DEPABTMENT OF THE INTEBIOB

BULLETIN

OP TUE

UNITED STATES

GEOLOGICAL SURVEY

No. 36

WASHINGTON

GOVERNMENT PRINTING- OFFICE 

1886

UNITED STATES GEOLOGICAL SUBVEY

J. TV. POWELL, DIRECTOR

SUBSIDENCE

OF

BY

CA.HL B.ARTJS

WASHINGTON

GOVERNMENT PRINTING OFFICE 

1886

CONTENTS.

Page.

Letter of transmittal........................................................ 9

CHAPTER I.

General relations of the phenomenon of subsidence ...................... .... 11

Introductory............................................................ 11

General inferences ...................................................... 13

Analogies........................................................... 13

The physical variables .............................................. 14

Stratification ...............-..........- ... .- .. - -.- -.- '- 15

Analogies........................................................... 15

Descriptive equation............ .................................... 16

Effect of density of mixture......................................... 19

Sharp demarkation ................................................. 20

Temperature.............................................. ....^......... 20

Chemical effect ...................................................... 20

Physical effect...................................................... 21

Precipitants ............................................................ 24

Chemical effect ..................................................... 24

Physical effect...................................................... 24

Experimental results................................................ 26

Discussion.............................................................. 33

Mechanical relations ..........................°...................... 33

Electrical relations.................................................. 35

Particles of larger dimensions....................................... 36

Subsidence and viscosity............................................ 38

Conclusion.............................................................. 39

CHAPTER II.

The dependence of rate of subsidence on order of surface, concentration, and

turbidity ......................................................... 41

Experimental results.................................................... 41

Introductory............................ ............................ 41

Data ............................................................... 42

Deductions ............................................................. 48

Surfaces of different orders...................... .................... 48

Concentration ...................................................... 49

Turbidity........................................................... 50

Sedimentation battery .............................................. 50

Index ............................................................ ......... 53

(509) 5

ILLUSTRATIONS.

/ Page. 

FIG. 1. Relation of opacity to time of subsidence at different depths.......... 18

2. Apparatus for subsidence at 100° ................... .................. 23

3. Relation of rate of subsidence to order of surface for different degrees

of turbidity....................................................... 49

4. Relation of rate of subsidence to turbidity for consecutive orders of surfaces .......... .................................................... 50

(511) 7

LETTER OF TRAHSMITTAL.

DEPARTMENT OF THE INTERIOR, 

UNITED STATES GEOLOGICAL SURVEY, 

DIVISION OF CHEMISTRY AND PHYSICS,

Washington, D. C., January 18,1886.

SIR : I have the honor to transmit, through Prof. F. W. Clarke, Chief 

Chemist, the accompanying paper on the subsidence of fine particles 

of insoluble solid in liquids for publication as a bulletin of the Survey. 

Very respectfully,

CABL BAEUS. 

Hon. J. W. POWELL,

Director U. 8. Geological Survey, Washington, D. C.

(513) 9

SOLID PARTICLES IN LIPS.

By CAUL BARUS.

CHAPTER I.

GENERAL RELATIONS OF THE PHENOMENON OF SUBSIDENCE.

INTRODUCTORY.

The remarks in this paper were suggested by Prof. W. H. Brewer's 

memoir on sedimentation, to a condensed account of which I had the 

honor of listening at the New Haven meeting of the National Academy 

of Sciences, November, 1883.

It is my endeavor in Chapter I to analyze the phenomenon of subsidence into parts such that the conditions under which subsidence is 

to be explained from a chemical or from a physical point of view 

may be better discernible. As an attempt is made to cover as much 

ground as possible, the chapter is largely qualitative in character. 

With these data in hand I then begin the quantitative study of but 

one of the more important features of subsidence. The results of this 

work are given in Chapter II.

I may add that the present interruption of the work, at a very interesting stage of progress, is unavoidable. Whether or not the work 

will be resumed at an early day, I cannot tell; I have therefore carried 

it as far as I can without special apparatus for very constant temperatures. Without these facilities the nice discrimination between the 

arbitrary thermal effects (convection, viscosity) and what I believe is 

an important subsidence phenomenon (stratification), is not satisfactorily feasible.

If thoroughly triturated insoluble material (clay, rock) is shaken 

up with distilled water and then allowed to subside, the solid particles 

will descend gradually and at a rate depending on their respective degrees of comminution. Particles may readily be obtained so fine that 

their rate of subsidence is practically infinite. These, therefore, remain 

suspended in the water indefinitely, giving rise to permanent opalescent

(515) 11
12 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. lnuu,36.

turbidity.1 In endeavoring to account for this occurrence some of the 

'gentlemen present at the meeting were inclined to refer it to a case of 

hydration. The ultimate particles are supposed to combine with water, 

forming colloidal hydrates in a way analogous to the known behavior of 

silica. I accepted this hypothesis in the above simple form with great 

hesitation. It is, I believe, without direct proof, and probably does not 

admit of it; and my original purpose in writing this paper was so to exhibit the phenomena that I could dispense with the auxiliary chemical 

assumption. When viewed in the light given by the details of physical 

experiment the hypothesis is also incomplete. It does not even account 

for the observed suspension, inasmuch as it gives no sufficient reason 

why hydrated particles should be more readily suspended than particles 

which are not so affected. At least, if we regard the rate of descent as 

a function of the dimensions of the subsiding particles, then the chemical view assumes that the very fine particles descend under conditions 

essentially different from the coarser ones a complication for which I 

saw no real necessity. Dust is suspended permanently in air under 

circumstances where hydration is impossible. Furthermore, what is 

the effect of hydration upon the particles ? Are they disintegrated into 

molecules? then the liquid should not be turbid, but clear. Or is the 

effect merely superficial 1? then fine and coarse particles present surfaces of like nature to the liquid in which they are suspended: their rate 

of descent, varying solely with the frictional resistance in their progress 

through the given liquid, must be expressible by a general and purely 

physical law in terms of their dimensions, figure, and density. From 

this law, moreover, must the effects to be anticipated be deducible when 

the particles are so small as to be comparable in size with the molecules 

of the liquid.

The application of this good working hypothesis showed, contrary to 

my expectations, that any theory which is based exclusively on physical causes is untenable.2 If, in the case of gases, internal friction is 

a kinetic phenomenon, it is certainly no longer wholly so in the case 

of liquids. It appears from my results, I think, that the chemical relation of the suspended solid to the liquid very materially influences the 

frictional resistance encountered by the particles. For given pairs of 

solid and liquid, however, this effect remains constant; it is thus seen 

that the auxiliary supposition of a chemical influence is neither essential 

to the physical explanations to be attempted nor incompatible with 

them, and that the whole discussion may be expediently subdivided into 

physical and chemical parts.

1 Professor Brewer found that even after five or six years this turbidity still continued. In studying these phenomena quantitatively particles of some convenient 

finite size must of course be dealt with. I shall use the term " descend" throughout. 

A particle which is " stationary " has an infinite rate of descent.

s Hydration or similar action might have been assumed as an immediate datum of 

the theory of mass-action.

(516)
BABUB.] FRICTIONAL RESISTANCE IN LIQUIDS. 13

When a liquid is forced through capillary tubes the outer layers 

adhere to the walls of the tubes, and the friction encountered is that 

between the layers of the liquid; and hence this friction, or, in other 

words, the viscosity of the respective liquids, is, cseteris paribus, proportional to the times of efflux of given fixed quantities. The same fact is 

observed in various ways indeed j wherever liquids flow over solids. 

But the rates of descent of given very fine solid particles suspended 

in liquids bear no obvious relation to the respective viscosities of the 

liquids. At least, so far as the evidence from my experiments goes, 

where unusually large ranges of viscosity are excluded, this is the unavoidable result. In the earlier portions of the present paper it will for 

this reason often be temporarily convenient to speak as though in the 

case of subsidence the solid particle itself actually falls through the 

liquid j that it is not surrounded by an adhering layer of liquid in a 

way to necessitate a descent of solid particle and liquid envelope, as a 

system.1

It may still be added that the comminuted material is not to be introduced into the liquid in such a quantity that the particles in their 

descent would interfere with one another. All remarks, therefore, apply 

as it were to dilute mixtures.

