100°, Table 56 

shows that in this case also the* two quantities increase and decrease

1 E\vin«: Pbil. Trans. Roy. Soc., II, 1885, p. 523; ibid., II, 1886, p. 361. Prof. Swing's earlier papers 

arc there given. Cf. also Colin : Wied. Ann., 1879, vol. 6, p. 403.

2 Barns and Strouhal: Am. Jour. Sci. (HI), 1887, vol. 33, pp. 26,27.
94 THE VISCOSITY OF SOLIDS. [COLL. 73.

together. Indeed, the data for 100° are the more uniform, a result due 

to the fact that at 100° much of the latent torsion is made to vanish 

because of the annealing effect of 100°. Data of even greater uniformity, cseteris paribus, are to be looked for at higher temperatures. 1

When a comparison is made between the mean rates at which viscous 

deformation and resistance increase together with temper, at 20° 

((<p (p'}/T and s0 «'o)» and at 100° (((p q>'}/T and sm s'20 ), it is seen 

that the mean rate of increase of ((p (p')/r relatively to s s' is about 

ten times as great at 100° as at 20°. This is the phenomenon in virtue 

of which the viscous behavior of steel, regarded as a test of Maxwell's 

theory, is almost crucially important. I will endeavor to explain it.

95. Viscosity at mean atmospheric temperature. Dr. Strouhal and I 

denned the glass-hard state of steel 2 as the stage of temper which undergoes incipient annealing at mean atmospheric temperature. Inasmuch 

therefore as annealing is demonstrably accompanied by chemical 

decomposition3 even at temperatures slightly above mean atmospheric, 

the molecular configuration of glass-hard steel is always in a state of 

incipient change.4 A part, though not the whole, of this change must 

be of a permanent kind; and I wish to keepjn mind that at the temperature of incipient annealing the heat motion is such that broken 

configurations are sometimes reconstructed.

Inasmuch therefore as glass-hard steel contains more unstable configuration^ than any other state of temper, at the same temperature, it 

follows from Maxwell's theory that glass-hard steel, despite extreme 

hardness, must be the least viscous member of the whole group of 

tempered and soft steels. This strikingly anomalous prediction of the 

theory is verified both by the results of Table 56, as well as in earlier 

work 5 in a way so pronounced as to be irrefragable.

If glass-hard steel is annealed at 100°, the greater number of the unstable configurations are broken up in virtue of the increased molecular 

vibration at the higher temperature. The cold rod, alter annealing, 

will show increased viscosity in proportion as the number of unstable 

configurations has decreased. Experiment proves this in a strikingly 

conclusive wa'y: the increase of viscosity thus produced is marked, 

being nearly half the difference between the soft and hard states of 

steel. This, too, is an observation favorable to Maxwell's theory; for

1 Max well's words are (loc. cit.); " . but if, on account of rise of temperature . . . the breaking up 

of the less stable groups is facilitated, the more stable groups may again assert their sway, and tend 

to restore the body to the shape it had before deformation."

2 Wied. Ann., vol. 11,1880, pp. 962,963.

8 Barus and Stroahal: Am. Jour. Sei., (Ill), 1886, p. 276.

* During the last three years I have been making experiments on the secular annealing of cold bard 

steel. The results are very striking, and show that mean atmospheric temperature acting on freshly 

quenched steel for a period of years produces a diminution of hardness nearly equal to that of 100° C. 

acting for a period of hours. '.I examined some twenty rods, the specific resistance of which, within 

thirty-seven months, has fallen from 46 -5 to 42'5, in the case of thin rods (diameter <0'08cm), and from 

43-7 to 35-4 in the case of thicker rods (diameter O f 13cm). Freshly quenched pieces showed resistances 

as high as 50, nearly.

 Barua and Strouhal: Am.Jour.Sci. (Ill), 1887, vol. 23, pp. 25,26.
MAXWELL'S THEORY APPLIED. 95

if there be configurations with an inherent tendency to collapse at ordinary temperatures, but a small fraction of them will survive at 100°. 

Moreover the configurations broken up cannot be reconstructed without 

expenditure of fresh energy (quenching). Since no such energy is ordinarily available, the viscous properties of the annealed rod are of a 

permanent kind.

Again, if glass-hard steel (or steel annealed at 100°) be softened by 

annealing at 200°, a greater number of. unstable groups will be broken 

up than in the foregoing case. The viscosity of the cold rod must 

therefore be considerably greater than that of the hard rod. Experiment proves the viscous increase to be about two-thirds of the whole 

viscous difference between hard and soft steel. Chemical analysis 

gives evidence of the occurrence of decomposition j and inasmuch as 

the unstable groups are permanently broken, the annealed rod shows

determinate viscous properties.

If glass-hard steel be annealed at 300°, 400°, 500°, etc., effects of the 

same nature as those just discussed, but differing from them in the degree of thorough removal of the unstable configurations, will result.

The phenomenon as a whole must be considered continuous, both as 

regards temperature and time. In proportion as temperature is higher, 

however, Maxwell's theory predicts that the effects of the same increment of the temperature of annealing, will produce increments of viscosity successively diminishing at a very rapid rate. Supposing molecular configurations originally present in all states of stability, it 

follows at once that the groups which retain this quality after annealing must very soon vanish when the temperature of annealing is increased. The data prove this in a convincing way: Bods annealed at 

300°, 400°, 500°,.... 1000°, show about the same viscous behavior 

(relatively speaking), notwithstanding the fact that chemical analysis 

proves that the decomposition incident to the successive application of 

these temperatures on glass-hard steel continues steadily to increase. 1 

Indeed, chemical decomposition above 300° is more marked than below 

300° 5 yet its bearing on Maxwell's theory is now without interest, because in none of the high annealed rods do configurations unstable at 

mean atrnosperic temperature survive after annealing.

96. Viscosity at 100°. Having analyzed the phenomena at mean atmospheric temperature, I come next to consider the conditions of mean 

relative viscosity at 100°. The glass-hard state must here be withdrawn for consideration in § 98 j because such a rod would undergo 

annealing during the viscous measurements at 100°.

Hard steel annealed at 100° bears the same relations to 100° that 

glass-hard steel does to mean atmospheric temperature. Hence the 

reasoning of the preceding paragraph, mutatis mutandis, applies at 

once. It is merely necessary to bear in mind that 100° is now the temperature of incipient annealing, and that therefore the temperatures

"Am. Jour. Sci., 1886, vol. 32, pp. 277,282.
96 THE VISCOSITY OF SOLIDS. BULL. 73.

which produce corresponding viscous effects are proportionately higher. 

Rods annealed at 200° now occupy about the same relative position that 

rods annealed at 100° did in § 95; rods annealed at 300° the same relative position as rods annealed at 200°, etc. Moreover, for equal increments of the temperature of annealing, the increment of viscosity shown 

by the rod at 100° diminishes rapidly as temperature increases, etc.

In one respect the present results differ from the above: the phenomena are here spread out over a scale (roughly estimated) about ten 

times as large. This means, following Maxwell's theory, that at 100° 

the number of unstable molecular configurations is relatively much 

larger than at mean atmospheric temperature. The reasons, though 

not far to seek, are exceedingly significant. In hard steel, at 100° two 

causes of molecular instability produce superposed effects. The first is 

the chemical or carbon instability already discussed; the second cause 

is purely thermal. Of. § 102.

The explanation of the diagram for 100° is now clear. Viscous deformation is marked in all the rods examined from annealed at 500° to 

annealed at 100°; but the deformability increases at a rapid pace in 

proportion as we pass from softer to harder steel, because in such a 

march the carburation instability, superimposed upon the thermal instability, increases rapidly. Molecular configurations on the verge of 

instability are encountered in continually increasing numbers.

97. Viscosity at higher temperatures. The line of argument followed 

out for 100° applies, mutatis mutandis, at 200°. Results of this kind I 

published elsewhere.1 The character of the evidence bearing on all the 

points in question is here even more pronounced and conclusive. Steel 

annealed at 200° is in a state of incipient annealing at 200°. Thermal 

and carburation instabilities of high degree being superposed, the

effects are correspondingly large,

Finally above 300° the molecular instability is largely thermal. The 

behavior of hard steel therefore approaches that of other metals more 

nearly.2 The effect of the carburation instability ceases to predominate, 

and finally vanishes altogether in proportion as the march is made from 

lower to higher temperatures of annealing.

98. Annealing and viscous deformations superposed. I have finally to 

touch upon the series of phenomena in which pronounced annealing 

occurs simultaneously with pronounced external viscous deformation. 

If, for instance, a glass-hard rod is twisted and then suddenly heated to 

100°, the rod is both annealed and suffers deformation in virtue of the 

applied twist at the given temperature. Conformably with the excessively greater amount of molecular instability which characterizes 

these experiments, the observed viscous deformation must be proportionately large. This prediction of Maxwell's theory is fully verified 

by experiment. In the case of the twisted rod postulatpd the motion

» Am. Jour. Sci.: (III), 1887, vol. 34, pp. 14-16, 

* Cf-, Chapter I.
BAUDS.] MAXWELL'S THEORY APPLIED. 97

of the image across the field of the telescope is so rapid that Gauss's 

method of angular measurement is no longer satisfactorily available. 

I may say without exaggeration that during the small interval of time 

within which appreciable annealing occurs, a glass-hard steel rod suddenly heated to 300° is a viscous fluid. I have shown 1 that if a glasshard and a soft rod (ceeteris paribus) be identically twisted and heated 

to 350° the former will have lost all its strain, whereas in the soft rod 

only about £ will have vanished. Of. § 60.

Advantage may be taken of two simultaneous causes of molecular 

instability in other and purely mechanical ways. Thus molecular instability is produced by drawing soft steel wire through a draw-plate, 

and the instability increases enormously with the intensity of the strain. 

Experiments which I made in some number by countertwisting soft 

and hard drawn steel wire at 30° and at 100° showed results quite

comparable in striking interest with the behavior of tempered steel. 

The character of both phenomena is the same, 80 that as far as viscous 

comparisons go the drawn strain replaces the temper strain perfectly. 

Of. § 102.

99. Viscosity and stress. Viscosity in the above pages has been considered apart from the stress-intensity under which the deformation 

takes place. This is liable to lead to confusion, unless the stress relative to which the constants of viscosity are defined be kept clearly in 

mind, or unless the terms viscosity be applied to solids in the restricted 

sense of "elastische Nachwirkung." Thus if a glass-hard and a soft 

steel rod be subjected alike and at ordinary temperature to torsional 

stress" of continually increasing magnitude, a stress value will be 

reached for which the viscosity of the hard rod will equal, and eventuually overtake, the viscosity of the soft rod. I was able to exhibit this 

phenomenon in even a more striking way at 190°, finding that for rates 

of twist less than r=3° steel rod (radius =0'041cm) is much less viscous 

and more susceptible to the influence of temperature in proportion as it 

permanently harder;2 whereas for rates of twist greater than r=6° 

steel ca3teris paribus is less viscous and more susceptible to the influence of temperature in proportion as it is softer.

Here I may profitably advert to certain considerations postulated in 

the earlier chapter 3 relative to the association of hardness with resistance against oo-forces acting through zero-time, and the association of 

viscosity with resistance against zero-forces acting through cc-time, all 

magnitudes being regarded from a relative point of view. "We may 

reasonably conceive," is there further stated, " that in case of viscous 

motion the molecules slide into each other, or even partially through 

each other, so that the molecular configuration is being continually 

reconstructed; whereas in the other case (hardness) the molecules are

1 Am. Jour. Sci. (Ill), 1887, vol. 34, pp. 4,5. Experiments made by annealing twisted systems.

2 An. 190°, being of course the maximum hardness admissible. 

8 Am. Jour. Sci. (Ill), 1887, vol. 33, p. 28; ot above chapter I.

Bull. 73 7
98 THE VISCOSITY OF SOLIDS. [BULL73.

urged over and across each other . . . ." In the ordinary case of 

scratching the action is usually accompanied by physical discontinuity ^ 

of the parts tangentially strained.

Viscosity and hardness may be clearly distinguished by an experimental method as follows: Imagine a round harder body sliding tangentially along the plane of a softer body without rotation. Let there 

be sufficient pressure on the round body normal to the plane of the 

softer body to insure cohesion at the point of contact. Then the softer 

body is subjected to a simple shear along the line of scratching. If the 

motion is sufficiently slow, the soft body may yield viscously and there 

will be no scratching. If the motion is sufficiently fast, the soft body 

will generally be scratched. Hence hardness and viscosity are each 

resistances against simple shearing, according as the tangential motion 

of the hard body is sufficiently rapid or sufficiently slow, respectively. 

The conditions for the occurrence of quiescent friction may therefore be 

stated thus: if there is sufficient time given for the molecules of two 

 bodies to react on each other at the point of contact, the friction is 

quiescent. If the time be insufficient, friction is kinetic.

The intensity of stress by which the above deformations are evoked 

was nearly constant and equal to 0-5 kg. on centimeter of arm. This 

couple, when applied to the given steel rods (radius 0'041cm ), is admirably adapted for the exhibition of the nearly pure viscous phenomenon, 

the "Nachwirkung" of Weber and Kohlrauseh. I

It is just here that certain cardinal distinctions must be made. According to Maxwell's views, viscosity is the same phenomenon in 

liquids and in solids, and the molecular mechanism by which it manifests 

itself quite the same in both cases. There is nothing in the theory to 

induce the reader to limit viscosity in solids to certain special changes 

of configuration. In solids at high temperatures, and of course in viscous fluids, there is indeed rao need of distinction, and viscosity appears 

as the one property into which the other configuration properties of 

solid matter eventually merge. In solids at low temperatures, on the 

other hand, the case is much more complex; and whereas viscosity 

("Nachwirkung") still appears as a property common to solids, whether 

soft or hard, plastic or brittle, these ulterior distinctions, softness, 

hardness, plasticity (permanent set), brittleuess, etc , separate solids by 

very broad lines. Hence it is improbable that the whole mechanism iu 

virtue of which viscous deformations are possible in viscous fluids is 

fully of the same nature as that by which viscous motion takes place in 

solids at ordinary temperatures. Viscosity in liquids is the mean result of divers superposed phenomena, the occurrence of any one of 

which in a solid would give rise to some special physical property of ^ 

that solid. From this point of view, since viscosity is independent of 

the other physical properties above enumerated, and since viscosity 

(Kachwirkung) is common to solids without exception, I have ventured 

to refer it to such action between contiguous molecules as involves the
MAXWELL'S THEORY APPLIED. 99

least amount of free motion. Viscosity in solids is the result of changes 

of configuration resulting from localized thermal agitation, and often 

superinduced by the atomic attraction of contiguous configurations in 

the manner explained by the Clausius-Maxwell principle.1

This premised, further distinctions may be made. Questions arise as 

to whether such action can be indefinitely repeated without rupture, as 

in plastic solids, or in viscous fluids; or whether it can not be indefinitely repeated, as in brittle solids, etc. The indefinite repetition of the 

phenomenon is equivalent to a passage of molecules over or across each 

other, the phraseology above used in reference to hardness.2 § 103.

The ideas underlying this puragraph maybe summarized thus: In 

passing from the fluid to the solid state of matter the residual or extrainolecular annuities acquire an increased importance relatively to the 

intermolecular affinities. At the same time the conditions of action 

have gradually become exceedingly unfavorable. In a liquid under 

impressed favorable conditions chemical reaction between molecules is 

demonstrable (electrolysis). In a solid under impressed favorable 

conditions (strain of dilatation) it is also demonstrable, for instance, 

in the marked secular annealing of glass-hard steel. It is not necessary 

for the manifestation of viscosity that the integrity of the molecule be 

actually invaded; but as the action intensifies one may pass continuously from Maxwell's into Clausius's hypothesis without being able to 

define the line of transition, at least from the character of the viscous 

phenomena.

100. The phenomenon of glass-hardness. The observations made in 

the above paragraphs relative to the visible viscous subsidence of a 

mechanical strain imposed on a steel rod apply for the complete explanation of the phenomenon of temper. With this purpose in view, it 

is merely necessary to conceive of hardening or quenching (sudden cooling of steel) as an operation by which a strain of dilatation is imparted 

to steel. . This strain, once supplied, is locked up in the metal in virtue of viscosity.3 The strained structure of hard steel is proved by 

the fact that massive pieces of hard steel often explode spontaneously,* 

and by the tendency to rupture during quenching exhibited by the 

metal. The temper strain may be studied optically and in other ways, 

in glass, and at low temperatures, even in resin.5

1 "Betrachten wir ferner das Verhalten dor Goaarumtmolecule unter einandor, so glaube ich dass ea 

auch bier zuweilen geachioht, dass das positive Theilmoleciil eines Gesamrntmoleciils zu dom negativen 

eines anderen in eine giinstigre Lagekoramt, als jedes dieser beiden Theilmolccule in Auceiibltcke 

gerade zu dem anderen Theilmoleciil seines eigenen Gosatmntmoleciila hat, etc." Mech. Warineth., 

1879, vol. 2,2 Aufl, p. 163. Again, following Maxwell: ". . . . Thus we may suppose that in a certain number of groups the ordinary agitation of the molecules is liable to accumulate so much that 

every now and then the configuration of one of the groups breaks up, and this whether It is in a state 

of strain or not. . . ..."

" But if a solid also contains .... groups of the first kind which break up of themselves ... ." 

Maxwell, loo. cit

* Of. Am. Jour. Soi. (Ill), 1887, vol. 34, pp. 1,18.

8 Cf. Bull. U. S. Geol. Survey, No. 14,1885, p. 88.

4 Batcheldor: Jour. Franklin Inst. (Ill), 1844, vol. 8, p. 133.

8 Marangoni: N.Cim. (Ill), vol. 5,1879, p. 116 (Rupert's drops of resin) j De Luynes: Phil. Mag. (IV), 

vol. 45,1873, p. 464 (Rupert's drops of glass); B. and S.: loo. cit.
100 THE VISCOSITY OF SOLIDS. [BULL. 73.

Beckoned from the observed volume increase1 due to quenching, the 

stress intensity corresponding to the observed strain may be estimated 

at 1010 dynes per square cm. in steel and 109 dynes per square cm. in 

glass. It is thus of the order of the respective tenacities of steel and 

of glass.

In view of the fact that the viscosity of glass-hard steel is not above 

that of glass,2 exceptionally great strain intensity, though impartible, 

would not be permanently retained. Hence the secular changes of 

glass-hard steel. Of. § 95, foot-note. At this point the function of carbon appears. Sudden cooling induces carbon ^and iron to remain in 

the combined state in a way favorable to the dilatation, in question. 

Throughout the process of cooling, carbon and iron, at any place within 

the metal, are united in conformity with the given degree of carburation and with the strain there experienced. In the cold metal, at the 

given place, strain is to a certain extent permanent and independent of 

the surrounding medium of steel.3 Hence if by gradual secular annealing of massive glass hard steel a sufficient number of carbon configurations are broken, stress may increase to an intensity sufficient to rupture 

the metal explosively.

In our earlier papers on this subject Dr. Strouhal and I were much 

puzzled to know whether the temper-strain, and in general the phenomena of annealing, were to be interpreted physically or chemically; 

whether annealing was a case of viscous subsidence of a mechanical 

temper-strain, or a mere case of decomposition of chemical hardness. 

In the light of the present advanced conceptions 'this distinction is 

superfluous. It makes no difference whether the configuration breaks 

up into parts chemically different, as carbon and iron (say) in steel, or 

into parts chemically though not structurally identical, as in homogeneous metals. Viscosity is conditioned by the degree of instability. 

Again, it is clear that the principles which account for the subsidence 

of the mechanical strain will also account at once for such chemical decomposition as is here in question, the difference in the two cases being 

vested in mere details of molecular mechanism. §§ 98, 99.

101. The phenomenon of annealing. However complex the nature of 

the temper-strain in steel may be, the behavior of hard steel, when subjected to the influence of temperature, offers sufficient proof of its occurrence. The laws of annealing hard steel4 are as follows:

(1) The annealing effect of any temperature acting on glass-hard steel 

increases gradually at a rate diminishing through infinite time; diminishing very slowly in case of low temperatures (<100°); diminishing 

very rapidly at first and then again slowly at high temperatures (> 200°);

« Am. Jonr. Sci. (Ill), 1886, vol. 31, pp. 441, 443; 1886, vol. 32, p. 191; 1887, vol. 33, p. 33; Bull. TJ. S. Geol. 

Survey, No. 27,1886, pp. 30-50.

2 Barus and Strouhal: Am. Jour. Sci. (Ill), 1887, vol. 33, p. 30.

3 Bull. TJ. S. Geol. Survey, No. 35,1886, p. 42. Structure studied by the density method. Shells consecutively removed by galvanic solution. , 

« Phil. Mag., V, 1879, vol. 8, p. 341; Bull. TJ. S. Geol. Survey, No. 14,1885, p. 195.
BARUB.] LAWS OF TEMPERING. 101

so that the highest and hardest of the states of temper possible at any 

given temperature is approached asymtotically.

(2) The ultimate annealing effect of any temperature (time =»o) decreases at a retarded rate with temperature, and practically reaches the 

limit of variation below 350°.

(3) The ultimate annealing effect of any temperature, <°, is independent of the possibly preexisting effects of the temperature £'°, and is 

not influenced by subsequent applications of £'°, provided t>t'. In 

case of partial annealing at t° (time finite), this law applies more fully 

as the ultimate effect of t° is more nearly reached.

Postulating the strain discussed in § 100, these laws follow at once 

from Maxwell's theory, and the explanation (mutatis mutandis) is 

identical in character with that given in §§ 95 to 98 with reference to 

the applied torsion strain. Inasmuch as annealing is accompanied by 

chemical decomposition, the conditions under which the temper-Strain 

is reduced are those of § 98.

The third law of annealing asserts that the heat effect is analytic, 

but not in the same degree synthetic. The carbon configuration dfcfinitely broken up by annealing does not recombiue on cooling. In pure 

metal, and up to a certain limiting (small) stress, configurations broken 

up by stress may recombiue when stress is released or reversed. § 102.

102. The temper-strain in other substances. In certain comparisons between the strain effect exhibited by glass and by steel, 1 we were led 

both by gravimetric and by polariscopic observations to this distinction: 

the strain in hard steel is very perceptibly affected by annealing temperature as low as 50°, whereas in the case of quenched glass (Rupert 

drop), perceptible annealing is incipient only at 200°. The bearing of 

this result on the present discussion is manifest: the difference of behavior is due to the absence in glass of anything equivalent to the 

unstable carbon configuration in hard steel. The case of glass is nearly 

that of soft steel, and the behavior as regards viscosity in these two 

instances is similar.

Schroeder's2 important result has relevancy here: in the case of hard 

drawn wire (Ag,Fe, german silver) minimum viscosity is found associated with maximum susceptibility to temperature. This is the general deduction from steel for varying intensities both of temper strain 

and of drawn strain.

103. Extremes of complex and of simple molecular structure. Following 

the suggestion of § 99, it may be inferred that in case of very complex 

molecular structure instability of configuration will be a more probable 

occurrence than in the case of simple bodies, cseteris paribus. Complex 

structured matter may be looked upon as a solidified mixture of homologous chemical series, with a predominating member to give the sub1 Barus and Strouhal: Am. Jour. Soi. (Ill), 1886, vol. 32, p. 185; vol. 31,1880, p. 451. 

»Schroeder: Wied. Ann., 1886, vol.28, p. 369.
102 ^ THE VISCOSITY OF SOLIDS. [BULL. 73.

stance character. Comformably with this view, the complex organic 

solids,1 like silk and ebonite, show more pronounced viscous deformation 

than metals or mineral solids. These kuowa facts are thus in general 

accordance with the present theory. Nor is it remarkable that a complex substance like glass lies somewhere between hard steel and soft 

steel in the scale of viscosity.

On the other hand, when the atoms of the molecule are all alike, and 

the structure of the substance is essentially atomic, we meet conditions 

favorable to permanent set. This is probably the case with many 

metals.

104. Thermal stability of magnetic configuration. Maxwell's theory 

lends itself at once to the explanation of superposition (perfect or imperfect) of viscous motions, inasmuch, as the interpretation given is 

independent of the special peculiarity of the strain to be discussed. I 

will adduce a few magnetic results which bear upon this point.

Considering the permanent effects of temperature on the residual 

magnetic induction of hard saturated steel, Dr. Strouhal and I2 

louid it necessary to discriminate between two species of magnetic 

loss:

(1) The direct effect, due simply to thermal action on the magnetic 

configuration;

(2) The indirect effect, due to the action of temperature in producing 

mechanical annealing.

These two kinds of loss of residual induction often occur together. 

Considered separately, the latter, cssteris paribus, is very decidedly the 

greater in amount, and its character is fully typified by the concomitant phenomenon of mechanical annealing. The former (1) is not only 

much smaller in relative magnitude, but subsides completely within a 

much smaller interval of time. In general, the occurrence of permanent 

magnetism in hard steel, in its thermal relations, is subject to nearly the 

same laws of variation as those adduced, §§ 94 to 98, for ordinary mechanical strains. Instability of the carbon configuration is more seriously 

detrimental to magnetic permanence than is instability of thermal configuration.

If the unstable carburation configuration be removed by thorough 

annealing at 100°, then the cold hard resaturated magnet must show 

exceptionally good magnetic stability as regards the effects of mean 

atmospheric temperature. If the saturated magnet is again thoroughly 

annealed at 100°, the exceptionally good magnetic stability in question 

is even further enhanced, because the magnetic configurations unstable 

as far as 100° have now also been removed. Experiment shows the 

second magnetic loss to be relatively small. The rods carry the maximum of permanent hardness and the maximum of permanent magnetization as far as 100°. This process of consecutive annealing is the one

1 Of. Kohlrausch: Pogg. Ann., 1866, vol. 128, p. 414, and many others.

» Strouhal and Barus: Wied. Ann., 1883, vol. 20, p. 662, * -
BARUS.] VISCOSITY AND RESIDUAL MAGNETISM. 103

we proposed when the magnets made are to withstand the effects of 

atmospheric temperature, of percussion, and of secular time. 1

106. Intensity of magnetic configurations. In the above paragraphs I 

have referred to thermal, carbon, and magnetic configurations, using 

the adjectives merely to designate the chief cause of the instability under 

special consideration, whereas the configurations themselves were not 

necessarily different. In the same way I contrasted thermal and motional instability. Thus a carbon and a thermal configuration may be 

one and the same grouping, considered from different points of view; 

so may a thermal and a magnetic configuration. The latter phrase is 

used advisedly, and the rod showing residual magnetic induction supposed to consist of configurations of all degrees of magnetic stability, 

as well as in all degrees of magnetic intensity. Stability and intensity 

are the qualities which in the present case correspond to stability and 

strain, respective^, in the above configurations.

Magnetic stability decreases from hard to soft steel and from soft steel 

to soft iron, following therefore the inverse order of viscosity; and its 

character, too, is different from viscosity, the tendency being toward 

sudden magnetic changes, even when the cause of such change is superinduced by heat. Of. §104.

The mean magnetic intensity of the configuration must depend on 

the dimensions of the saturated rod. In the normal case of linear rods 

this magnetic intensity increases from hard to soft steel 2 and from steel 

to iron. Hence from one point of view carbon configurations interfere 

with the occurrence of intense magnetic configurations; from the other , 

point of view magnetic intensity increases in the direct order of viscos- , 

ity or stability of molecular configuration.

Among methods for elucidating the nature of the magnetic configuration, a comparison of the effect of a magnetic field on torsional rigidity is probably best. Extending the classic researches of G. Wiedemann,3 1 commenced a series of such measurements. In the case of a 

given field of great intensity, if two identical iron wires, respectively 

magnetic and unmagnetic, be countertwisted to the same maximum 

shear (obliquity of external fiber, fi?=0-003, say), then the product of the 

detorsion due to longitudinal magnetization and the diameter of the 

wires is constant and proportional to the product of the shear and the 

magnetic coefficient of rigidity. This remarkable relation implies that 

the increment of the twisting couple evolved by magnetization increases 

as the third power of the radius, casteris paribus.