Mr. Durham2 was the first to make experiments on the phenomenon 

of suspension, and our knowledge of the effect of precipitants is largely 

due to him. Similar experiments were made at about the same time by 

Hunt.3 To Professor Brewer's paper reference has been made. I am 

aware that Prof. C. E. Stuntz, of Cincinnati, has made similar experiments. But the general trend of the researches of these gentlemen is 

not such, I believe, as to be intersected by my work. My thanks are 

due to Prof. M. 0. White, of New Haven, by whose large experience in 

microscopic research I have profited.

GENERAL INFERENCES.

Analogies. The problem immediately suggests an inquiry into the 

general cause for the suspension of finely comminuted material. If a 

solid particle is so small that the force of the efficient gravity-component acting upon it is less than the frictional resistance which would 

be encountered during a downward motion through the molecules of 

the liquid, then the particle must remain fixed in position relative to 

the walls of the liquid which inclose it. The degree of comminution 

necessary for apparent suspension is readily obtainable, even in the

a ln the cases both of gases and of liquids the friction (external) of the fluid on the 

solid is enormously large in comparison with the friction (internal) of the fluid on 

itself. The external friction of gases is measurable only when the gas is in a state 

of great tenuity. (Kundt and Warburg, Pogg. Ann., CLV, pp. 337 and 525, 1875.) 

Successful experiments on the external friction of liquids were made by Heliuholtz 

and Piotrowski. (Wiener Sitzungsber., XL, p. 607, 1860.)

2 Durham, Chem. News, XXX, p. 57, 1874; ibid., XXXVII, pp. 47,48,1878.

3 Hunt, Proc. Bost. Soc. Nat. Hist., p. 302, Feb., 1874.

(517)
14 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 36.

case of gases. Maxwell,1 using Stokes's formulae and his own value for 

the viscosity of air, shows that a drop of water whose diameter (0.0025 

cm.) is about one-half that of a human hair would descend in air one 

thousand times rarer than itself at a rate of only 2 cm. per second. 

The rate of descent of particles of like figure and density varies as the 

square of their linear dimensions. It follows that if we diminish the 

diameter of the particle a hundred fold we diminish its rate of descent 

ten thousand fold; hence a drop the dimensions of which lie near 

the limit of microscopic vision2 (say, 0.000025 cm.) is practically stationary, its rate being 0.0002 cm. per second.

Eeturning from this digression to water, which is comparatively so 

much more viscous than air, we find the conditions for suspension proportionately favorable. We reasonably infer that the dimensions of the 

particle which will just descend are correspondingly increased. We 

conclude that the suspension of solid dust in a fluid is to be referred 

to the occurrence of molecular friction.

The physical variables. Problems connected with the motion of solids 

in an incompressible fluid frequently present formidable difficulties or 

lead to involved results. But for the comparatively simple case in hand 

i. e., the conditions of uniform motion of a small spherule of radius E 

falling through a liquid by its own weight the final result is fortunately simple. Let P be the resistance encountered by a spherule moving through a liquid whose frictional constant is & at a given rate x. 

Then3

P = 67rkJRx .......... (1)

on the other hand, the effective part of the force of gravity is expressible 

by

P'=^&(p-p'}g ....... (2)

where P' is the actuating force, g the acceleration of gravity, and p and 

p1 the densities of the solid particle and the liquid, respectively. Under 

conditions of uniform motion P = P4 ', and hence

...... (3)

where A is a constant.

If there be no chemical relation between the solid and the liquid, then 

the constants in equation (3), or values proportional to them, are all experimentally deterininable. The equation yields the mean value of R. 

If, however, the liquid acts chemically on the suspended solid (as would

1 Theory of Heat. (Appleton & Co., 1883, pp. 299, 300.)

3 Theoretically, according to Helmholtz, ssi'eir cm- and TsiTO cm- f°r *ne ordinary and 

immersion systems, respectively. The limit of visibility, as experimentally found by 

Harting, is 3-3+3-7 cm-> an<i by Dippel, 33-^577 cm- On the other hand, strong coloring 

matter may be diluted as much as IGO.,000,000 times (Muschenbrceck, Achard, Hoffmann) without fading beyond recognition.

3 Kirchhoff(Math. Physik, p. 381, Leipzig, 1876) deduces this equation.

(518)
STRATIFICATION. 15

be the case, for instance, in hydration), then equation (3) is but a single 

relation for three unknown quantities, ft, R, p. We may add that the 

relation between R, p, aiid mass of particle, leads us no further, since 

we know nothing of the change of mass involved.

Here, I think, we strike the keynote of one of the main difficulties 

which these phenomena present. Our assurance that the particle is 

not in some way acted on by the liquid is never perfect, nor have we 

to guide us any clew as to the effect of " mass-action," the amount of 

superficial change, or the depth of penetration pf water, for instance. 

Water shows a striking selective power in discriminating between degrees of comminution. At ordinary temperatures the particles remain 

granular. The impression received in the case of subsidence in ether 

is almost that of particles falling in vacuo; barring flotation, small 

and large particles seem to fall equally fast; the precipitate is flocculent. Let water and ether be mixed, so that there shall be equal bulks 

of etherized water below and aqueous ether above, and then let the 

dust be added. If now this mixture is violently shaken and thereupon allowed to subside, the ether is washed clean of particles in a few 

minutes, whereas the sediment remains suspended in the water for 

weeks or even months. Another experiment, very nearly the converse 

of this, may be added. If a turbid solution of shellac in alcohol be 

shaken with naphtha, the opaque material is washed out, gradually 

ascending to float in the naphtha on the shellac. Subsidence then 

takes place in the naphtha. Eventually the two liquids (naphtha above 

and the clear alcoholic solution of shellac below) are separated by a 

layer of compacted sediment.

Whatever the surface change may be, it necessarily becomes more and 

more effective in proportion as the particle decreases in size. That the 

radius of many particles is smaller than the depth of surface penetration is 

quite probable. And hence, in equation (3), p and R must be regarded 

as variable the former very largely so; whereas & may a priori be assumed as constant.1 When liquids are forced through capillary tubes 

none of these difficulties are encountered, and hence their observed 

friction is the true viscosity of the transpiring liquid.

STRATIFICATION.

Analogies. If very finely comminuted material be suspended in distilled water, the subsidence usually takes place in such a way that 

while the very slow descent of particles is in progress-the liquid presents a stratified appearance. A single surface or plane of demarkation 

is readily "observable, or indeed a number of planes, oftentimes sharply

1 Unfortunately mere variation of p aud.E in plausible amounts for constant k does 

not satisfactorily account for the observed enormous changes of rate. An attempt 

to reconcile this discrepancy is made in the sequel. It is difficult to retain a fixed 

value of fc throughout. If the viscosity of water is studied with particles of graded 

size the large corpuscles may exhibit distinct relations to the'viscosity of the liquid, 

such as gradually vanish when we approach the extremely fine particles.

(519)
16 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 36.

defined. This phenomenon is quite puzzling. At first sight we call 

to mind that air rendered densely turbid by suspended particles of 

water behaves practically like a distinct liquid, possessing determinate hydrostatic properties. A heavy fog will fall through pure air 

and subside in the valleys. Fogs of less specific gravity than air rise 

as clouds. Hence it would appear that in the case of subsidence of 

solid particles in liquids cognizance must be taken of two kinds of motion : a gradual descent of the whole mass of particles in virtue of 

gravity in the first place and a rearrangement of the various parts of 

the liquid in a way consistent with their respective specific gravities in 

the second. It follows that, to allow the second process or redistribution to come fully into effect, the rate of subsidence must be sufficiently 

small. Now, the experiments given below (p. 27) seem to show.that 

this is often the case. If, for instance, we so adjust the consistency 

of the liquids in a number of sedimentation glasses that the rate of 

subsidence increases from tube to tube in some regular order a condition of things which we may easily effect in a way to be indicated 

in the next paragraph we shall find that surfaces are obtainable only 

when the rate of subsidence falls below a certain value. After this the 

liquid clarifies in such a manner that surfaces of demarkation are nowhere visible, passing from opaque turbidity through translucency to 

clearness sooner at the top than at the bottom of the tube.