1 Details in Bull. TJ. S. Geol. Survey, No. 14, chapter VI; or loc. cit.

2 Strouhal and Barus: Wied. Ann., 1883, vol. 20, p. 621.

8 Wiederaann: ElectricitSt, 1883,3ded. (HI), pp. 683 to 698; Barus: Am.Jour. Sci.(in), 1887,vol. 34, p. 

180. I believe my researches are the first attempt to interpret these relations quantitatively, and they 

lead to the law expressed hi the text. Other results I will communicate later. '' (0£, Chapter IV.)
104 THE VISCOSITY OF SOLIDS. [BULL. 73.

SUMMARY.

CLAUSIUS'S AND MAXWELL'S THEORIES COMPARED.

107. Summarizing the results of the above paragraphs, I believe the 

introductory statements to be fully verified. I have shown that the 

effect of distributing unstable molecular configurations uniformly 

throughout the substance of a rigid metal like steel is analogous to 

that of dissolving molecules of acid or of salt in a nonconductor like 

water. These added molecules are the unstable groups with which 

Clausius's theory deals. In both cases the effect produced is proportional to the number of unstable groups distributed. If the number be 

sufficiently increased, the medium will ultimately be a viscous fluid in 

the one case and an electrolytic conductor in the other. At the outset, 

pure water typifies the rigid solid.

The applied stress imparts a permanent strain to the solid. Viscous 

deformation is therefore accompanied by a residual phenomenon, which ' 

manifests itself when the applied stress is reversed or removed.1 In 

liquids acted on by an electromotive force the analogous reaction is 

the reciprocating force of galvanic polarization.

Again, Clausius's and Maxwell's theories mutually sustain each 

other. For if the conception that molecular configurations are present 

in a solid in all degrees of stability is necessary to explain the behavior of strained solid matter, it follows that configurations of more V 

pronounced instability will be present in electrolytic systems. Conversely, the fact that many solids can be electrolyzed points to.the 

occurrence in these of a very advanced state of molecular instability. 

To take the concrete example of glass, the same molecular mechanism 

which at 300° promotes electrolytic conduction, when the solid is influenced by electromotive force, manifests itself at low temperatures as 

the viscosity of the solid under stress.

1 Kohlrausch: Pogg. Ann., 1866, vol. 128, p. 419.
OHAPTEE IY.

THE EFFECT OF MAGNETIZATION ON THE VISCOSITY AND THE 

RIGIDITY OF IRON AND OF STEEL.

INTRODUCTION.

108. Mr. Herbert Tomlinson 1 has recently communicated results on 

the changes of viscosity and of elasticity produced by magnetizing iron. 

As both classes of data are obtained by the vibration method, it seems 

not undesirable to attempt to verify them by some static method, and 

the one described in Chapter II, Fig. 20, is so easily applicable that I 

have made use of it.

My original purpose was to confine the investigation to measurements 

of viscosity, inasmuch as such results have an immediate bearing on 

Chapter III; but I found in the course of the work that the incidental 

data on the rigidity of iron and steel could be grouped together. Taken 

collectively in this way, they led to inferences which the well-known 

and comprehensive researches of Wiedernann 2 fail to point out. I 

refer to the effect of magnetization on the rigidity of iron and steel 

as modified by the dimensions of the metal temporarily strained, lu 

this respect, too, the results are supplementary to Chapter III, for the 

chapter virtually applies a magnetic method to study the character of 

a strained atomic configuration. I shall show that the increment of 

rigidity due to magnetization increases at an accelerated rate as the 

soft, temporarily twisted wire becomes more nearly filirneutary. Now, 

since the said increment is independent of the sign of the current in the 

helix, and, moreover, increases with the current intensity in a way which 

I have found not seriously irregular, it seems profitable to attempt to 

utilize this principle for the construction of electric dynamometers.3 

This is the point of view from which much of the present chapter has 

been written. It also contains a series of results on the rigidity of 

magnetized steel temporarily strained and varying in temper from extreme hard to extreme soft.

1 Tomlinson: Beibliitter No. 3,1887, p. 176; original in Proc. Roy. Soc., 1886, vol. 40, p. 417, Is unfortunately not at my disposal.

a Wicdemann: Pogg. Ann., 1858, vol.103, p. 571; ibid., 1859, vol. 108, p. 161; Galvanistuus, 3d ed. (Ill), 

1883, p. 683-698. Less closely allied researches on the effect of magnetization on torsion, etc., are due 

to Matteuci: C. E., 1847, p. 301, and to Weftheim: C. E., 1852, vol. 35, p. 702, as well aa to Wiedemann 

(loc. cit.), and more lately to JEwing (Proc. Koy. Soc., 1883, No. 228, p..H7).

3 Cf.p.m.

105
106 VISCOSITY OF SOLIDS.

VISCOSITY OP MAGNETIZED STEEL AND IRON.

109. Apparatus and method. To make the present measurements it is 

merely necessary to replace, by an appropriate helix, the heating apparatus described in Chapter II. The two wires to be examined are in the 

same vertical line, separated by a rigid piece of .brass which carries the 

index mirror. Any desirable rate of twist may be imparted by rotating and then fastening either the upper or the lower end of the system. 

If both ends be rotated symmetrically in opposite directions, the mirror 

remains stationary. In this way any reasonable amount of twist may 

be stored without moving the image of the scale out of the field of the 

telescope.

The wires of the system were identical as regards length, diameter, 

and composition; and the arrangement adopted was such that at any 

time the upper wire might be under the influence of a powerful magnetic field. The helix used for this purpose consisted of ten layers of 

230 turns each, doubly wound in such a way as to form two independ 

ent partial helices of 115 turns of wire for each layer. For the same 

current the fields of these partial helices were identical; by connecting 

them, either diiferentially or in series, the field obtained was either 

zero or the maximum for the given conditions. The length of the helix 

being 20cm, its internal radius l'25cm, its external radius 2-07cm, the magnetizing force at the center proves to be 1425 c. g. s. units of intensity 

per c. g. s. unit of current or 142-5 (g*/c\s) per ampere. Current was 

obtained from five flat Grove cells, in mean intensity of about one Ampere. Hence the iron wires were probably not far from saturation, 

supposing that a field of 140 c. g. s. units of intensity is sufficient to 

magnetically saturate soft iron.

Without elaborate precautions it is impossible to produce a strong 

field for great lengths of time in this way, without perceptibly heating 

the helix. This introduces a serious error, for the viscous detorsion 

actually observed is due to a heat effect superposed on a magnetic 

effect, both of which are of the same order of minuteness. By using a 

helix like the one above, in which the current may be passed through 

the two partial coils in the same or in opposite directions, the full heat 

effect may be observed either with or without the magnetic effect. For 

when the coils are joined differentially the field produced is zero, 

whereas the heat generated in the helix is, ceeteris paribus, not changed 

in amount. This is the way in which I endeavored to eliminate the 

temperature discrepancy.

It is difficult to find two wires which are absolutely identical; after 

softening some parts of a wire yield more easily to stress than other 

parts. It is not until the less rigid parts have been stiffened by receiving permanent set that the rate of twist temporarily stored is the same 

throughout the length of the wire. All viscous motion which is due to 

differences in the mechanical or chemical properties of the metals may 

be detected by allowing a series of observations for open circuit to 

alternate with similar series for closed circuit.
BARU8.] VISCOSITY OP MAGNETIZED STEEL. 107

110. Results. Table 60 contains results as obtained with steel annealed about midway between soft and hard. Here 6 is the temperature of the helix and of the upper wire, 6' the temperature of the lower 

wire, I and p respectively the length and radius of each, ((p cp1 ) denotes the amount of viscous detorsion per centimeter per wire (i. e., per 

two centimeters of the system), in radians, at the time h in hours. In 

other words (<p (p') has the meaning already fully defined in § 56, except that in the present case the essential difference of. <p and <p' is to 

be induced by magnetization, r denotes the rate of twist in degrees 

imparted to the system at the unmagnetic end. If (<p <p') increases or 

decreases according as the sign of the twist is positive or negative, then 

the nnmagnetic wire i« of greater viscosity than the magnetic wire; 

and vice versa. Intervals of observation corresponding to open and 

closed circuits are appropriately indicated. Whenever the circuit is 

closed differentially in the helix so as to produce a zero magnetic field, 

this is also stated. (<p <p') is correct to three or four units of the last 

place.

The three parts of this table show that the viscous differences in 

question are invariably minute. In part first the originally less viscous 

lower wire becomes perceptibly more viscous when the circuit is closed 

around the upper wire. The apparent effect of magnetization is here 

a decrement of viscosity. In the second part the wires for open circuit 

are equally viscous; for closed circuit the results are the same as in 

part first both as regards sign and amount. The apparent effect of 

magnetization is again a decrement of viscosity. Part third, finally, 

contains the interpretation of these results: it is seen that results of 

the same magnitude and character are obtained when the magnetic 

field due to the helix (other effects remaining the same) is zero. The 

viscous effects here observed are therefore wholly due to temperature, 

and it may be safely inferred that magnetized and unmaguetized steel 

differ in viscosity by an amount less than is produced by 5° difference 

of temperature.

TABLE 60.

Viscosity of steel, annealed 360°. Z=30oln ; 2p=0-083CB1 ; fl'=20°.

h

hours. 0-00

2-67 

4-33 

24-00

25-42

25-60

25-67 

25-83

26-00

26-25

26-75

o-oo

1-00

10fi

radians.

 0

 33 

 35 

 50

 50

-35

-15 

 3

+ 7

+10

+ 15

 0

 3

9

°C.

Remarks.

1

I Circuit open.

f T= + 6°. I

Circuit

I Circuit open.

$ T= C°.

h

hours. 1-10

1-12 

1-40 

1-67 1-92

2-08

2-40 

2.80

o-oo

0-18

0-43

0-60

0-85

1-00

4-52 

23-25

(</>-<*>') X 108

radians.

-21

 10 

-23 

-23 

 34

 38

 42 

 49

 0

 30

 46

-63

 58

 63

 7 

 17

0

°C.

mm

19 

23 

25 

27

28 

29

17

21

26

28

29

30

 

Remarks.

1

Circuit 

closed.

Circuit

closed;

field zero.

T= 6°.

\ Circuit open.
108 THE VISCOSITY OP SOLIDS. [BULL. 73.

Inasmuch as the steel wire of Table CO is permanently a magnet after 

the first induction, sharper results may be looked for in experimenting 

with iron. As regards viscosity, iron is less susceptible to the influence of temperature than annealed steel or even soft steel; it is more 

magnetically permeable and it loses its magnetization completely when 

slightly jarred in a zero field.

111. Table 61 contains results for soft iron, the arrangement being 

identical in plan with Table 60.

In the first part of Table 61 (cp cp'} increases whenever both wires 

are unmagnetic and decreases at a gradually diminishing rate whenever the upper wire is magnetic. The apparent effect of magnetization 

is therefore a diminution of viscosity, a result in accordance with the 

inferences from Table 60. To interpret this apparent result the second 

part of Table 61 is available. It shows that when the current is passed 

through the helix .differentially, ((p cp1 ) increases at the same rate aa 

before, notwithstanding the fact that the field is now zero. Hence the 

amount of viscous detorsion observed is a temperature discrepancy and 

no viscous effect due to magnetization is discernible.

TABLE 61.

Viscosity of magnetized iron. Kods Nos. 7,8, annealed soft. Z = 30cm ; 2p=0'110cm ; #' = 20°; r= 3'6°.

h

o-oo

0-57

0-58

0-9:2 1-23

1-80 

T85 

2'00 2-17

2-48 

2-50 2-97

3-47

«>-*') X 10«

0 

 3

+65

30 

8

 58 

 53 

+18 

+10 

0

-71 

-60

 52

e

 

33 

34

33 

28

29 

33

34 

34 

29

26

Circuit.

/Open.

^

> Closed.

> Open. 

I Closed.

> Open.

*

h

3-48 3-68

4 -05 4-U."> 

4-47

. 4'5i 4-75

4-92

5-07 

538

5-00 

22-30

(4>-0')X 

10s

+15 

+ *

 5

 72 

 62

 55 

-^65 

-63 

 70 

 73

 73 

-50

e

26 

30

34

34 

29

32 

33 

34

-

Circuit.

> Closed.

j

? Open.

i Closed differentially ; 

magnetic; 

field zero.

> Open.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 73 PL. V

3oo

EFFECT OF MAGNETIZATION ON THE VISCOSITY AND RIGIDITY OF IRON, <t> VARYING WITH TIME.
13AUU8.] VISCOSITY OF MAGNETIZED IRON. 109

In Table 62,1 give similar results with a thinner wire.

TABLE 62.

Viscosity of magnetized iron. Z=30cm ; 2p=0'OS3cm ; 0'=20°; T= 3°.

h

o-oo

0-38

0-42

0'50

0-75 1-05

1-38

1-42

1-68 1-95

2-17

2-18

2-48 

2'88 3-23

3-25 3-50

4-17 4-20

4-67

5-08

(*-*') x

10s

0 

80

189

195

220 

245

205

161

183 

203

218

328

334 

348 

360

255 

270

298 

407

410

420

e

 

21

21

26 

29

30

30

28 

25

23

24

27 

30 

32

 -

 

is

30

Circuit.

| Opeii.

i

[> Closed.

1

Open.

Closed.

> Open.

J

( Closed.

)

h

5-13 6-57

23-00

2310

23-33 

23-67

24-00

24-05

24-42 

24-95

24'97

25-33

26-17 

26-20 

27-12

27-27 

28-28

28-35 

48-00

(*-*') X 106

310 

328

545

653

645 

643

645

538

550 

560

670

6GO

668 

561 

580

690 

685

580 

740

0

25

18

28

30

30

26 

23

..

28

32 

23

Hi

 

Circuit.

> Open.

j

> Closed.

1

j

\ Open.

j

I Closed.

j Open.

| Closed.

| Open.

112. In these results the thermal and magnetic effects are superposed 

on the continuous viscous motion due to inequalities in the wires, the 

upper wire being more viscous than the lower wire. In every case, 

however, this normal viscous detorsiou is perceptibly retarded whenever the upper wire is magnetized. It follows conformably with the 

above results that the viscosity of iron is apparently diminished by 

magnetization; that the amount of this diminution is no larger than is 

quite in keeping with the heating effects due to the passage of current 

through the helix. My results therefore fail to give any satisfactory 

proof that magnetized and unmagnetized iron differ in viscosity by 

more than the equivalent of one or two degrees centigrade, at ordinary 

temperatures.

In PI. V the results of the above Tables 61 and 62 for soft iron are 

graphically given, time as abscissa and deformation (<p <p'\ as ordiuate. 

The breaks in the curve show the time at which current was made and 

broken and the (cp (p1 )- effect produced. In Table 61 the two wires 

are originally identical, as is shown by the " off" branches. The effect 

of magnetization as apparent diminution of viscosity is shown by the 

slope of the "on" branches; but the effect of the zero field with current 

" on " at the end of the curve, is the same in sense and approximate 

magnitude, as the effect of magnetization. Hence the latter is obscure. 

Similar interpretation is to be made with reference to the curve for 

Table 62, in which viscous motion preexists. But this motion, due to 

greater viscosity of the upper wire (in the helix), is invariably retarded 

by magnetization. In the second part of this figure the preexisting 

viscous motion is nil, and the effects are therefore clearer.

In the figure for Table 61, note the tendency to concavity upward in 

the "on" branches. This is also true of the second half of Table 62.
110 THE VISCOSITY OF SOLIDS. [BULL. 73.

O

In Table 61, moreover, prolonged magnetic twisting stiffens the wire; 

hence the tendency of the " off" branches to slope upward toward the 

end of the curves.

I am far from wishing to assert, however, that Tomlinson's results 

are temperature phenomena. It is possible that the marked tendency 

of soft iron to assume permanent set, and consequently the relatively 

large viscous motion immediately after strain is imparted, makes the 

vibration method particularly sensitive in registering the viscous effect 

of magnetizing iron.1 But by using static methods and observing in 

the interval of gradual or purely viscous deformation, no satisfactory 

evidence of such an effect is discernible. Moreover, magnetization 

changes the rigidity of iron and therefore necessarily jars a twisted wire. 

There result such changes of viscosity as are produced by any sudden 

vibratory disturbance; changes which of course are purely mechanical, 

but which may obscure the direct result of magnetic induction.

I may state, in concluding, that inasmuch as Weber's theory associates magnetism with certain rotations of molecule, while divers theories mentioned in Chapter III refer viscosity to a similar mechanism, 

it would be permissible to look for a marked effect of magnetization on 

viscosity. The vanishing results of the above paragraphs do not sustain such an inference.

RIGIDITY OF MAGNETIZED IRON.

113. Definitions and results. The effect of longitudinal magnetization 

on iron or steel twisted within the elastic limits is marked detorsion, 

increasing in amount with the intensity of magnetic field, increasing 

also with the rate of twist, at a retarded rate in both instances, toward 

a maximum. If the sense of the magnetization be reversed (i. e., if the 

helix current be changed in direction) the amount of detorsiou is in 

general unchanged.2

In Tables 60 to 62, discontinuous but perfectly regular variations of 

((p cp') on passing from unmagnetized to magnetized iron or steel are 

strikingly apparent. Inasmuch, however, as the differences in question 

are now to be considered in their bearing on rigidity, and not on viscosity, I will replace (cp <p') in subsequent tables by q>. Hence <p is 

the deflection observed at the index placed at the junction of the two 

identical wires forming the system, per centimeter of length of each, 

immediately after one only of the wires is magnetized. Thus cp is 

evoked and vanishes with the magnetization.

Table 63 contains special results for large rates of twist (r), and has 

been drawn up to exhibit the independence of qj of any possible irregularities in the position of the helix as well as the change of sign of cp 

with the sign of r. The-table shows also that the sign of cp is reversed 

when the helix is passed from the upper to the lower wire. It follows,

1 See "Wiederaann's remarks on the vibration method, Wied. Ann., vi, ]879, p. 485.

2 Tho above phenomena have been elaborately discussed by Wiedemann (Galvanismus, pp. 683-698).
BARU8.] RIGIDITY OF MAGNETIZED IRON. Ill

therefore, that cp is not influenced by errors which in my apparatus 

might result from the increase of length due to magnetization. In 

other words, in the mechanism adopted, magnetic elongation has no 

rotational effect. I and p denote length and radius each in centimetres. T is in degrees, cp in radians, as above.

TABLE 63. Showing the effect of sign of tioisl and of position of helix.

Kern arks.

symmetrically, on lower wire ...................

No.

17,18

Z=30 

10,20 2p-0-083cm

Z=30cm

15,16 2p-0-110 

UrSO""

T

+6 4-5

+6

Q.A

Q«A

-a-o

o.n

Q.A

3-0

-3-0

-3-0 

4-3-0

</>xio6

 130

i i«»q

 139

+93

95

04

<H

95

94

97

88

+(56

«o

114. These sudden changes in the values of cp due to magnetization are 

equivalent to an increase of the rigidity 1 of steel, and 1 shall therefore 

describe them as such. If T be the torsional rigidity of a wire, i. e., the 

reciprocal of the amount of twist per unit length per unit moment of 

twisting couple; and if G be the absolute rigidity of the material, i. e., 

the reciprocal of the amount of shear per unit of shearing force, then

Now if in the present apparatus r' be the rate of twist in radians and 

tp the change of t' due to magnetization; if moreover Gm and G be the 

rigidities of the magnetized and unmagnetized wires respectively; 

then since the radii (p) are identical

Gm (r'-cp)=G(r'+cp), 

which if cp is small in comparison with r' may be written

115. A final datum of interest is the obliquity, a?, of the external fiber, 

or the angle in radians between the axis of the wire and any tangent of 

the helix into which a straight surface fiber, or generatrix has been 

twisted. This is approximately

1 The retrograde motion formerly observed when the upper wire heated to a high temperature 

(100° 300°), is cooled to the temperature of the lower wire (A.ra. Jour. Soi. (Ill), 1887, vol. 34, p. 17), 

might in like manner be used to compute the variations of rigidity due to temperature. In such a 

case, however, the variations of temperature from the high value to the low value must be as nearly 

instantaneous as possible, otherwise elastic and viscous detoraiona will bo erroneously confounded.
112 THE VISCOSITY OP SOLIDS. [BULL. 73.

r being the rate of twist in degrees. This variable a? is intended to 

have no more than geometrical significance. It is. known that on twisting and again untwisting an iron wire beyond the elastic limits, the 

fibers do not return upon themselves to their original forms and positions, but that they become irregularly sinuous lines. Perard's 1 -investigations on this subject are to the point.

TABLE 64. 

Showing the effect of magnetization on the rigidity of soft iron. 1= 30cm.

T

0

 0'43 

 0-75 

_ 1-12 

 1-5D 

_ 2-25 

 3-00 

 3-75 

 4-50 

 5-25 

 6-00 

 7-50 

 9-00 

 12-50 

 15-00

Nos. 1,2. 

2p 0231

2>

X 

3

0-8 

1-5 

2-3 

3-1

S>

X 9-

12 

18 

23 

30

o

X

a.

3-2 

2-7 

2-3 

23

Nos. 3, 4. 

2p=0136

S.

X 

3

0-9

1-8

2-7 

3-6

&

X-e24

43 

49 

51

0

X

i

3-7

3-3 

25 2-0

Nos. 5, 6. 

2p =0-090

o

X 

3

0.6

1-2 

1-8 

2-3

3-5

&

X © 

42

68 

75 

78

77

o

X

4

6-4

5-2 

3.8 3-0

2-0

Nos. 7, 8. 

2p = 0-110

a,

X 

3

0-7

1.4 2'2 

2-9 

3-2

£>

X

-s34

54 

62 

65 

66

o

X 

4

5-2

41 3-2 

2-5 

2'0

No.«. 9, 10. 2p-- 0-070

o

X 

3

0.5

0-9

1-8

2-7 

3-2

o

X

 e37

82

95

L04 

103

s>

X

4

5-6

6-3

3-6

2-7 

2-3

Nos. 11, 12. 

2p = 0-048

&

X 

3

0-3

0-6 

0-9 

1-2

19

2-5 

3-1

o

X-© 

60

107 

116 

131

148

156

148

o

X

4

9.2

8-2 

5-9 

5-0

3-8

3-0 

2-3

Nos. 13, 14. 

2p^= 0-022

&

X

3

0-6

1-2

1-7 

2-4 

2-9

o

X

-© 

86

166

205 

220 

237

&

X 

4

3-3

3-2

2-6 

2.0 1-8

In Table 64,1 have given values for these variables as obtained with 

soft iron wires of different thicknesses. The intensity of magnetic field 

has been stated above. Commencing at low values, the rate of twist (T) 

is successively increased to the maximum value, which can be imparted, 

i. e., until, with the occurrence of marked permanent set, the limits of 

resilience of soft iron are fully reached. After this it was usual to 

twist the wires further, imparting several thousand degrees of permanent set, whereupon r was decreased from the maximum to zero. In 

the table, cw, <p, /*, are means of the values obtained by thus successively increasing and decreasing r. As before p is the radius and I the 

length of the wires, of which Nos. 1-6 were drawn down from a single 

piece of wire, Nos. 7-12 from a second piece of wire, Nos. 15-18 from & 

third piece of wire. A priori, comparison of data is to be made only 

for wires drawn to different diameters from the same sample of iron;2 

but inasmuch as iron to be ductile must be nearly pure, the results may 

safely be grouped in a single series. All wires are annealed at red heat 

in air.

1 Perard: Revue d'univers. des Mines (2), 1881, vol. 15, p. 346; ibid., 1879.

2 Imperfections in the wire plate prevented me from drawing all the wires from a single sample of
RIGIDITY OF MAGNETIZED IRON. 113

To this may be added the following data for soft iron filaments drawn 

from the same wire, &? is the maximum.

TABLE 65. Data for filaments of iron.

No.

15,16 

17,18

2p

0-032 

0-025

*>X103

2-9 

2-8

<J>X106

212 

241

(xXlO3

2-4 

2"3

DEDUCTIONS.

116. Constant fields. It has been stated that the wires to which Table 

64 refers were all soft. Their diameters vary over the very large interval 0-022cm to 0'234cra , and the rates of stored twist from 0.4° to 15°- 

Nevertheless the maximum obliquity, GO, of the external fiber is nearly 

the same for all the rods. In other words, the limits of torsional resilience of soft iron are reached when the obliquity of the external fiber 

exceeds 0.0032 radians.1 After this, iron yields to the torsional couple 

and the result is indefinite permanent set.

Inasmuch therefore as &? is comprehended within about the same interval (0 to 0-003) for all the wires irrespective of thickness, it is expedient to discuss the variation of <p with reference to GO. Indeed, the diagram of cp as a function of ft? shows the characteristic family of curves 

with remarkable terseness. Figure 25 shows that cp increases with a? 

at a rate which is greater in proportion as the thickness of the wires, 

2p, diminishes, and which decreases and finally approaches zero when 

&? is a maximum. The detorsiou due to magnetization ceases to increase 

when the sections of the rod slide on each other. Indefinite twisting 

beyond the elastic limits has no effect so long as the wire is not appreciably hardened. But it is the dependence of cp on p to which I desire 

principally to advert. The following series of values obtain for 

&?=0-003.

TABLE 66. Effect of dimensions.

2pX103 

<t>X\Or'=

234 

30

136 

50

110 

65

90 

80

70 

105

48 

150

22 

240

To these data add the values on Table 65.

1 The literature on torsional strains is so voluminous that I can scarcely suppose similar simplifying 

observations have not been made. But I have found none. Permanent and temporary torsions have 

been compared with regard to their relations to stress, to the mechanical condition of the material carrying stress, etc., by Wertheira (Comptes Rendus., 1855, vol. 40, p. 411; Ann.de Chim. (3), 1857, vol. 50, p. 

195; more elaborately even by Wiedemann (Wied. Ann., 1879,vol. 6, p. 485; ibid., 1879,vol. 7, p. 496; Phil. 

Mag. (5), 1880, vol. 9, pp. 1,97, and by Perard (Bevue univ. d. Mines, 1879). Reference is also to be made 

to Tresca (C. R., 1871, vol. 73, p. 1104), to De Saint-Venant, who has investigated the mechanics of ductile 

substances, and to others. In Wiedemann's last research, correlated values of temporary and~pennaiient torsions are discussed both as they exist immediately after imparting strain and as they exist 

after an indefinite lapse of time. I have no such comprehensive purpose in view; nevertheless the 

great convenience of the variable w is obvious from the way in which I am able to use it.

; Bull. 73 8 ~ ~~ " ~ - 
114 THE VISCOSITY OF SOLIDS. [BULL. 73.

Recent experiments made with iron wire drawn down finer emphasized the above results. In the case of maximum permanent set the 

following results were obtained:

TABLE 67. Effect of dimensions.

2p=0-018cn> 

2p=0-015rm

106 X</>=280 

106 X</)=370

The importance of these results induced me to exhibit their mean 

variation in a chart. This is done in Fig. 25. In this plate the curves 

concave to X denote the variation of (pxlO6 and c^xlO3. They make 

up a family. The other line of the contour of an equilateral hyperbola 

denotes the variations of <px 106 with 2px 10.

G. 25. Increments of rigidity varying with obliquity of fibers. Increments of rigidity varying

with diameter of wire.
BAKUS.J EFFECT OF DIMENSIONS. 115

The great interest which attaches to these results is the fact that the 

observed increase of rigidity, as registered by (p, takes place at an exceedingly rapid rate when the diameter of the wires is small. I was 

not able to make 2p smaller than 0'015cm with the means at my disposal; 

but copper and platinum wire may be had commercially in diameter as 

low as 2p=0 OOScm or even 2p=0-004cm, and no doubt, by skilled hands, 

iron wire can be much further diminished in diameter than I have 

drawn it. Here therefore is a method of investigating the magnetics 

of filamentary wires; a method which increases in sensitiveness in proportion as thickness of wire nearly vanishes. From the importance of 

the properties of filamentary wires this method therefore deserves careful attention.

117. With copper no results were obtained even for 2p=0'OOScm. g> 

is zero in all fields.