Descriptive equation. The serious objection to this plausible view is 

that it presupposes a degree of imperfect mixture of the parts of the 

turbid liquid which at the outset of the actual experiment is hardly met 

with.1 Indeed I believe that the occurrence of sharply defined surfaces singly is rather to be regarded as the result of accident, for .the 

particles with which our experiments are most usually conducted (clayey 

material, tripoli) have already undergone subsidence in nature. They 

have passed through a selective process which has thrown particles of 

like rates of subsidence together. These particles need not be of a size; 

but their figures, dimensions, densities must be such as in each case to 

correspond to the observed rate. I will suppose, therefore, that in a 

general case of triturated material the particles vary in size from a 

very small to a relatively large value, but that by far the greater number approach a certain mean figure and dimension.

There is a distributive equation of frequent occurrence in mathematical physics which contains a characteristic maximum. In the kinetic 

theory of gases it expresses Maxwell's well known law, and may then 

be reduced to the very elegant form

A

____ yi2 p X

where y is the probability of occurrence of the molecular velocity, a?, expressed in terms of the most probable velocity. This law of distribu1 See p. 20. 

(520)
BABUB.] UNSTKATIFIED SUBSIDENCE. , 17

tion may advantageously be adopted here, granting of course that the 

selection made is wholly empiric. I therefore postulate

where y is the probability of the rate of subsidence x expressed in terms 

of the most probable rate. Hence ydx denotes the number of particles, 

relative to the total number, Avhoso velocity in terms of the unit l specified lies between x and 'x + dx. The' maximum of equation (4) is well 

adapted to illustrate the consequences of subsidence, when the particles vary in size as much as in an ordinary case of trituration.

Suppose the turbid liquid characterized by the function y to be inclosed between vertical parallel plates, then the degree of opacity observed on looking through the trough in the direction of .a normally

impinging beam of light is due partially to absorption and partially to 

diffuse reflection at the surfaces of the particles. As regards their effect on the transmitted beam, these two phenomena are here not essentially dissimilar and may be described by a common equation. I assume 

therefore the law of absorption

. ......... (5)

where «0 is the original intensity, i the reduced intensity of transmitted 

light in consequence of the thickness of turbid liquid #, through which 

the beam has passed. e~° is the coefficient of absorption, with the understanding that 0 is to refer both to the phenomena of absorption and 

of reflection j or, perhaps more logically, that i be the sum of two. expressions each of which has the character of (5), one however referring 

to absorption and the other to diffuse reflection.

The signification of this constant is very clear in the differential equation

di = Oi0d#,

and the problem now reduces to a consideration of the variation of 0 

consequent upon a change in the number and position of the suspended 

particles. Moreover, since 0 varies from zero to infinity as the liquid 

passes continuously from blear to opaque, the constant 0 may conveniently be termed the opacity of the turbid liquid.

The degree of opacity, dO, which ydx particles add to the liquitl is 

dependent on

ydx (c'frR3 ) and (c4*R2 ) ydx ....... (0)

where E is the radius of the particle whose rate of subsidence is #, and 

c' and c are constants. In the expressions (6), c' and its coefficient refer

1 If the unit of time be 1 s. then the unit of length involved ia the distance passed 

over, per second, by the particle whose velocity is the most probable velocity. These 

units give compactness to Maxwell's equation. To secure similar facility of expression rates of subsidence and not radii of particles arc distributed.

(521) 

Bull. 36 2
18 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS.

solely to light absorbed, o and its coefficient to light reflected; 1 but it 

is a fact of observation that all the phenomena under consideration appear with equal clearness when the particles illuminated by a vertical 

beam of light are viewed in a horizontal direction. Hence the first of 

the terms within the parenthesis is made negligible in comparison with 

the second. It follows, in view of equations (3) and (4), that the total 

opacity at the inception of the experiment is

16C-/7T

A

Sc

From the elementary equations the opacity 0 apparent at a depth d 

after a time t dated from the moment at which sedimentation commenced is deducible. In view of the simplifying condition of uniformity

of motion, the particle, whose rate is # = -- (expressed in .terms of the

unit above), will just-have passed through the section, 

residual opacity is

Hence the

A

an integrable form readily reduced to

(8)

(9)

FIG. 1. Relation of opacity to time of subsidence at different depths.

A clear view of the character of 0 is exhibited in Fig. 1, which contains the second factor of the second member of'equation (9), time (t)

as abscissa, relative opacity ^- as ordinate.

OQ

The function Oas given by equation (9), taken conjointly with equation (5), reproduces the march of the actual phenomenon pretty well, so 

long as very slow rates of descent and particles very nearly alike in 

size are excluded. The plane of deniarkation has more fully vanished 

in proportion as the depth at which an observation is made is greater. 

An inspection of equation (9), moreover, shows that if, in place of y, 

we had selected a function containing a more striking and abrupt raax-

'The optical properties of a beam of light reflected from particles small in comparison with the wave length of light are discussed by Stokes (Phil. Trans., p. 530, 1852).

(522)
UARUB.] EFFECT OF TUKBID1TY. 19

imam1 , the function 0 would be characterized by steep declivity throughout greater depths or that the plane of demarkation would be more persistent. The reverse of this takes place where y is replaced by a function of flat maximum. But the important deduction is this, that if 

the rate of all particles is increased in like ratio the character of the 

phenomenon will not be changed.

Effect of density* of mixture. When the particles under experiment 

are practically identical in size and exceedingly small, a second phenomenon having an immediate bearing on clearness of stratification 

may bo discerned. Indeed this new fact seems to show that for the circumstances under consideration, at least, it is not permissible to treat 

the particles individually; that an analysis based upon the conditions 

of motion of descending integrant systems of particles alone leads to 

the observed results, lu other words, in addition to the size of the 

particles themselves, the dimensions of the interstitial canals separating the particles show pronounced relations to the rate of subsidence. 

I regard this observation sufficiently important to deserve special investigation and discussion, and shall therefore in this paper only advert to 

a few pertinent data.

Three test tubes, 2 cm. in diameter and 15 cm. long, were filled with 

distilled water to which very different quantities of tripoli had been 

added. The first of these, after shaking, was densely opaque; the second 

much less so; the third only just translucent. After the coarser material 

had subsided, the following results were obtained with the very fine 

particles, d is the distance between surface of liquid and surface of 

demarkation after the lapse of time h (expressed in hours); tf, therefore, 

is the length of the clear column:

Date.

October 13, 1885..............................................

October 15, 1885....... ................... I..... .....-..-.-...

October 16, 1885..............................................

Eateof subsidence mm... ....... ........................

h

h

234

331

385

408

Very 

opaque.

mm. 

12

20

2!)

33

0.12

Opaque. 

d

mm. 

35

00

05

0.17

4

Trrmslucent. 

d

mm. 

50

77

no

90

0.28

.1

The amount of substance originally in suspension is fairly indicated 

by the height of the column of sediment after subsidence is complete.

1 The actual work usually leads to imperfect gamma-functions and involved results. 

This is quite unnecessary here, since the essential points are illustrated with sufficient 

clearness by the above. I may add that it would probably have been simpler, and at 

the same time more in keeping with tho point of departure taken in Chapter II, to 

have avoided optical considerations altogether to havo simply defined turbidity as 

mass of sediment of a given kind per unit of volume of liquid and then to have dis-v 

cussed turbidity essentially in tho manner pursued in tho text.

3 Measured by the u.umber of particles per unit of volume, for instance.,

C52?)
20 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 36.

The deduction from these precursory experiments of immediate interest here is this: Since the rate of descent decreases with the density 

of the mixture turbid liquids manifest a marked tendency toward maintaining their surfaces of deinarkatiou clearly defined, so long at least 

as the particles are very nearly of a size and descend very slowly. For 

it is difficult to remove material out of such a surface without diluting 

ifc, but in virtue of this dilution the transported system again descends 

at greater rates, finally to merge into the surface out of which it was 

taken. Furthermore, if within a turbid liquid there exist a region of 

low density, these particles must subside at greater rates and eventually 

merge into an interior surface.

Sharp demarcation. The presence of surfaces of separation furnishes 

the best available means for the investigation of rates of subsidence. 

When the experiment is made under satisfactory conditions the surfaces 

descend uniformly,and the observation maybe inadewith some accuracy 

by projecting them upon a scale read off at a distance with a telescope. 

I have found it advantageous to place the tubes behind a black screen 

and illuminate the particles from above. The number and position of 

the surfaces is then clearly discernible, until the turbidity fades beyond recognition. With fine particles distinct surfaces appear gradually after two hundred hours for instance, in the example discussed in 

the last paragraph. But they appear more rapidly on second and subsequent subsidences. We infer a time-effect due to continued contact 

with water.

An essential requisite for the production of sharp stratification is 

constancy of temperature. When temperature fluctuates convective 

currents arise in the liquid, transporting above its normal level and 

diluting some of the finer material. This in turn rearranges itself, 

forming a second (false) surface, as SOOll as the parts of the liquid are 

again at rest. Here, therefore, is an example of a fog subsiding in the 

liquid in the way explained in the first part of this section. But, supposing the order of occurrences reversible, this new surface would not 

show a depth d = 0 for t = 0, nor could the old surface, after this interference, be brought back to d = 0 for t = 0. Hence the effect of convection is virtually a change of the co-ordinates to which 0, <?, and t are 

referred. This change is irregular, and may, therefore, seriously confuse 

the results, since the corrective effect due to differences of density is not 

always sufficient, or sufficiently prolonged, to annul this discrepancy. 

It increases with the width of the glass; but in very narrow tubes surfaces are not discernible at all. The diameter 2.3 cm. is perhaps a good 

mean.

TEMPERATURE.

Chemical effect. The subsidence of fine earthy dust, suspended in distilled water is enormously more rapid at 100° than at 0°. This is easily 

accounted for by the hydration theory, for it is merely necessary to as-

(524)
HAKIM.] PHYSICAL VARIABLES. 21

sume that hypothetical hydrates, which occur and are formed spontaneously at ordinary temperatures, are no longer possible at 100°. When 

we call to mind the augmented thermal activity of the water molecule 

at 100°.this explanation gains much in plausibility.

Physical effect. At this stage of the investigation it seemed to monecessary to call to mind that we are frequently operating with particles 

smaller than any physically measurable quantity; with particles, in 

other words, small even in comparison with the wave length of light; 

and at once commensurable with molecular dimensions. It behooves 

us, therefore, to inquire what the auticipative conditions of subsidence 

will be when the dimensions of the particles decrease from some estimable mean value indefinitely. Obviously these conditions for very small 

particles include those for larger particles, and the special considerations to be made in the former case vanish when the dimensions increase. 

Hence in the sequel 1 shall interpret all results, with special reference 

to small particles, with the proviso that if the degree of comminution 

under experiment be insufficiently small the considerations simplify and 

revert to views which have already been expressed for relatively coarse 

particles.

In the first section I compared the effective weight of a suspended 

particle with the frictional resistance of the liquid. It is to be remembered, however, that the molecules of water are in a state of incessant 

vibration. The atoms oscillate in virtue of the internal molecular 

energy, and the molecule itself continually changes place and position. 

For very small particles, and during very small intervals of time, it is 

evident that this state of motion is not compatible with absolute constancy of the frictioual force. We rather infer that its value varies within 

relatively wide limits, and the early remarks in reference to permanent 

opalescence have therefore tacitly assumed that the times during which 

gravity acts sensibly on any suspended particle are negligible in comparison with the times during which .its action is without effect.

But even particles of relatively large rates of descent in water are 

still quite invisible microscopically (see page 35). Their linear dimensions must therefore be estimated as considerably smaller than 0.00003 

cm. Hence it is safe to accept 0.000005 cm. as a fair mean expression 

for the diameter of the subsiding solid spherules. On the other hand 

the distance between the centers of two adjacent water molecules is 

probably not smaller than 0.00000005 cm., or about one one-hundredth 

of the mean diameter of the solid corpuscles. 1 It follows that the num1 0. E. Mcyer (following Maxwell and Van derWaals), Kinot. Theorie tier Gaso, p. 

220, Brcslau, 1877. The value given above, which is taken directly from the kinetic 

theory of gases, is usually conceded, to be a better estimate than the other values derived by Thomson, Maxwell, and Lorcnz from capillary or electrical phenomena. Of. 

Am. Journ. (2), L, pp. 38 and 258; Phil. Mag. (4), XLVJ, p. 453, 1873; Pogg. Ann., 

CXL, p. 644, 1870.

(525)
22 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL.36.

m 

ber of liquid molecules surrounding and impinging upoira suspended

particle of average size varies between 10,000 and 50,000; that if, for 

instance, the distance between centers of two adjacent water molecules 

be magnified to the diameter of a pea, the subsiding solid may be typified by a bomb between a foot and a yard in diameter. The distance 

between the centers of two adjacent molecules is riot to be confounded, 

however, with the diameters of the molecules themselves, and a better 

statement of the mean conditions involved is that of a spherical shell 

0.000005 cm. in diameter and 0.00000005 cm. thick, within which, say, 

30,000 molecules are free to oscillate. This number again decreases 

with the square of the linear dimensions of the particle. The number 

of molecules producing the pressure in any observable case of Boyle's 

law is measured in trillions. It seems to me, therefore, that where we 

are observing'effects due to particles whose dimensions frequently fall 

below these mean values indefinitely, we have to take frictioual forces 

into consideration, which, as regards all feasible measurements, are constant, but are no longer so when viewed minutely,, i. e., in their variation from the beginning of any small interval of time to the next consecutive. It follows that it is possible for such a particle to descend in 

a liquid in virtue of the action of gravity alone, although its weight is 

below the mean or measurable value of the friction encountered.

Whatever the difference between the greatest and least values of 

factional resistance during the unit of time may be (it is difficult to 

form a satisfactory estimate, since we know but little about the liquid 

molecule and its rate and manner of motion or the variation of molecular forces), we may argue fairly, I think, that the interval between the 

limits in question will increase with the degree of molecular activity 

of the liquid.1 The particles, under conditions of intense agitation of 

the surrounding molecules, are more liable to be shaken through the 

liquid, as it Were (as powders are shaken or jarred through a series of 

sieves, to use a common but apt comparison), than when the molecule 

is comparatively quiet. Hence any means which may tend decidedly 

to increase this molecular disturbance, even though it slightly increase 

viscosity (as in the case of salt solutions), may effect an increment in the 

rate of subsidence. These views are to be examined with some detail.

The most direct means of increasing the molecular agitation of a 

liquid is temperature. It is to be anticipated that the rate of subsidence of suspended particles of a given degree of comminution will be 

greater when the liquid is at 100°, for instance, than when i't is at ordinary temperatures. I made this experiment:

Two identical glass tubes, closed at one end and drawn to a fine 

aperture at the other, were half filled with distilled water rendered

irrhe mean velocity of particles of air, at 0° C., for instance, is inucli over 400 

meters per second. The velocity of the molecules of liquids is not known, but must 

be of like order.

(526)
BAHUS.'I SUBSIDENCE AT HIGH TEMPEKATURES. 23

densely turbid by dust of white bolus. Both were kept at 100° for 

some time, for the purpose of expelling air, then hermetically sealed 

with a blast lamp. The tubes measured about 

0.8 cm. in diameter and 15 cm. in length. One 

of these was left in the room, Avithout interference, at ordinary temperatures; the other, 

shakeu up simultaneously with the first, was 

exposed to the constant temperature 100°, by 

suspending it in a boiling point apparatus, as 

shown in the annexed diagram. 1 (Fig. 2.)

The following results were obtained: The 

third and fourth columns of Table 1 give the 

depth d (ill millimeters) of the plane of eleinarkation below the bottom of the meniscus,

after a lapse of time li (in hours) given in the 

second column.

TABLTC 1. Subsidence at 15° and at 100° compared.

 Ruto fmm\ Kate (^ h J ...............................

h

n

 Md loo.

0

(0.1)

3

0.1

d 100°.

1.0

(2.0)

After three hours a difference in rate is 

already clearly perceptible. Within 24 hours 

(experiment prolonged overnight) the sedi- FlG>2:~tu'roa ti()ooor8Ubsid 

ment in the hot tube has completely subsided

in the form of a flocculent precipitate somewhat like alumina. The cold 

tube is almost i'ree from precipitate,2 while the surface of demarkation 

is down only 2 to 3 mm. below the bottom of the meniscus.