118. To return again to Fig. 25,1 will note that /*=-T, T/ being in 

radians. Now, Go=pr', and therefore

.. 2<PP

Hence, since experiment shows the approximate constancy of GO and of 

/*, it follows that cp=f(2p) is to the same degree an equilateral hyperbola. The mean value of JJL taken from Table 64 is, /*=2*1/103 j and 

the mean value of GO corresponding, &j=3 2/103. Hence

and this is the hyperbola with reference to which the points of PI. V 

are coordinated.

Again put I= Then is the length of each wire of the system of 

two wires, which, if the upper wire only be magnetized to saturation, 

will show a deflection =1 radian. It appears therefore that x= » an

exceedingly remarkable result.

Hence in the case of a torsion system of two wires, of the same length 

and radius, but respectively magnetic and unmagnetic, if the twist 

stored produces maximum obliquity (coxlW=3'2) of the external fiber, 

then the lengths of wire corresponding to a given fixed deflection at 

the point of junction will vary linearly with the thickness of the wires. 

These results deserve special tabulation.

TABLE 68. Effect of dimensions. 

Meanco=3-2/103 ;

2pX10

 234

 136 tio

<J>X106

30

61

66

x/io3

33-3

19-6

15-1

2pX10

 090

 070

 048

4>X106

77

103

Ho

X/103

13-0

9-7

6-8

2pXlO

 022

 018

 015

*X106

237

278

370

x/ios

4-2

3-6

2-7
116 THE VISCOSITY OP SOLIDS. [BULL. 73.

From this table the proportionality of x and 2p clearly appears, as 

may be seen at once by graphic construction.

119. Since the couple for a given angle cp will vary as p4 /^ where I is 

the length of the wire, it follows that in case of maximum GO x 103=3*2, the 

force with which the wire is twisted in virtue of the occurrence of magnetism increases as the cube of the radius. The couple, in other words,

is nearly (AE}-^j-(p. And since <pp is constant for all values of p

within the limits of observation, and since E the modulus of elasticity, 

and L the length of the iron wire are also constant, the couple in question becomes

i=.4$-^^p3==coust.p3, nearly.

120. There are certain curious considerations to which I can only 

advert here. Suppose the obliquity of the external fiber, &?, to remain 

the constant maximum. Suppose also the diameter of the iron filament 

decreases indefinitely until we have reached the diameter of a single 

molecule. In this case the twisted fiber would be an elementary helix, 

the spires of which are a continuous succession of oblique molecules. 

The axis of each molecule is inclined o>, by agreement.

Now it is supposable that if an elementary helix of this kind is placed 

in a magnetic field of great intensity, that the effect would be (proper adiustment presupposed) to rotate the molecules parallel to the axis of the 

filament; in other words to reduce GO to zero. In a given system of two 

countertwisted filaments, such as have been operated on in the above 

work, the elementary result would be double the rate of twist T' of 

the lower unmagnetic filament, and reduce T' of the upper magnetic 

filament to zero ; thus retaining the same mean rate of twist. More 

simply the numerical result would be r' q). But this ultimate effect 

runs directly against the datum of experiment: for Table 64 shows that 

throughout a considerable range of diameter (2p =. -022cm to 2p = '234cin ),

u the final value of (p/t'^=-^ when <»=0-003, is nearly constant, jw/2='001

nearly. It is certain that the results show no increase of /* for decreasing p.

It is difficult without further experiments to reconcile these conflicting deductions. Probably some light may be obtained by increasing 

the intensity of field. But (constancy of GO presupposed) the hypothetical result r'=(p for 2p= molecular diameter, seems to me an inference

of Weber's theory of magnetism, whereas /~=T> CODi3^ ant* independent of diameter conflicts with it.

121. Intermittent fields. The accelerated rate of increase of cp with p 

as exhibited by these data has suggested the remarks already made, 

viz: since cp is independent of the sign of the current in the helix it is 

probable that p may be taken sufficiently small to render these phe-
BATIUS.1 RIGIDITY IN INTERMITTENT FIELDS 117

nomena practically available for the measurement of induced or alternating currents. The chief difficulties encountered are the phenomena 

of "accommodation" already very carefully discussed in Chapter III. 

Twisting by magnetic means has of course the same effect on the unstable 

configuration, as does twisting by ordinary mechanical couples. To 

return, however, to the subject in hand, the actual deflection increases 

with the length of the iron wire. It would be expedient therefore to 

suspend a light mirror bifilarly from very long filaments of iron and of 

glass or metal, surrounded by a long cylindrical helix. 1 The rate of 

twist temporarily stored in the soft iron filament is the maximum within 

the elastic limits. I give the following example of deflections produced 

by the current of an ordinary induction coil, acting on a relatively thick 

and short iron wire.2 The currents are alternately off and on. The 

two series were made about an hour apart.

TABLE 69. Intermittent currents. 

Nos. 5, 6 ; 20 0-090 ; Z=30cm ; defleotion =

30

52

75

85

40

40

80

75

40 

35

83

73

40 

35

0=20 X 10 

<f>= 19X10-6

In so thick a wire the heat effect of alternating magnetizations soon 

becomes apparent. The result is temporary diminution of the rigidity 

of the wire. Much better results are already apparent when the above 

thin wires are used. For instance (same coil),

TABLE 70. Intermittent currents.

Nos. 15, 16; 2p = 0-034cm ; Z=30cm ; deflections =

50 

70

1RO 

200

50 

CO

200 

200

70 

65

190 

200

70; 

60;

4> = C5X 10 6 

<}> 69 X 10-°

Further discussion of these results (the errors of which are largely 

due to the apparatus) is not now expedient.

The values of q> in Table 64 are means of five observations with the 

circuit alternately made and broken. A small amount of permanent 

detorsion is always imparted to the wire after the magnetism has disappeared, as Wiederaann3 first pointed out. The following example 

may be given frpm very many results of my own. In the case of Nos. 

3, 4, the scale readings for currents alternately off and on, were as 

follows:

1 It is needless to state that I am well aware of the difficulties heie in the way, difficulties which 

"Wiedemann has so carefully digested. In my apparatus, however, all pivot and pulley rotations are 

avoided. I have also repeated tho results relating to fine wires at length with very light mirrors, hy 

which no errors due to an asymmetrical mirror adjustments are encountered. The very small couples 

which come into play in operating with filamentary wires often make damping hy submerged vanes 

objectionable. I have therefore often discarded them.

2 The wire plates at my disposal were such that 2p = o-02cm was the smallest diameter obtainable. But 

tho above series of results are fully sufficient and sufficiently in accordance to justify the inferences 

drawn.

3 Wiedomann: Galvanismus, p. 689.
118 THE VISCOSITY OF SOLIDS. 

TABLE 71. Experiments in cycles.

[BULL. 73.

-

(off)

(on)

(off)

(on)

(off)

0-7°

130

150

SO

160

80

1-5°

110

200

85

188

. 82

2-3°

90

185

70

180

70

2-2°

80

180

70

178

72

1-5°

50

128

38

130

40

0-7°

60

100

58

MO

60

This is very perceptible in the first part of the measurements where 

r or a?increase from zero to the maximum; it generally becomes smaller 

in amount when a) decreases from the maximum to zero. The method 

of varying GO from zero to the high value and then from the high value 

to zero leads to a cycle of results. In the case of Nos. 7,8, for instance 

the data ran thus:

TABLE 72. Experiments in cycles.

co X 103= 

</>X10«= 

coXlQS 

0X106

o-o

5 3-2 

67

0-7 

40 2-9 

64

1-4 

57 2-2 

61

2-2

63 1-4 

51

29 

66 0-7 

28

3'2> 

65( 

0-0) 

3}

to increasing, 

co decreasing.

These observations might perhaps be grouped with Mr. Ewing's 1 

"hysteresis." But in some of the many other like experiments which 

I made there is an element of vagueness.

Table 64 shows finally that the influence of magnetism on the rigidity of soft iron is greatest when GO is zero. It is obvious since cp increases at a retarded rate while t or GO increase uniformly, that jj. must 

continually decrease. The large values of // differ considerably, being 

greater as a rule for smaller diameters. The minimum values of /*

obtained are of about the same magnitude, ^=0-0021. If the conditions 

of indefinite permanent set are such that the obliquity of the external 

fiber, attain a fixed value, then these conditions imply that the rigidity 

of steel is changed by magnetization by a fixed minimum amount.

RIGIDITY OF MAGNETIZED STEEL.

122. In the following Table 73 I give the values of cp which hold for 

steel for the large rate of twist r=6°. The wires are carefully annealed 

as described elsewhere. Diameter 2/>=0-083cm. A soft iron wire for 

which maximum GO is only 0-0021 is also tested for comparison.

The curious result of this table is this, that during the first phase 2 of 

annealing, the effect of magnetization on the rigidity of steel is almost 

nil. This effect becomes of marked importance during the second

1 Ewing: Trails. Boy. Soc., 1885, vol. 2, p. 523-4.

2 Am. Jour. Sci. (Ill), 1880, vol. 31, p. 443.
BARU8.] RIGIDITY OF MAGNETIZED STEEL. 119

phase.1 In other words, if we suppose the wire to pass continuously 

from hard to soft, the increase of the magnetic coefficient of rigidity, jw, is 

particularly pronounced after the variations of the thermo-electric, the galvanic and the viscous properties of steel have practically subsided. JA 

therefore shows close affinities to the induced and to the residual magnetization of an iron-carburet. Agreeing with Wiedemanu's results, /* 

is invariably smaller for steel than for iron. In general if n be regarded 

in its dependence both on K> and on hardness, it appears that the increment of rigidity of an iron-carburet produced by magnetization is greater 

in proportion as the metal shows greater tendency to assume permanent 

set a result which applies for iron and for steel.

TABLE 73. Rigidity of magnetized SMs's steel. (s=0'0043.

Temper.

" 190°........................

360°........................

" 450°........................

</>XlO"

3

4

4

22

25

41

05

ftXlO3

0-06

0-08

0-08

0-42

0-48

0-78

3-83

°

1 In a letter to the Am. Jour. Sci. (Ill), vol. 33, p. 308, Prof. W. F. Barrett has taken exception to certain remarks made by Dr. Strouhal and myself (ibid., p. 35) on phenomena more or less connected with 

the second phase of annealing. We regret exceedingly to have overlooked Prof. Barrett's papers. 

Our object, however, was only to give an enumeration of such observations as had occnired to us incidentally. Of Gore's discovery we were awnre, and the statement is thus made iu the text and in TJ. S. 

Geol. Survey, Bull. 14. Owing to a misconstruction of the foot-note in the Journal (p. 35, J) "ibid." 

happens to refer to "Wied. Ann." instead of to "Phil. Mag." The reference is otherwise correct.

We avail onrselvea of the present opportunity to state that in Prof. J.A. Ewing's paper on the 

"effects of stress and magnetization on the thermo-electric quality of iron" (Phil. Trans. II, 1886, p. 

301), mention is made of onr results only in a final note dated Sept. 17,1880. Our work was accessibly 

published much earlier (Wied. Ann., 1881, vol. 14, p. 54; of. also ibid., 1879, vol. 7, p. 408). We believe we 

were the first to actually measure Thomson's thermo-electric effect of magnetization as well as to 

point out its probable relations to the strain of a magnetized rod.
CHAPTEE V.

THE CHANGE OF THE ORDER OF ABSOLUTE VISCOSITY ENCOUNTERED ON PASSING FROM FLUID TO SOLID.

INTRODUCTION.

123. Notwithstanding the abundance of the literature on viscosity, 

nobody has defined the difference between the solid state and the fluid 

state quantitatively. In case of liquids and gases viscosity can be 

absolutely expressed with facility, and the data may be stated with 

considerable rigor. This is not true for solids. The results are relative 

throughout, no attempt having as yet been made to coordinate their 

viscous behavior with that of liquids. The present chapter makes use 

of two methods for this purpose.

In proposing a differential method for studying the viscosity of solids, 

Dr. Strouhal and I 1 pointed out the way in which the viscosity of solids 

may be expressed in terms of the respective sectional areas, by which 

the motion at the junction of two countertwisted wires or rods is annulled. Suppose now that one of the wires is a true solid, whereas the 

other is a very viscous fluid. Then, since the viscosity of the latter is 

just capable of being arrived at by transpiration methods, it follows 

that the viscosity of the solid with which it was countertwisted may 

also be absolutely expressed. This indicates the first method of procedure adopted. I measured the viscosity of marine glue, by observing 

the excessively slow transpiration of this substance throughout many 

months. Knowing this datum, a very thick rod of the cement was 

compared in viscous behavior with a fine steel wire. §§ 126,127,130,131.

My second method for expressing the absolute viscosity of solids is 

direct and dynamic. It is capable of yielding results of any desirable 

degree of rigor, supposing the necessary facilities for work to be given. 

§§ 134, 135.

GASES AND VAPORS.

124. It is well to note the viscosities 77, of typical substances in passing. The viscosity of vapors and gases has been measured by many 

observers.2 The data present some curious aspects : Thus, for instance, 

the viscosity of vapors 3 like ether, is frequently less than the viscosity

1 Bams and Sfcrouhal: Am. Jour. Sci., 1887, vol. 33, p. 29.

2 0. E. Meyer: Kinetisclie Theorie der Gase, Breslau, 1877, p. 138, et seq.

3 Cf. Puluj: Phil. Mag. (5)d 1878, vol. 6, p. 157. 

120
BARU6.] ABSOLUTE VISCOSITY OF LIQUIDS.. 121

of gases. The absolute values encountered in the present case at mean 

atmospheric temperature are of the order of ^=-0001 to 77=-0002 (g/cs). 

Cf. § 140.

LIQUIDS.

125. Eesults are also available in great numbers. The literature is 

systematized in Landolt and Boerustein's 1 tables, and the data may 

easily be expressed absolutely by means of Slotte's 2 values of the viscosity of water at different temperatures. Water may be taken as the 

type liquid. Slotte's value for 20° is 77=-0100 (gfes). Cf. § 140.

VISCOUS FLUIDS.

126. Apparatus. Data are wanting.3

My experiments were made with marine glue.4 The method of procedure is simple. A fairly wide capillary tube, a b, Fig. 26, provided 

with a cylindrical open reservoir, a, at one end, was half filled with 

marine glue. The thread extended from the reservoir a as far down 

as the middle, &, of the tube. The other (open) end of the tube was 

iutroduced into a flask, dddd, from which the air was then exhausted. 