The rate of subsidence proves, therefore, to be very much greater at 

100° than at 15°. A result of this general character was to be anticipated, but the enormous difference of rate in the two cases is exceedingly striking. The effect of the diminished viscosity3 at 100° would not 

have sunk the dust iu the hot tube more than 15mm. below the meniscus.

1 The diagram is readily intelligible. The direction of the currents of steam is shown 

by the arrows. The sedimentation tube occupies a central position and is thus 

doubly jacketed with steam.

2 The large amount of precipitate in the hot tube is good evidence in favor of the 

views on the coherence of particles, as discussed on page 37.

3 The viscosity of water at different temperatures has been measured by Poiseuillc. 

Eosencrauz, andSlottc. (See digest of the latter, in the, Ann. derPhysik, XX, pp. 2o(>, 

2G7, 1883.) At 100° the viscosity of water is aboufc one-sixth of its value, at zero. But 

the corresponding rates of subsidence are in a ratio which, although qualitatively,in 

accordance, is quantitatively out of all proportion herewith.

(527)
24 SUBSIDENCE OF FINE SOLID PAETICLES IN LIQUIDS. [BULL. 3(5.

I will waive further discussion of this result here in consequence of 

quantitative comparisons which I have in view, comparisons made at 

different temperatures, varying between 0° and 100°. Below 100° we 

experiment with solid particles of a given mean size, descending or subsiding in a given liquid at determinate rates. Regarded from this 

standpoint the experiment is of sufficient importance to demand careful 

measurements.

BECIPITANTS.

Chemical effect. Acids, salts, alkalies, indeed foreign material in general.1 when added to distilled water permanently turbid with some finely 

comminuted insoluble solid in quantities not too large, increase the rate 

of subsidence in a marked degree, in numerous cases even many hundred fold.

The chemical theory appears very readily to suggest these phenomena. 

The addition of the substances enumerated interferes with or prevents 

the formation of the hypothetical hydrates ; but the force of this explanation is apparently weakened when we pass from purely qualitative 

to quantitative data. By reducing some of the results below to a molecular basis, I find that a single molecule of acid or salt, in molecules of 

water varying in number from 10,000 to 50,000, is sufficient to produce 

very marked changes in the rate of subsidence. It is conceivable 

that this amount of dissolved material may in some instances be commensurable with the amount of suspended material, and therefore act 

appreciably on it. In such a case there should be a difference of rate 

due to a difference in the degree of turbidity of otherwise identical turbid solutions. I have failed thus far to bring satisfactory quantitative 

evidence to bear upon this point. I am pursuing these experiments 

with considerable care and therefore need merely indicate the nature 

of the difficulties euco untered here. Instead of considering the particles

individually, as has been done above (p. 14), all the particles in the 

unit of volume may be taken collectively. A priori, the only available force is gravity, and we must regard, the weight of the particles in unit of volume to be the measure of th.e influence in virtue of 

which water is forced through the capillary interstices of the descending system. The analysis shows that the rate of descent of this system 

must decrease rapidly with the number of particles per unit of volume. 

Hence, the purely mechanical effect has the same sense as the hypothetical chemical effect to be investigated, and it is therefore exceedingly difficult to discriminate between the two.

Physical effect. On the other hand, the examination into the molecular conditions of subsidence, commenced in the last section, ^here suggests so many analogies that further discussion is at once demanded. 

We have reasons for inferring that in the case of water, or perhaps any 

other simple liquid, there is presented to us a comparatively quiet mole1 The definite organic compounds (alcohols, ethers) are frequently exceptions.

(528)
"ABUB.J PRECIPITANTS. 25

cule 5 by which I mean that dissociations and recombinations of the 

molecule H2O, akin to those premised by Williamson1 in his views on 

tho process of etherificatiou, and byClausius2 in his theory of electrolysis, are, at ordinary temperatures at least, of rare occurrence. The electrical conductivity of pure water3 is at most one ten-billionth of that of 

pure mercury. It needs but very trifling admixture of acid or salt or 

alkali to increase this minimum value enormously. If it be remembered 

that as small an addition as 18 per cent, by weight of hydrochloric acid 

increases tho conductivity of water more than a million times, it may 

easily be estimated how insignificant is the amount of HC1 which would 

suffice to increase the conductmty by a fraction of itself. Even very 

perfect liquid insulators, like alcohol and turpentine, when added to 

water, produce incremental electrolytic effects. Indeed HC1, in the 

pure state, is an insulator of the same order as water,4 According to 

ClaUSiuS, 110 electrolytic effect will be produced by electromotive forces 

of practicable magnitude, in a space where temporary dissociation5 does 

not occur and partial molecules are therefore absent. Hence ab ordinary temperatures the solution of one substance in another ("electrolytic 

system") is the essential condition of good electrolytic conductivity. 

It is on the basis of these facts that the assumption of a "quiet" molecule 

of water, in the above sense, was made. The result of mixture is 

molecular kinetic energy permanently gained in large amount.

Now, I believe that the dissociations which Clausius and Williamson premise present a more plausible occurrence if the separation is 

superinduced by an intermediate substance of known affinity for one or 

the other partial molecule. If a solid particle is introduced iuto an 

electrolytic system its effect upon the meandering partial molecules 

may be regarded as somewhat similar to electromotive force, inasmuch 

as in a general case different parts of the suspended solid attract partial molecules of different kinds. Furthermore, in view of the occurrence of mass-action, in view of the continually recurring dissociations 

and recombinations between solid and liquid, I see no avoidance of the

'Williamson: Aim. dor Cliera. uud Pharra., LXXVII, p. 37, 1857.

s Clausiiis: Mech. Wilrmetheoric, 2d cd., Vol. II, p. 155-169, 1879.

3 Measured l>y a number of observers, among tliem by JT. Kolilrausch, Pogg. Ann., 

Erg. VIII, p. 1,187G. Kohlrausch's last value is 30X1012 (Borl. Sitzb., XL, p. 3, 1884).

4 Gore: Proc. Roy. Soc. London, p. 250, Vol. XVII, 1868-1869, and others.

r> According to Clausius tho substance (acid, salt, alkali, &c.) after solution may 

be regarded as an aggregate of partial molecules, such that opposite electrical properties are equally represented. Electromotive force produces a moving effect whenover the other conditions which influence a partial molecule are favorable, i. e., 

temporarily at a minimum. If any imaginary interface be described between tho 

positive and tho negative electrode, then more positive than negative partial molecules will pass in tho direction from the positive to the negative side and more negative than positive partial molecules in the contrary direction. The result is practi-' 

cally this: During tho action of the electromotive force a certain number of positive 

partial molecules pass through the interface in a positive direction and the same 

number of negative partial molecules in the negative direction.

(529)
26 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 36.

hypothesis that the surface of the suspended particle must, in particular, be a locus of violent molecular agitation.

Beturningfrom this digression to the subject in hand, I infer that, just 

as in the above instance a marked increment of the rate of subsidence 

of extremely small particles suspended in water was obtained in consequence of the augmented thermal energy of the water molecules (heating to 100°), so must also an analogously increased rate result at ordinary temperatures from the intensified molecular agitation due to the 

solution of foreign material in water. I offer the following experiments 

on this point:

Experimental results. In Table 2 the results obtained with finely comminuted white bolus, red bolus, and tripoli, respectively, each suspended 

in distilled water, are given. Stand-glasses, about3 cm. in diameter and 

30 cm. high, hold these mixtures. The fourth, fifth, and sixth columns of 

the table show the depth, <7, of the respective surface or surfaces of demarkation below the level of the liquids at the times given in the second 

column. The surfaces were distinct for tripoli, less so for white bolus, 

washed in the case of red bolus; d is given in arbitrary units; 1 li in hours. 

Where two sets of figures are given, two surfaces were apparent.

TABLE 2. Subsidence in distilled water.

Date.

December "4

December 25 ......................................

December 27 ........................ . 

B

Rate M) ...... A.. ..................... .... ^ A/

day.

12 p. in..

9 a. m . .

12 m ....

12 m ....

h

0

24 

38

41

49

' 57

68

73

83

98

107

121

132

147

156

White 

bolus.

0

0 

11

12

14

If.

20

Pi *22> 

22

,24,

<30* 

HJ32i

, < 34 * 

*2fl5

H< OO >

0.28

d

Red 

bolus.

0

3 

5

4

5

5

c

6

7

7

8

9

10

0.09

Tripoli.

0

28 

58

61

71

. 81

93

rlOO

I 104 

flS8 

J120

121

131

140

148

fl5C 

 M65

1 180 

(160

) 170 

1.3

About 2 mm. each. 

(530)
BARUS.] SUBSIDENCE IN SALT SOLUTIONS. 27

If we regard d as a function of h we find it linear in the case of white 

and of red bolus and quadratically retarded in the case of tripoli, but 

to the latter fact I would attach no significance. It may be due to the 

unavoidable fluctuations of temperature.1 So long as the descent is 

uniform (d proportional to/t) the force acting on the particle is nil. The 

effect of gravity is exhausted in doing work against the frictional resistance.

In Table 3 are given the results obtained with fine tripoli suspended 

in distilled water to which various percentages (by weight) of common 

salt (NaCl) have been added. The precipitation tubes in this series of 

experiments were 3 cm. in diameter and 15 cm. long. Values for d are 

given only wheu,planes of demarkatiou were observable. In other respects the table is like the preceding one, except that d is here expressed 

in millimeters. Where two sets of figures are given, two surfaces were

apparent,

TABLE. 3. Subsidence in salt solutions.

Date.

December 27, 1883 ..........

December 27, 1883 ..........

December 27, 1883 ........:.

December 28, 1883 ..........

December 28, 1883 ..........

December 29, 1883 .........

DflOflinbftr 20 IKfi*} '

December 30, 1883 ..........

December 30, 1883 ..........

December 31, 1883 ..........

December 31, 1883 ..........

Ratn fmm\

k

Time of 

day.

10 a. m..

2 p.m..

6 p. m..

1 a. m . .

4 p. m..

2 a. m..

12 m ....

1 a. m . . 

12m ....

3 a. m..

12 m ....

h

0

4

8

15

30

40

50

63 

74

89

08

' ' d

a

£<B

P.

iH

0

0

5

7

^ 14

C 17 

) 26

C 42 

I 62

< 30

\ ro

C 41 

I 69 

< 47 

) 80

C 56 

J 95

C 63 

U05

1

"5

p<

mCM

O

0

9

14

\ 29

j 58

| 85

} 104

| 135 

| Bottom.

(

)

\

)

2

a o> 

o

P.

m

o

0

13

C 16 

I 30

45

87.

128

Bottom.

3

q 

o 

o

V

p.

o

1-1

0

C Largely 

\ down.

'

<0

1

m

a

o

w

s

3 

S

OJ

o

(20) 

"H "S

&> o 

« 0

h h

Q? 05

Pi Pi

CM m

0 0

t ! s :

t-> a

 o c

»' e

0

a "c

; <v ^ o 

^ u

1 0

X p.

> m

,

0 0

 Sediment falls rapid) v in fl 1 tli«

tnboa ; rate not

observable, from 

absence of stratification.

J

The experiments show that the rate of sedimentation increases rapidly 

with the quantity of salt in solution ; that even small quantities of salt 

produce very marked effects; Ovaries linearly with h. The absence 

of stratification in cases of greater rates of subsidence (solutions 1 to 15 

per cent.) is confirmatory of the remarks made in an earlier paragraph 

(p. 1C) on the rearrangement of particles according to the density of 

different parts of the liquid and accords well with the other views there 

given. The remarkably accelerated increase of rate observed on passing from fractional to integral per cents, (composition) is to be noticed. 

l See p. 20 as to convective currents and the change of co-ordinates resulting.

(531)
28 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 36.

Table 4 gives tbe results obtained with red bolus, white bolus, tripoli, 

talc, and boue ash, respectively, all finely comminuted and suspended in 

weak brine. The percentage of salt dissolved is shown at the head of 

each column. The solutions are held in test tubes about 1 cm. in diameter and 13 cm. long. They were mixed in a way to be indicated at 

the head of Table 5. In.most cases surfaces of demarkation were 

either absent or not clearly observable; tf, therefore, shows the depth 

of tints or turbidities of like density, or degree below the level of the 

liquid measured on an arbitrary scale; cl. denotes clear; tr. translucent.

TABLE 4. Subsidence in salt solutions.

Date.

January 7, 1884 ...... 

January 7, 1884 ...... 

January 7, 38S4 ..... 

January 7, 18o4 ...... 

January 7, 1884 ...... 

January 7, 1884 ...... 

Januarys, 1884 ...... 

Januarys, 1884 ...... 

January 8, 1884 ...... 

January 8, 1884 ...... 

January 9, 1884...... 

January 12, 1884..... 

January 13, 1884..... 

Bate (*).... \7t /

Date.

January ,7, 1884...... 

January 7, 1884...... 

January 7, 1884...... 

January 7, 1884...... 

January 7, 1884...... 

Jr.miary 7, 1884...... 

Januarys, 1884...... 

January 8, 1884......

January 8, 1884...... 

January 0, 1884...... 

Januaiy 12, 1884.....

K-.tc 1 tc (u;---- d }

Time of 

day.

2 p.m.. 

3 p.m.. 

5 p. m . . 

C p. m . . 

9 p. m . . 

12 p.m.. 

3 a. m . . 

11 a. m . . 

7 p.m.. 

12 p. m . . 

10 a. m.. 

1 p.m.. 

3 p.m..

Time of 

day.

2 p.m.. 

3 p.m.. 

5 p.m.. 

0 p.m.. 

9 p. m . . 

12 p. m.. 

3 a. ra.. 

lla. m ..

12 p.m.. 

10 a.m.. 

1 p. in . .

h

0 

' 1 

3 

4 

7 

10 

13 

21 

29 

34 

44 

119 

145

h

0 

1 

3 

4 

7 

10 

13 

21

90

34 

44 

119

d

Red bolus.

cent. 0.5 per 

0 

0 

0 

0 

1 

1 ' 

2 

2 

3 

4 

5 

12 

12 

0.09

cent. 0. 1per 

0 

0 

0 

0 

1 

1 

2. 

2 

3 

5 

4 

13 

13 

0.10

cent. 0. 2per 

0 

0 

0 

0 

1 

1 

2 

2

3 

C 

5 

15 

15 

0.12

0. 4cent. per 

0 

0 

0 

0 

o

4 

5 

4 

7 

10 

9 

25 

30 

0.2.

8 cent. 0. per 

0 

0 

0 

0

30 

tr.

cl.

> 2

Wliitoljolus.

cent. 05. per 

0 

1 

, 1 

1 

1 

ON

3 

3 

8 

9 

C 

21 

28 

0.2

cent. 0. 1per 

0 

1 

2 

1 

o

2 

3 

3 

7 

10 

7 

33 

38 

0.3

2 0.cent. per 

0 

0 

. 0 

0 

3 

4 

20 

tr.

cl.

0.8

q

01

u 

t* 

o 

P. * 

o

0 

3 

G 

tr. 

d.

2

o 

o

w 

P.

00

o

0 

40 

d.

5

d

Tripoli.

rcent.

Pi

m

o

o

0 

2

2 

3

4 

7 

8 

8 

1?

13 

13 

tr.

0.4

o

Pi

rH

O

0 

2

3 

6

7 

12 

14 

10

90

oo

25 

tr.

0.0

0

IN

O

0 

o

3 

3 

5 

7 

10 

9 

"4

tr.

cl.

0.7

a

o<o

P, 

 **

0

1

3 

4 

9 

14 

30 

tr.

cl

1.5

3, 

U

00

O

0 

o

3 

7 

7 

tr. 

I.

"

"Talc.

^j

«

!J

O

o

0

2 

23

cl.

o

n

0

o

A

rt

o

0 

2

cl.

-

a 

o

0.

C-J

0 

3

cl.

3

,e 

o ^

 * 

o

0 

3 

cl.

3

2 

y

p.

CO 't

"= <

0 

4 

Cl.