By this adjustment a pressure of about one atmosphere was continually 

brought to bear on the reservoir a, of the tube a &, the other end being in vacuo. To facilitate exhaustion, the flask is provided with a 

lateral arm, e, closed by fusion. A small vacuum gauge, g g, held in 

place by a layer of paraffine, h, shows the observer to what degree the 

vacuum is maintained. It is necessary to cover the rubber stopper// 

with cement. A number of tubes, a &, may be inserted, side by side.

127. Computation. The transpiration equation due to Poiseuille and 

theoretically corrected by Hagenbach 5 has the form

r *^ m 1 (1) '~ ~8^T 2l°/*7tl t V ;

where 77 is the absolute viscosity of the liquid, v the volume, in the mass 

transpiring through the capillary of length I and radius r in the time t. 

In the present case of excessively slow transpiration the corrective 

member may be neglected. P is the pressure-excess in dynes per square 

centimetre. Since all the magnitudes are to be expressed in cgs units, 

the dimensions of r/ are (g/cs).

1 Berlin, J. Springer, 1883, p. 153.

2 Slotte: Wied. Ann., 1888, vol. 20, p. 2C7. Similar results are obtained by others. Slotte gives the 

references.

"Since this was written Prof. J. D. Evorott, of Belfast, has kindly called my attention to certain 

experiments of v. Obermayer. Looking up this research iu the Wion. Ber., (2), vol. 75,1877, p. GC6,1 

found important data for pitch and storax obtained by a method quite different from mine, but agree 

ing very well with the order of my results for marine glno, and for paraffine. V. Obermayer finds for 

pituhat6-5° fj=2lX10"at 10'1°, T)=5'3X108, and at 12-2°, T)=2'6X108 . His datum for storax at J5-5°is 

!)=13X1010. Attention may here also bo called to some data for glycerine duo to Schiittner (Wien. 

Ber., 1879, vol. 79.)

* A valuable cement, being (nominally) a specially prepared mixture of rubber and shellac. It has 

a pitchy consistency.

6 Hagenbach: Pogg. Ann., 1860, vol. 109, p. 358. This reference is incidental or I should have to 

refer to Poisson, Navier, Stokes, Stefan, Helmholtz and others.
122 THE VISCOSITY OF SOLIDS. [BULL. 73.

In the above form of apparatus I is not constant, and v is measured 

in terms of the increase of length of the capillary thread ab, Fig. 26. 

Hence the equation corresponding to (1) 

(since dv = nr^dl] is

(2)

Integrating this equation between 0 and 

t, and between ^ and /2, and again solving 

for 77, there results \

ff = PrH/4: (V-tf) ....... (3)

an exceedingly simple expression. Here li 

is the original length (£ = 0) and Z2 the final 

length (t = t) of the capillary thread. The 

effect of the cylinder of viscous fluid in the 

reservoir may obviously be neglected in 

virtue of its large radius.

By way of digression I may insert another similar and interesting case, viz, 

that of a viscous liquid like glycerine transpiring in a vertical capillary tube in virtue 

of the weight of its own column only. In 

this case P=(L+l) 6g, where tf is the 

density of the liquid, g the acceleration of 

gravity, L the initial head of the column. 

Inserting these quantities in equation (2) it 

becomes

L + l~- 877 

whence by integration

77 = 

| FIG. 26. Apparatus for the secular 

transpiration of viscous liquids.

I give an example of the application of this equation in Table 74. 

Gylcerine is the liquid chosen, a substance which Graham1 pronounced 

too viscous for his apparatus, and for which no data are in hand.

'Graham: Phil. Trans., 18C1, vol. 151, p, 382. His glycerine work was done with " 18-hydrates." 

"The liquid (glycerine) is too viscous to be transpired by means of the bulb and capillary employed 

in these experiments." Graham, loc. cit.
BARUB.] LIQUIDS OF HIGH VISCOSITY.

TABLE 74. Viscosity of glycerine. 

r=-0505cm ; i = l-35cul ; fi = l'26; At=120>M'

123

t

sec.

30

150

60

180

90

210

120

240

270

390

300

420

330

450

360

480

t

cm.

10-07

20-30

12-72

22-75

15-30

25-10

17-80

27-43

29-82

38-60

31-95

40-83

34-20

43-04

36-40

45-22

Lln ^ + l<

- 80

 73

- 62

- 52

- 34

- 32

- 30

- 28

g/ca5-05

5-07

5-11

513

5-53

5-44

5-44

5-43

The observations though made upon a single descending thread at the 

end of each half minute are grouped in two batches. The tube was 

dry ; perhaps a moist tube (adhering thin film of glycerine) would have 

been preferable. To account for the difference of rj in the two sets of 

results is beyond the present purpose. It is noteworthy that each 

measurement occupies but 2 minutes, even admitting that the tube 

is unfavorably wide; for in the case of viscous liquids the temperature 

effect is of paramount importance, and this expedious method therefore has some advantages. The experiment may be varied by noting 

the descending upper meniscus while the lower end of the capillary is 

submerged in glycerine.

128. Data for marine glue. Applying equation (3) to the data of the 

following table, rf may be at once computed.

TABO!' 75. Transpiration of marine glue. 

P = 108 dynes; r = .0406""; temperature 25°.

Date.

May 7, 1889, 12"- ...

Dec. 7,1889,12'-...

t

sec 

0

18,490,000

I

cm 3-7

7-2

>)X10-6

gjcm sec

200

This is a remarkable result. -Since P in the above apparatus was 

probably not much smaller than one atmosphere, it follows that 17 was 

not much smaller; and yet the substance can easily be fashioned by 

the fingers, and a sphere if placed on a plane will run out to a flat 

cake in a few months. This type of viscous fluid is nevertheless 20 

billion times as viscous as water at the same temperature.

After long continued transpiration the thread of marine glue shows 

two strata. The advance portion is amber colored and less viscous}
124 THE VISCOSITY OP SOLIDS. . 73.

the rear portion brown, clearly containing most of the shellac. For 

this reason the observed datum for rj is probably somewhat too low. Of. 

§132.

129. Results for paraffine. Paraffine (melting point 55°), treated in 

this way showed absolutely no transpiration. The tube was nearly of 

the same bore as above (p=-0408cm), and the length of thread 2-2cm. 

The motion of the paraffine thread must have been below -Olcm, or it 

would have been detected. Hence the viscosity of paraffine must be 

considerably greater than 2xlOu g/cs, at about 25°.

SOLIDS.

130. Method of comparison. Having obtained the result of § 128,1 

proceeded to use it for obtaining the viscosity of hard steel by the 

method of comparison indicated.in § l&J. The apparatus was essentially like that used in my earlier experiments.1 To secure additional 

safety, however, I introduced the principle of substitution, whereby 

the steel wire and rod of marine glue were consecutively subjected to 

known torsion couples in ways otherwise identical. From the enormous 

viscosity of'steel as compared even with marine glue, a beam of this 

substance something like a decimeter thick would show about the same 

deformation, cseteris paribus, as a hard steel wire only a millimeter 

thick. So large a mass of marine glue would have been inconvenient 

to handle. 1 therefore used a rod about 4om thick and suitably apportioned the torsion couples in the two cases. The results are given in 

the following Tables, 76 and 77. Here 2p is the diameter, I the length 

of the similarly twisted rods. This twist, r, is given in the first columns, 

per cm. of length. The applied couples are proportional to 77. N denotes the viscous motion at*the index, at the time specified, and is given 

in scale parts, the distance between mirror and scale being 200cm.

Eeduction of JV is not necessary, since the present method is comparative. The steel wire was twisted alternately in opposite directions to 

allow for the accommodation. In the other case (Table 77), this precaution is not necessary, the substance being a viscous fluid. Three 

special twists are given in the table merely to show the behavior. 

Other experiments which I made with the cement may be omitted.

TABLE 76. Viscous deformation of hard steel wire No. 1. 

p = -040<:m i Z = 30 .

Twist, T

o

IK. 7

Time.

minutes. 

02' 

3 

4 

6 

8 

10 

12

JV

em.

 00 

 70 

1-15 

1-87 

2-35 

2'78 3-15

Twist, r

o 

V7

Time.

minutes. 

0

2 

3 

4 

6 

8 

10 

12

N

cm.

 -00 

 -71 

 1-25 

 2'00 

 2-58 

 3-01 

 3-40

Twist, r

o

5-8

Time.

minutes. 

0

2 

3 

4 

G 

8 

10 

12

If

cm.

 00 

 40 

 72 

1-22 

1-60 

1-90 2-12

1 Am. Jour. Sci. (Ill), 1887, vol. 34, p. 2. PI. I, this Bulletin.
*m

BAUUS.] ABSOLUTE VISCOSITY OF STEEL. 

TABLE 77. Viscous deformation of marine glue.

125

Twist, T

o

*l-4

Time.

minutes.

0

2

3

4

5

N

cm. 0

2-6

4-8

7-1

91

Twist, r

0

1-4

Time.

 minutes.

0

2

3

4

5

-ZV

cm. 0

2-5

4-5

7-0

9-0

Twist, T

0

1-4

Time.

minutes.

0

2

3

4

5

6

N

cm. o

2'2

426-1

8'1

101

' This refers to the steel wire (normal). The initial twist of the bar of marine glue is practically zero.

'1

FIG. 27. Viscous deformation of 

a bar of marine glue compared with 

a bard steel wire.

131. Discussion of results. From these tables (graphically constructed in Fig. 27) it 

appears that the mean rate of motion in case 

of marine glue is 2cm per minute, whereas the 

corresponding motion for hard steel is (say) 

0-4cm per minute, this being the mean for the 

three cases. Further distinction will be made 

below, §133 et seq.,but is here unnecessary. 

Again, the couple acting on the cement is 

l'4o?, while the couple in the other case is 

5-7x. Since the cement is a liquid, the rate 

of viscous motion will increase as the couples. 

Hence for identical couples (5-6#, say) the 

motion for marine glue would be 8cm, whereas 

the rate for steel is 0-4cm, as above. 1 will 

now apply the principle1 mentioned in § 123, 

whereby viscosities are, cseteris paribus, inversely as the fourth power of the radii. If 

rf and 7/be the viscosities of marine glue and 

hard steel, respectively, then

rf_ /-04V 04 (1)

From Table 75, //=200xlOG g/cs. Hence

(2)

where ?? is the mean viscosity of originally 

untwisted glass-hard steel, during three consecutive alternate twists of about 12m duration each.

132. Errors encountered. To fully interpret the result (2) it would have been necessary to compute the 77 for consecutive 

times during each of the consecutive twists. 

This I will do below, where the method used 

is direct and much more sensitive. The pres-

"Anj. Jour. Sci., 1887, vol. 33, p. 36.
126 THE VISCOSITY OF SOLIDS. [BULL. 73.

ent results subserve their chief purpose in furnishing an estimate of 

the order of viscosity of glass hard steel, which may then be compared 

with the more detailed statements. Of. § § 134, L35.

The errors encountered in the above comparative method are these: 

In the first place, the thread of marine glue which transpires, § 128, is 

not identical with the rod of this material which is twisted, either as 

to temperature or composition. Cf. § 128. These difficulties are almost 

insuperable, though possibly better results .might be obtained with 

pitch. Again, the. rod of marine glue, while it is being twisted, is 

also being stretched by its own weight. This makes the angular measurement difficult, for it is hard to manage a thick rod satisfactorily. 

Finally, from this cause and the difficulty of obtaining and keeping a 

rod of the cement free from bubbles, straight and round, the sectional 

error is considerable. Regarding the above result, I should be surprised if hard steel were less viscous than 1016 or more viscous than 

1017, under the conditions given.

133. General remarks on solid viscosity. Before giving the results of 

the following direct method, it is desirable to insert a word on the viscosity of solids generally. In the above case, § 130, while the steel wire 

is strained by the couple almost as far as the limits of elasticity permit^ 

the rod of marine glue is initially scarcely strained at all. In the latter 

case, however, the unstable configurations essential to viscous motion 

are continually supplied in very great number by the ever changing 

distribution of the heat agitation within the body. In a homogeneous 

solid (soft steel) these configurations are supplied only in vanishing 

number. I doubt whether in soft steel the viscous deformation due to 

instantaneous exceptionally intense heat motion at different points of 

the solid could be recognized at ordinary temperatures. The case is 

different when the solid is under stress. Any twist, no matter how

small, is accompanied by a proportionate amount of permanent strain. 

With this a similarly proportionate amount of instability is necessarily 

associated. Hence it must be carefully borne in mind that the viscosities expressed absolutely below refer to steel in a condition of strain 

just within the limits of elasticity.1

Now it is clear that if the stressed steel be left to itself the number 

of unstable configurations becomes rapidly less as the time after twisting increases. The viscosity of solids is therefore essentially a time 

function as well as a strain function.

134. Apparatus for direct method. The apparatus with which the 

following absolute results were obtained is shown in .Fig. 28. AA and 

BB are two massive torsion circles, the hollow cylindrical shafts oo 

of which are firmly clamped to supports projecting from the wall of the 

room. The steel wire ww to be tested is tensely drawn between the

'I can here merely allude to the recent and suggestive paper of C. H. Cams-Wilson (Nat., vol. 41, 

p. 213, 1890), in which the behavior of steel near the elastic limits is interpreted in analogy with the 

well-known circumflexed isothermala of Jamea Thomson.
BAUDS. J APPARATUS FOR ABSOLUTE VISCOSITY. 127

cylindrical cores ala'l' of AA and BE, and clamped without torsion. 

To accomplish this the ends of the wire ww are bent hookshaped and 

inserted in a fissure at the ends of the rods al a'l1 , the clamp screw 

(shown at a') passing through the loop of the wire. The middle part of 

the wire icw carries a pair of small brass plates 6c, screwed together

FIG. 28.-Apparatus for measuring the absolute visooaity of solids.

by four screws in such a way as to hold the wire firmly between the 

plates. A brass rod of screw wire dd is soldered to the upper plate, 

and when in adjustment is at right angles to the axis of ww. The rod 

dd is virtually the beam of a balance, and two small nuts mm', symmetrically placed near the ends of dd, are provided with hooks, from 

which a scale pan hh may be suspended. The latter carries a light 

horizontal disk vv, to be submerged in water (not shown), with the 

object of deadening vibrations when the apparatus is in adjustment. 