4

Uono a.sli.

i §

" 0

 > ~

D -'

= o

a

0

o

ei

o

J c 

o -

0 0

5 5

 * 00

d o

0000 0

'. larifics rapidly, at 

rates increasing 

with the quantity 

of salt dissolved.
SUBSIDENCE IN SALT SOLUTIONS. 29

The absence of stratification which frequently occurs for thin walled 

tubes of small diameter I refer to convection due to fluctuations of 

temperature. The results of this table have, a smaller claim to accuracy.1 The difference in the rates of subsidence in case of solutions of 

the same percentage quantity of salt is probably wholly due to differences of comminution in the various cases. . An accelerated increase of 

rate with the strength of the brine is again generally apparent.

In Tables 5 and C various stages of subsidence of tripoli, in solutions 

of different chemical composition, are given, Table 5 showing the results obtained with 0.01 per cent, solutions, Table 6 the results for 0.05 

per cent, solutions, of the anhydrous compounds HC1, H2SO4, CuSO4 , 

ZuSO4, MgSO4 , KI, NaOl. In addition to the mean rates the electrical conductivities2 of the divers solutions are added. The tables are 

readily intelligible. The particles subsided in tubes 3 em, in diameter and 20 cm. long. In order to warrant the assumption that the contents of the tubes are identical, except ^in the respects mentioned, the 

following plan of mixture was pursued: One per cent, solutions of each 

of the substances enumerated were first prepared, after which 1 cubic 

centimeter and 5 cubic centimeters of each were diluted to 100 cubic 

centimeters with distilled water permanently turbid with tripoli. In 

the case of Table 4 above, equal volumes of turbid water were added 

to each of the tubes and the contents then diluted to the desired 

amount with clear distilled water. This general method gives assurance that both the number and the mean dimensions of the solid particles in each cubic centimeter of the different solutions were originally 

identical a condition of essential importance.

TABLE 5. Subsidence in 0.01 per cent, solutions.

January 7, 1884 ..............................

Conductivity (XlO9 ) ...................

Time

of day.

9 a. m.

12 m ...

h

0

13

99

28

40

47

CuSO*.

0

11

I 25 

30

50

tr.

1.0

4

KI.

0

5

10

20

0.3

C

C

NaCl.

0

5

10

20

0.3

13

I

H,SO,

0

tr.

el.

(10)

40

HC1.

0

cl.(a)

(100)

75

HZ0.

0

18

0.3

a Translucent in 1 hour and 30 minutes.

1 Measurements of this kind, unless \vo resort to special optical apparatus, are :ilways unsatisfactory. To the eye, however, the evidence furnished by these experiments was quite conclusive. After the expiration of a month the tubes with red 

bolus, for instance, were still distinctly colored, the mean tint varyin g in height and 

in degree inversely as the quantity of salt contained in the liquid. 

, 2 In terms of mercury.

(533)
30 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 36. 

TABLE G.--Subsidence in 0.05 per cent, sohilio'ns.

Kate (mm\

Time

of day. h

0

17

192

CuSO-i.

0

cl.

8

KI.

0

22

CO

0 5

12.

NaCl.

0

20

CO

0.5

26

d

H2S04.

0

cl.

80

MgS04 .

0

tr.

10

ZnS04 .

0

cl.

8

Iii Table 5 surfaces of separation were apparent except in the case of 

HC1 and H2SO4 ; in Table 6, however, they were apparent only in the 

case of KI and NaCl. I avoid greater length of detail in the present 

data, since all other desirable relations are sufficiently indicated in the 

earlier results. 1

Table 7 contains the results obtained with tripoli falling through concentrated ether, absolute alccrhol, water, and glycerine, respectively. 

Subsidence takes place iu tubes like those described on page 23; li is in 

hours, d in millimeters.

TABLE 7. Subsidence in divers liquids.

January 22, 1884....................;..........

V. ft /

. Time

of day. h

0.00

0.03

0.07

0.10

0

1 Q

0.17

0.20

0.25

0.48

0.75

1.00

1.25

16

Etber.

0

9

1C

21

26

30

32

30

434*5

250

Alcohol.

0 ^

5

10

23

34

44

53

45

d

Water.

0

0.1

Glycerine.

0

6

13

25

35

52

0.02

From these tables it appears that the descent is much more rapid 

in ether than in alcohol and enormously more so in these liquids than in 

water. In the case of ether the rate of subsidence decreases rapidly as 

time increases; but the tube is not long enough for the study of sedimentation occurring at such phenomenally large rates. Particles reach 

their lowest positions and pack before a normal rate is fully obvious.

1 The effect of HNOu is analogous to that of the other acids, 

(534)
HAUL'S.] BULK OF SEDIMENT. 31

The supernatant liquid is clear. In case of alcohol and water it remains 

slightly opalescent. Surfaces of deraarkatioii are in all cases sharp.

Values for rate of subsidence, such as are obtainable from Table 7, 

cannot bo immediately compared. To arrive at data of this kind, the 

liquids (ether, alcohol, water) should be examined when in similar molecular conditions. This would, for instance, be the case when each is at 

its boiling point. Differences of rate, in these cases, will bo much less 

pronounced. (See Table 1.)

An interesting feature of this experiment may be noticed here. After 

subsidence has taken place, in the case where about equal amounts of 

tripoli are originally suspended (the liquids being in tubes of like caliber), the permanent column1 of sediment was found to bo longest for 

ether, shortest for water, of intermediate length for alcohol: directly, 

therefore, as the respective rates of subsidence, But further experiments show that this is not always the rule. In the following Tables 

8 and 9 the results obtained by suspending 1 gram of tripoli in various 

liquids are contained. I denotes the length (mm.) of a column of sediuient, of a given diameter and weighing 1 gram, after complete subsidence has taken place.

TABLE 8. Bulk of sediment after subsidence.

After 40 days, 1 

Methyl 

alcohol.

45

Ethyl 

alcohol.

6G

Ether.

134

Water.

58

TABLE 9. Subsidence in divers liquids bulk.

Ttatn fm/m'\ Kate ( h ) .... 

After 21 days, lh

0.0

0.7

1.1

2.7

12.7

23.7

45.7

Methyl 

alcohol.

0

34

38

44

48

49

49

70

55

Ethyl 

alcohol.

0

21

88

55

67

70

72

 59

Ether.

118

Water.

49

Methyl alcohol shows an exceptional value. In all cases the rate materially decreases as time increases and finally reaches zero asymptotically. As the particles descend they interfere with one another, and 

this in proportion as the quantity of sediment in the unit of volume increases. The friction of particles on themselves complicates the phenomena2 and is without interest in the present discussion.

1 Bulk here varies linearly with length.

 "Packing" is probably due to slow descent of smaller particles between the interstices of the larger, on the hour-glass principle, until the equilibrium of position of 

larger masses or corpuscles is undermined.

(535)
32 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS.

A final exhibit of the divers rates of sedimentation encountered in

the above tables, reduced to ^~ and to is desirable. li sec

TABLE 10. Rates of subsidence final digest. 

1. Subsidence in distilled water, 15° and 100°, respectively bolus.

15°

mm ~T

0.1 

0.1

cm , 

 10° 

sec

3 

3

100°

mm ~JT

1.0 

2.0

5>

« 30 

60

2. Subsidence in distilled water.

"White bole'.

mm ~lT

0. G

~ 

cm 106 

sec

20

Red bole.

inm~/r

0.2

c?n. i^r108

6

Tripoli.

mm~F

2.0

. cm 

TeJ10°

80

3. Subsidence in weak brine tripoli.

0. 1 per cent.

mm

1

cm

30

0. 2 per cent.

mm

2

cm

l^"10

60

0. 5 per cent.

mm

3

cm

90

1 per cent.

mm

(20)

cm-^-10°

(600)

4. Subsidence in iveak brine bole, tripoli, talc.

Bod bolus....

White bolus .

Tripoli ......

Tain

0. 05 per cent.

mm,

h

0.2

0.5

1.0 '5

cm 

sec

6

1.5

30 

150

0. 1 per cent.

mm

/i

0.2

0.7

1.5 

5

cm

sec

1

20

45, 

150

0.2 per cent.

mm.

h

0.3

2.0

1.8

7

cm

sec 

9

60

54. 

210

0.4 per cent. .

mm

h.