The upper plate &c also carries an adjustable mirror N" for angular 

measurement, as well as an index fg, moving across a stationary graduated dial (not shown in figure), by which the amount of twist which 

holds the weight P in equilibrium is roughly registered.

In adjusting the apparatus the scale pan hh is removed, and the rods 

al so placed that the lever dd is vertical. After thoroughly clamping 

al (care being taken to avoid twisting the wire ww), the scale pan is attached at m', and additional weights P added, such as hold the lever 

dd horizontal. Hence the two halves of the wire ww are twisted 90° 

each for the whole length. Other twists may be applied by rotating 

the torsion circles and adding suitable weights P.

To fasten the wire between the plates ab the lower one is clamped 

in a vise, and the four screws then fastened securely. There is no rotational sliding here under the given stresses, as is proved by exam-
128 THE VISCOSITY OF SOLIDS.

ining wires of exceedingly high viscosity. Some difficulty is experienced in originally fixing the wire ww in place quite free from torsioual 

strain. There is also some flexure. But for wires of the radius given 

these discrepancies are negligible in comparison with other errors inherent in the wires. In examining the effect of strain on viscosity it 

would be desirable to connect A and B rigidly together and express the 

strain in terms of the weight P; but this is beyond the purpose of the 

present paper.

135. Method of computation. To compute 1 the results obtained with 

the apparatus just described, let 2cp be the amount of viscous angular 

motion in radians of any, right section of the wire relative to another 

right section whose distance from the first is the unit of length. Then 

in the given adjustment the mirror registers an angle corresponding to 

2cp ; since at each section, though equal angular detorsion takes place 

in opposite directions, both must influence the mirror in view of the 

constancy of the twisting couple. Furthermore, suppose that in the 

plane of a right section there is no shearing. Then 2dcp/dt=2Ct is the 

common angular velocity with which the shear is increased throughout 

the length of the wire. Consider any elementary cylindrical shell whose 

length I is the effective length of either half of the wire ww and whose 

right section is Znrdr, where r is the radius of the section. Then the 

amount of force distributed uniformly over 2nrdr will be

Multiplying by r and integrating, both sides between 0 and p, the radius 

of the wire, .

P\=2Ct ....'..... (5)

where P is the weight at the end of the lever arm A, by which the system is held in equilibrium. In any given adjustment PA/;rp4=A, and 

is constant. Hence

r?t=A/2Ct ......... (6)

In these equations it has been tacitly assumed that frjr3dr=r[tfr3dr. 

Under any conditions, therefore, r/t is a mean value for the sections defined by these integrals.

136. Data obtained. With these equations at hand it is not difficult to 

understand the results of the following tables, 78 to 81. Here p is the 

radius and I the length of each effective half of the steel wire. P is the 

total force (being the weight plus the weight of scale pan) acting at the 

end of the lever arm A (see Fig. 28). The rate of twist is given under r 

in degrees, and 2<p' is the total yield (in degrees) observed at the end of 

the experiment. N denotes the actual scale reading in the telescope at 

the time given, and 2cp is the viscous angular motion in radians between 

two right sections whoso distance apart is lcm.

1 The quantity 2</> ia here used conformably with my earlier papers,
HARU8.] ABSOLUTE VISCOSITY OF STEEL. 129

In the second half of the tables 2(7 the time rate of change of 299 is 

inscribed, and the final column coutains the computed viscosity for the 

time specified. All times are reckoned from the moment at which the 

twist is applied. To obtain 2(7,, I availed myself of graphic methods, 

these being quite in conformity with the mean accuracy of the work. 

Table 78 contains results for the wire No. 1, already twisted in Table 

75 above. Three twists are applied alternately in opposite directions. 

In Table 79 the same wire is similarly examined after it has been 

softened by heating to redness and cooling in air. Table 80 supplies 

data for a new glass-hard steel wire, originally free from stored twist. 

Table 81, finally, contains the viscous constants of a wire tempered at 

450°. This is the identical wire with which I made my earlier differential observations.

TABLE 78. Absolute viscosity of glass-hard steel wire No. 1. 

7i' = 200cm ; Z = 12-9cra ; P=82X 981 dynes; p=-0105cm jA=9-43cin. 

FOURTH TWIST.

T 

24,'

O

+7

Time.

sec.

0

420 

720 

1020 

.1800 

22"0 

2820 

3480

JV

cm.

Twisted. 00 

1-04 

1-80 

3-20 

3 'GO 

4-17 4'Gj

106 X 2<f>

radians 

per cm.

0 

202 

349 

021 

COS 

808 -901

Time.

sec.

500 

1000 

1500 

2000 

2500 

3000

2<7t X10'

radians 

per cm. 

per sec. 

735 

462 

310 

222 

183 

150

V10"

Olcs.

122 

194 

291 

405 

491 

UOO

FIFTH TWIST.

7

 5 0

480

840

1320

18CO

2400

2940

3180

 00

1-20

2-35

3-29

4-02

4-04

5'20

0

233

456

638

779

900

1008

500

1000

1500

2000

2500

3000

910

474

347

270

230

210

ino

259

333

391

428

SIXTH TWIST.

7 5

_ 

0

360 

9CO 

1260 

1800 

2340 

3120 

3900

 00 

1-20 

1-60 

2-10 

2-50 3-06' 

3-53

0 

233 

310 

407 

485 

593 

C48

500 

1000 

]500 

2000 

2500 

3000

467 

265 

193 

156 

138 

126

193 

339 

460 

577 

652 

715

Bull. 73 0
THE VISCOSITY OF SOLIDS. 

TADLE 79. Absolute viscosity of soft steel, being ivire No. 1.

| DULL. 73.

; A = 9-43 ; Z = 13-0cm ; p=r'0405i:m. 

HEATED TO REDNESS IN AIR. FIRST TWIST.

T

O

+7 4

Time.

sec.

0

420

900

1500

2100

2700

3300

3780

N

cm.

 00

 40

 63

 80

 92

 98

1-03

2$X106

radians

per cm.

0

77

121

154

177

188

198

Time.

sec.

Kf\f\ UUU

1000

1500

2000

2500

3000

2(7t X 109

radians

per cm.

per sec.

&£.\t 99fl

89

63

47

34

26

V10'6

g/cs.

409

1010

14JJO

1920

26fO

34UO

SOFTENED. SECOND' TWIST.

7

 6 0

360

1020

1500

1980

2520

3120

.00 50

 70

 82

 93

1-00

0

96

135

158

179

192

500

1000

1500

2000

2600

3000

116

59

40

30

15

550

776

1520

2250

3000

6000

SOFTENED. THIRD TWIST.

+.J 0

240

840

1560

2100

2520

2640

3120

 00

 42

 64

 74

 76

 78

 81

0

81

123

142

146

150

156

Cflrt ouu 

1000

1500

2000

2500

3000

1 QQ loo

70

40

28

17

14

ft f=i 9 DO^

1290

2250

3210

5300

6400

TABLE 80. Absolute viscosity of glass-hard steel wire No. 2.

J=13-0cm ; p='0405cm i -B=200 ;P=82XS81 dynes; A=9-43cm. 

FIRST TWIST.

r 

2$

0

7.0

 6

Time.

sec.

0

120

420

720

1080

1620

2100

2580

3000

2V

cm.

 00

1-86

2-70

3-35

4-JO

4-58

4-95

5-18

'2<f>X10B

radians

per cm.

0

358

520

644

789

881

« 952

996

Time.

fee.

500

1000

1500

2000

2500

2(7tX109

radians

per cm.

per sec.

fiftn

325

230

180

140

WIO'6

g/cs.

277-2

391-5

500-0

643-0
ABSOLUTE VISCOSITY OP STEEL. 131 

TABLE 80. Alsolule viscosity of glass-hard steel wire, No. 2 Continued.

GLASS-HARD. SECOND TWIST.

r

H

O

n.o/ O

 6

Time.

sec.

0 

240

COO

QUO

1200

1800

2100

2460

2700

3000

N

cm.

 00

1-44

2-20

2-88

3-65

4-04

4-50

4-70

5-02

2<J>X106

radians

per cm.

0

277

423

554

702

777

8G5

004

965

Time.

sec.

500

1000

J500

2000

2500

actxio9

radians

per cm.

per sec.

/too Uoo

392

285

240

205

VIO"

gleg.

IQl'i 4uL *

229 '5

3100

375-0

439-0

GLASS-HARD. THIRD TWIST.

 0 

240 

GOO

 00 

1-17 

Wire bre

0 

225 

iks sponta neously

TAIII.E 81. Absolute viscosity of steel annealed at 450°, wire No. 15.

J = 13'6 ; p = '0405°«>; 72=200 ; P=82 X 981 dynes; \ = 9'43"".

TWISTED INDEFINITELY.

T

20'

o

4-7°

 I

'Time.

sec.

0

240

720

1200

1866

2520

3000

N

cm.

 . 

 00

 51

 71

 80

 95

1-01

2<f>X106

radians

per cm.

 

0

94

131

158

175

186

Time.

sec.

500

1000

1500

2000

2500

3000

2Ct X109

radians

per cm.

per sec.

177

69

40

32

25

20

, t /10's

g/cs.

508

1300

2250

2810

3600

4500

NEXT TWIST.

-7°

 2 0

240

COO

1200

1740

2580

3240

 00

 26

 43

 54

 68

 81

0

48

80

100

125

149

500

1000

1500

2000

2500

3000

111

46

40

34

31

30

fill

1950

2250

2650

2910

3000

NEXT TWIST.

4.70

 2 0

240

C60

1260

1740

2520

3120

 00

 48

 78

 92

1-12

1-26

0

88

143

J69

206

232

500

lOuO

1500

2000

2500

3000

180

82

57

48

45

42

500

1100

1570

1870

2000

2140
132 THE VISCOSITY OP SOLIDS. [BULL. 73.

Some few irregularities are introduced into the above data, from the 

fact that vibrations could not be rigorously excluded. Inasmuch as 

vibration increases the rate of twist periodically, it thus supplies a 

greater number of instabilities than exactly correspond to the mean 

twist (position of equilibrium) in question. Hence viscosity is decreased 

by vibration. .

In case of No. 15 and No. 2, etc., the rate of twist of the two halves 

of the wire ww (Fig. 28) was possibly not quite the same. Hence the 

viscous motion would also be slightly too large. In case of different 

mean lengths Z, in two different wires, the rate of twist for the same 

load P would again be different, thus introducing small discrepancies. 

Finally for No. 15, which had become somewhat worn after long use, 

the load P probably strained the wire too near the elastic limits. This 

supplies fresh instabilities by which viscosity is successively decreased 

from twist to twist and accords with the results actually obtained. 

Hence it is best to accept the behavior of the softened wire No. 2 as 

typical of No. 15. Steel annealed at 450° and at 1000° is of equal viscosity, as I have shown in numerous experiments.

DISCUSSION.

137. Retrospective. Turning first to the values (p, it is seen at once 

that they substantiate the results of my earlier papers throughout.1 

They need not therefore be further commented on here. Table 81 perhaps has special interest, since the <p here contained is the datum for 

the normal wire formerly used. With this datum in hand, the results 

of the earlier papers may easily be reduced to absolute values, for I have 

endeavored to make the angles r of the same value in both cases, so 

that gj/r may be comparable at once.

138. Spontaneous breaking. The spontaneous breaking of the glasshard wire in Table 80 is worthy of remark. It occurred during the third 

twist, and at a time when the wire was in no way interfered with. This 

corresponds to the spontaneous explosion of tempered projectiles frequently observed. It also corresponds to the spontaneous rupture of 

stressed glass, whether the stress be stored internally or applied externally. I have observed this interesting phenomenon in glass under 

a great variety of conditions. In all cases there is gradual molecular 

change, or slow viscous yielding to the point of rupture.

139. Time variation of absolute viscosity. The chief results of Tables 

78 to 81 are the values rjt , whether they be regarded as time functions 

or as exponents of the degree of solid state. In PI.VI, I have therefore 

constructed them graphically. As an inspection of the figure shows at 

once, both the viscosity and its rate of increase with time are greater in 

case of hard steel (Tables 78,80) than in soft steel (Tables 79,81). After 

about an hour's time the final viscosity of hard steel may be quite as

1 Am. Jour. Sci.(ITI), 1866, vol. 32, p. 181-192, and 1887, vol. 33, p. 20-36.
U. S. GEOLOGICAL SURVEY BULLETIN NO. 73 PL. VI

ZOOO OOOO

CHART SHOWING THE ABSOLUTE VISCOSITY OF HARD STEEL (TABLES 78 AND 80) AND OF SOFT STEEL (TABLES 79 

ANn P,1) DURING THP FIR°.T HOUR AFT^B TWISTING .IU«VT WITHIN THF FI ASTIO I IMItP
BARUS.] EATE OF INCEEASE OF SOLID VISCOSITY. 133

large as the initial viscosity of soft steel. For equal times after twisting, the viscosity of soft steel is enormously the greater.

The curves show no pronounced curvature, being in part convex and 

in part concave. This is particularly clear in the case of hard wires, 

where the viscosities are smaller, the viscous deformations large, and the 

observations therefore, as a whole, much more accurate (Tables 78, 80). 

The extended curves (Tables 79, 81) for soft wires, on the contrary, are 

less certain, because the viscous deformation is proportionately smaller. 

Hence I may regard the promiscuous irregularities of the, curves of PL 

VI clue to errors of observation and construction. .It is exceedingly 

difficult to draw tangents correctly. Again, the observations are hampered by vibrations, etc., in the way indicated at the end of § 136. According to Kohlrausch's law,2 d(p/dt=a,(p/tn, where a and n are 

constants. In case of small torsions, or during short times, the simple 

relation d(pl'dt=a(p/t suffices. Thus the character of the curves of 

Fig. 33 may be considered linear during the first 3000 sec. after twisting. Viscosity therefore increases proportionally to time, at the rates 

expressed in the following Table 82:

TABLE S2, Eate of increase of the absolute viscosity of steel.

Hard 

steel.

Tab. 4

Tab. 0

Twist.

+4

 5

+G

+1

-2

ID-'* 

T)/sec

0/«'

220

140

240

230

140

Soft 

steel.

Tab. 5

Tab. 7

Twist.

+1

 2

+3

+1

-2

+3

10-1*

Tj/see.

fif/cs2

1200

1400

1900

1500

1200

1000

Table 82 shows the mean rate 77 / see. for hard steel to be 194 xlO12 

and its mean viscosity 77 at 500 sec. to be 140 x 1015 ; for soft steel r)/sec.= 

1400xlO12 and mean viscosity at 500 sec., ?7=570xl01&. The general 

explanation of these results has been indicated in §133. In a liquid or a 

viscous fluid under moderate stress the instabilities are supplied by the 

mere thermal agitation at ordinary temperatures at the same rate in 

which they are usediu promoting the viscous motion. Hence viscosity is 

constant at a given temperature. In a solid this is not the case; instabilities are here expended at a rate decidedly greater than the small rate 

of continuous supply. Thus viscosity decidedly increases with time. 

Suppose therefore a substance of initially greater viscosity to start 

on its viscous deformation at an instant when the viscosity of a substance of initially smaller viscosity has been increased by tiipe to the 

initial value of the former case. This can be realized by twisting the soft 

steel about an hour after the hard steel rod has been twisted. Then 

in the succeeding times, even though the substance of greater and the 

substance of less viscosity start at a stage of equal viscosity, the visz.Kolilr.auscb: Pogg. Ann., vol. 128,1800, p. 216.
134 THE VISCOSITY OP SOLIDS. ;{BULL. 73.

cosity of the former will rapidly overtake the viscosity of the latter; 

for the supply of instability due to temperature alone is continuously 

greater in one case than in the other.

140. Solidity of the three states of aggregation. Summarizing the results 

of the above paragraphs, the viscosities of the three states of aggregation may be expressed in terms of the absolute g/cs scale as follows:

TABLE 83. Viscosity in its variation with the &tate of aggregation.

GaHds and vapors.

Substance.

*Etber,0°

*H2> 0°.

*Air, 0°.

toa,o°.

Range . .

1

6-8 X10-6

8-7 X10-6

I-75X10-"

2'12X10-4

10-6 to?

Andrews's

critical

Substance.

1

Range

1

?

?to?

Liquids. J

Substance.

t Etber, 30°

t Ethery 10°

{Water, 97°

I Water ,20°

Glycerine**

Eange .....

i)

9 X10-4

1-9 X10-3

3-0 X10- 3

1-OOX10-2

5

? to 108

Viscous fluids.

Substance.

Marine ? 

glue }

Range . .

I

4XI08

lonoio"

Solids.

Parafline, )

(m.p. 55°)>>4X10" 

at 20°. )

ttHard steel, ?10" to

glass, etc. J 10 18.

ttSoffc ?CX10" to

steel. }6X1018.

Range... 10" to 102U

* Puluj : loc. cit.

10. E. Meyer: loc. cit., p. 142.

J Landolt and Boernstein's tables (loc. cit.) and Slotte (loc. cit.).

** Bough measurement of my own, § 127.

tt During the first hour (500 to 3,000 seconds) after twisting just within the elastic limits.

The limits here defined are of course somewhat arbitrary. They will 

be made more definite when a greater number of bodies lying on the 

boundary between the classes have been examined. Information is 

notably lacking in relation to Andrews's critical temperature, which, in 

the light of the context of Table 83, is particularly interesting.1 It is 

not improbable that the critical temperature may be definable by a 

narrow limit of viscosity, quite independent of the substance operated 

on. What this limit will probably be I do not venture to assert, seeing 

that the viscosity of gases decreases on cooling, whereas that of liquids 

increases on cooling.

Table 83 gives the positively astounding range of variation of 77, the 

chief variable of our material environment a variable which throughout the whole enormous interval nowhere fails to appeal to our senses. 

Knowing these data, it will be possible to look somewhat into the insides of solids and to express the existing state of instability statistically. But this calls for an application of more searching mathematics 

than I am justified in attempting.

1 Professor Warburg has had the kindness to refer me to an elaborate paper by himself and v. Babo, 

in wbich the vicosity of carbon-dioxide passing continuously through the critical temperature is elaborately considered. (Wied. Ann., vol. 17,1882, p. 390.) Unfortunately, I can here do no more than call 

attention to this valuable contribution, wbich was inadvertently overlooked in my original study of 

the subject. Warburg and v. Babo's results are such as conform with the substance of the above text 

and I am glad to acknowledge that they were the first in the field to to approach the question.
BAKUS.J THOMSON'S VISCOSITY. 135

In concluding, 1 may state that though I am cognizant of the reasons 

which induced Sir William Thomson to apply the word viscosity to the 

phenomena of the present paper, I wish he had chosen some other 

term. Viscosity is misleading. Undoubtedly a substance which is 

infinitely viscous is solid, for the parts of such a body are stuck together beyond the possibility of permanent yielding. This truth, however, is of the kind which Gauss' in referring to Lagrange's extension 

of the principle of least action, called "niehr witzig als wahr." Unfortunately the impressions conveyed in speaking of a very viscous body 

and of a solid body are different. I do not know, but I think solidity 

\\ould have been a better word than viscosity.

JCf. Klein: Die Piincipien der Mecliauik, Leipzig, Teubner, 1872, p.33.

INDEX.

A.

Page.

Absolute viscosity of the three states of

aggregation...................--. 134

Accommodation in hard steel......... 63,88,90,92

Alloying, effect of, on viscosity........... 86,88

Alloys of platinum, viscosity of.......... 84

Alternate twisting....................... 90

Analogies of Clausius's and Maxwell's

theories.......................... 78

Andrews's critical state, viscosity of..... . 134

Annealing,defined....................... 55

laws of............................... 101

effect of, on magnetization............ 102

Annealing steel, method of............... 8

Apparatus, bifllar, for torsional viscosity 3 

tubular, for torsional viscosity....... 5,38

for annealing steel................... 8

quadrifilar, for torsional viscosity ... 37 

unifllar, for torsional viscosity....... 53

for quenching steel .................. ' 76

for magnetic detorsion............... 106

for secular transpiration............. 121

for absolute viscosity of solids....... 126

Areas of bifllar wires .................... 45

B.

Barrett, on molecular changes in iron...51,52,119 

Earns, Anna H. experiments of........... 73

Batchelder, on exploding steel......°...... 50

Banr, magnetic work of.................. 52

Bifllar apparatus for torsional viscosity.. 3, 9,28,

39,44

Boiling crucible.......................... 9

Boiling tube.............................. 8,54

Boltzmann's theory of viscosity.......... 75,89

Braun's experiments in viscosity........ 76

C.

Carburation instability .................. 78

Cast iron, density of ..................... 49

Chernoff, on temperature of hardening... 52

Cheesman, researches of ................. 51

Chwolson, on resistance of iron .......... 52

Clauaius's theory of electrolysis ......... 74,78

Clausius's views on shear................ 75

Clausius's and Maxwell's theories compared .............................. 78,104

Configurations, molecular, classified..... 102

unstable, supply of .................. 126,134

Copper, viscosity of...................... 35

Couple, intensity of...................... 42,98

Critical state, viscosity at................ 134

Cyclic twisting ......................... 93

D.

Paga. 

Deformations, sudden and gradual, com.

pared .......................i...... 72

Dimensions, effect of, on magnetic rigidity 113,114 

Drawn strain, effect of, on viscosity...... 88

Dynamometer, electric................... 105,116

E.

Elasticity of tempered steel.............. 45

Elementary magnetic helix.............. 116

Electric dynamometer................... 105,116

Electrics and viscosity of steel........... 44,93

Errors of the bifllar apparatus........... 9,28

Everett, elastic experiments of .......... 49

E verett, J. D., suggests data............. 121

Ewing,work of........................ 51,93,118

F.

Filamentary wires,magneticadvantagesof 115

Friction, static, nature of................ 49

Fromme, magnetic and other work of ... 51,52

G.

Gases, absolute viscosity of.. ........ 120

Glass, viscosity of ...................29,47,49,100

Glasshardness defined.................... 99

Glycerine, viscosity of ................... 123

Gore on molecular changes in iron....... 119

Gore's phenomenon in steel.............. 48,51

Graham, transpirations of ............... 122

H.

Hagenbach's transpiration equation ..... 121

Hardness defined ...... ............... 44

Hardness and viscosity compared ........ 42,44

Hardness and viscosity contrasted....... 97,98

Helix for magnetization.................. 106,116

Hopkinson defines coercive force........ 50

Howe, on rigidity of hot iron............. 52

Hysteresis.........---.-. ........ ... 92,118

I.

Intermittent fields .................... 116

Iron, viscosity of .........................31,47,51

magnetized, viscosity of ............. 108

magnetized,rigidity of ............110,112,118

J. 

Jeans, on cementation of steel............ 52

137
138 INDEX.

K.

King Clarence, aids research............. xi

Kohlrausch, researches of................ 2,45, 75

views of, on viscosity................75, 77, 89

law of................................. 133

L.

Liquids, absolute viscosity of............ 121

M.

Magnetic coefficient of rigidity.......... Ill

Magnetic effect of annealing.............. 102

Magnetic intensity and viscosity ........ 50

Magnetic stability ....................... 103

Magnetism and viscosity ................ 103

Marine glue, viscosity of ................ 121,123

Maxima of viscosity and of magnetism... 50 

Maxima obtained in viscous comparisons'. 33,46 

Maxwell's theory of viscosity............ 2,77

Maxwell and Clausius's theories compared 78,104 

Metals, effect of temperature on viscosity

of................................ 70

Meyer's theory of viscosity.............. 75,76

Molecular structure, complex and simple. 102 

Molecular configurations classified....... 102

Molecules rotated in magnetism and viscosity ............................ 110

Motional annealing...................... 92

N.

Newton's definition of viscosity ......... 46

Neesen's theory of viscosity............. 75,76

Nickel, viscosity of ......................* 35

Nissen's theory of viscosity.............. 77

Notation ................................12,14,55

0.

Obermayer (v.) on viscosity of pitch and

storax............................ 121

Obliquity of external fibers... .92,103, 111, 113,115

124

2

6

83

45

71

Paraffine, viscosity of..................

Pisati, experiments of .................

Plane-dot-slot arrangement ............

Platinum alloys, viscosity of...........

Polarization ...........................

Pressure, effect of, on viscosity........

Q.

Quadrifllar apparatus for torsional viscosity............................... 37,47

Quenching steel, method of.............. 6

Quenching, effect of, on viscosity........ 48

E.

Eesidual induction, thermal relations of.. 102

Eesidual phenomenon.................... 45

Eesidual twist........................... 58

Eeynolds, Osborne, defines dilitancy..... 77

Eigidity, change of, with temperature.... 71

magnetic coefficient of............... Ill

Eigidity of magnetized iron .....

of magnetized steel..........

Eoberts, Austen, defines temper. 

Eolation of molecules ...........

Eowland, H. A., aids research....

.. 110

.. 118 

.. 55 

.. 110 

.. 6 

Eupert drop, viscosity of ........ .48, 49, 50, 71,101

S.

Secular annealing of hard steel.......... 94

transpiration......................... 121

Schmidt, researches of................... 2

Schroeder, experiments of.......... 2,3,86,' 70,101

Slotte on viscosity of water.............. 121

Spontaneous rupture of hard steel....... 132

Stability magnetic, thermal, etc.......... 102,103

States of aggregation, absolute viscosity

of................................ 134

Steel, phenomenal quality of............. xi

method of quenching ................ 6

method of annealing................. 8

annealed, viscosity of................ 82

soft, viscosity of..... .25, 34,37,60,63,64, 66,96

annealed at 25° and 100, viscosity of. .14, 61,81,

94, 95,99 

annealed at 190°, viscosity of........18,61, 64,

80, 81,82,96 

annealed at 360°, viscosity of....... .21,30,62,

64,66, 96 

annealed at 450°, viscosity of........23, 62,64,

67, 80,96 

magnetized, viscosity of ............. 107

magnetized, rigidity of............... 118

absolute viscosity of ................ 124,128

spontaneous breaking of............. 132

Strain, effect of, on viscosity............. 47, 88

intensity of, in steel and glass.... 100

Stress, intensity of, in hard steel and glass 49 

and viscosity .................... 72,97

Streintz, researches of................. 2,75,88,92

Strouhal aids research.......... xi, xn, 94, loo, 120

T.

Tables, index of.......................... 13

Tait, thermoelectrics of..... ......... 51,52

Temper defined.......................... 55

Temper, effect of, on viscosity............ 41

Temper strain in general ................ 101

Temperature, effect of, on viscosity. 60,68,69,70,72 

. 190°, effect of, on viscosity........... 64

360°, effect of, on viscosity........... 66

Theories of viscosity..................... 74,75

Theory of the bifilar apparatus ........9, 28,39, 44

Theory of the unifllar apparatus......... 55

Thomson, researches of.................. 2,42

Thomson defines viscosity ............... 135

Time variation of absolute viscosity..... 132,133

Tomlinson on the viscous effect of magnetization ....................... 105

Torsion couple, intensity of.............. 42

Torsion, literature of.................... 113

Transpiration secular, apparatus for..... 121

Tubular apparatus for torsional viscosity. 5, 38
INDEX. 139

Twist, residual, after annealing. 

Twihting alternately............

Page. 

58 

90

TJnifllar apparatus for torsional viscosity. 53 

TJnifilar apparatus, theory of ............ 55

Unstable configurations, supply of....... 120,134

V. 

Vapors, absolute viscosity of ..........

Viscosity of viscous fluids..............

Viscosity, definition of.................

W-cruciblo for annealing ..............

120

121

135

8,9

W.

Page. 

Warburg, electrolyses glass ............. 45,71

magnetic work of.................... 51

theory of viscosity................... 76, 77

suggests data ........................ 134

"Weber "W., discovers viscosity........... 2

views of, on viscositj ...'............. 75, 77

theory of magnetization.............. 110

Wieclemann, G., on alternate magnetization ................................ 51

on accommodation ................... 89,92

on magnetism and torsion............ 103,105

Williamaon's theory of etheriflcation .... 74