0.6

5

3.7 

8

Cm .f.r,

sec 10

18

150

110 

240

0. 8 por cent.

mm

h

5

13

5 

10

cm

sec

. 150

390

150 

300

5. Subsidence in 0.01 per cent, solutions of dioers substances tripoli.

CuS04

mm

h

1.0

cm in*

sec W

30

KI

inm

h

0.3

Cm in»

sec 

9

Nad

mm

h

0. 3/

cm io«

sec

' 9

H2SOa

mm

h

(10)

cm. ~^10

(300)

nci

mm

h

(100)

cm

sec

(3000)

H20

mm

h

0.3

cm

sec

9

(536)
1IAUUS. I DIGEST DISCUSSION. 33

TAUL.E 10. Rates of subsidence final digest Continued. 

0. Subsidence in 0.05 per cent, solutions of divers substances tripoli.

CuSOj

mm ~T~ cm \(f

set 10

KI

mm

h

0.5

cm

sec 

1.5

NaCl

mm

h

O.G

cm

sec

1.5

1I2S04

mm,

h

cm

 sec

MgSCh

mm

h

cm

nee

ZnSOj

mm

h

cm . M,

sec

1. Subsidence iii divers liquids tripoli.

Ethor.

mm ~T

250

1>

7500

Alcohol.

 mm ~h~

45

cm 

 10C 

sec

1300

Water.

mm ~7T

0.1

-^10« 

sec

3

Qlycerino.

mm ~T~

0.02

cm l^106

0.6

9. Subsidence in divers liquids-tripoli.

Metbyl alcohol.

mm, 

IT

70

Wcm 10°

2000

Alcohol.

~Fmm 

40

 10° 

sec

1200

Facilities for obtaining absolutely constant temperatures would have 

much improved these crude results; but they are the best available 

under the circumstances. I may add that the sedimentation effect of 

the addition of ether and of alcohol to distilled water seems to be a 

decided retardation of rate, 1 and that the rate is not independent of 

the amount of sediment in suspension but decreases with the turbidity of 

the mixture. Hence even in the above experiments different rates occur 

in different series of experiments for this reason alone; but to these results I attach crucial importance, and shall therefore treat them specially 

in another paper.

DISCUSSION.

Mechanical relations. In the equation by which I endeavored to 

describe the appearance of the tube at different times (p. 18), it was convenient to express depth, d, in terms of the distance traveled per second 

by a particle whose rate, tf, is the most probable rate. If D be tbe actual

depth in centimeters, then d = - ; and hence equation (9) takes the form

0 = -( 1

Inasmuch as 6 and t cuter this equation symmetrically it is evident 

at once that if the rate of all particles be increased ?&-fold the column

J It is Avell to desiccate the particles intended for subsidence in ether.

(537) 

Bull. 36 =^3
34 ' SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL.36.

of turbid liquid will present a given appearance or stage of subsidence 

in- of the original time; the character of the phenomenon is not essen-.

7Z

tially changed. If, however, the increase of velocities is produced by 

solution of precipitants, we find experimentally that the column which 

presents surfaces of demarkation -for the class of very weak solutions 

clarifies without exhibiting this characteristic feature during any stage 

of subsidence for the class of stronger solutions, and, furthermore, that 

the transition from stratified subsidence to uustratified subsidence is 

apparently abrupt. I infer that in the case of subsidence superinduced 

by precipitants the equation for the original distribution of rates, 

y = /(#), is radically changed, and this in proportion^as the amount of 

precipitant dissolved is greater. Furthermore, that this change is 

equivalent to a flattening of the maximum in the direction of greater 

rates; or that the difference of rate between consecutive particles is 

largely'incremented, although not in uniform measure for all the particles. Again, surfaces of demarkation remain distinct until the (long) 

column as a whole fades beyond recognition. This is the essential 

difference between subsidence of tine particles in water, as actually observed, and simple viscous subsidence as described by equation (9), for 

instance. -

If we accept Slotte's 1 value for the viscosity of water at 20°, lc = 

0.0101 (g cm-1 sec-1 ), Poiseuille's 2 value for the viscosity of ether, 0.3 k. 

and Graham's 3 values for the viscosity of methyl alcohol and of ethyl 

alcohol, 0.63 fc and 1.20 fc, respectively; if, furthermore, we assume as the 

density of the subsiding substance (quartz, clay) the value p = 2.5 

whence p' p = 1.5 in round numbers; if, finally, g = 080 (cm. sec~2 ), 

then Table 10 (7.and 9) supplies the remaining data a (cm. sec" 1 ) for 

estimating the mean linear dimensions of the subsiding particles. We 

obtain ^

Centimeters.

Water"............................. .........:.................... .'.-..R = 0.00001

Ethyl alcohol .........................................................22 = 0.00019

Methyl alcohol........................................................22 = 0.00020

Ether............. .................................. ..................72 = 0.00024

These results point out in a striking way the essential difference between subsidence in distilled water and subsidence in liquids (alcohols, 

ethers) whose affinities for silica and silicates are demoustrably feeble. 

The value of .B is smallest in the case of water; certainly too large in 

the case of the remaining liquids. The dimensions found are therefore 

just in the inverse order of the values, which hydration would compel 

us to infer. The discrepancy is due in part to the value of density 

entering into the arguments; but the large-error is more simply ex-

!Slotte, Wied. Ann., XX, p. 202, 1883.

2 Poi8euille, Ann. de Chim. ct do Phys. (3), VII, p. 50, 1843; ibid., p. 76, 1847. 

"Graham, Phil. Mag. (4), XXIV, p. 238, 1861. 

' . (538)
DAKUS.] ELECTRICAL RELATIONS. 35

plained by the fact that in the two classes of experiment, even though 

made upon the same material, we have different particles under observation. I have adverted to the coagulated appearance of the sediment 

when submerged in ether or in alcohol. The particles cohere closely, 

and the coarser material sweeps the finer material down, particularly in 

the case of dense mixtures; hence the poor selective power, the bulky 

sediment, and hence we fail to arrive tit values for the rates of subsidence of the thoroughly comminuted dust at all. In the tripoli. employed 

I indeed measured particles microscopically1 as large as 0.00005 centimeter to 0.0007 centimeter, but these are at once ejected by water as 

well as by ether, are found at the bottom before the surface of demarkatiou has fallen 0.05 centimeter, and have no bearing on the phenomenon in hand. 

Mectri-cal relations. - If we compare the results for rate of precipitation taken from Tables 5 and 0, or from Table 10, with the known values 

of electrical conductivity of the respective solutions, we fail to find any 

. detailed similarity in the two sets of data. In a general way, perhaps, 

the strong mineral acids show marked power to increase both rate of subsidence and electrical conductivity. But the salts of copper, of magnesium, and of zinc increase the rate of precipitation to a much larger degree than can be inferred from their electrical constants. Much of the 

discordance is no doubt to be referred to the coarseness even of the best 

available methods for measuring rates of subsidence. Chemical affinity 

produces a distortion ; in the case of acids, for instance, effecting actual 

solution of particles of extreme fineness.- But with due allowance for 

all these sources of error, I feel convinced that more elaborate experiments will not substantially change the results. Eegarding this question from a theoretical point of view, greater accordance of results than 

has here been obtained is not at all to be anticipated. The electrical 

conductivity in case of dilute solutions is dependent on the friction 

against which the'ion moves in its passage through water a quantity 

which has not an immediate bearing on the subsidence of a small solid 

particle.

Precipitation increases in a marked degree with the amount of salt 

of a given kind in solution. This is equally true of electrical conductivity. Nevertheless, here again there is probably not perfect parallelism in the march of the two phenomena. The increase of conductivity

diffraction method applies, of course, only to much larger particles; at least 

the exceptionally largo corpuscles "which are just within rcach-of violet light fall 

too rapidly for uniformity of distribution. In. connection with the values of It it is 

interesting to note that the dimensions of the vesicles of mist in the air as obtained 

by Frauuhofer, (Schumacher, Astr. Nachr., Ill, p. 62) and later by Kaemtz (Meteorologie, III, p. Ill, Mousson, Phys., II, 1872), arc 0.0017 centimeter and 0.0033 centimeter, respectively, the numbers varying with climatic conditions. It is well known 

that lyeopodium spores (0.003 centimeter) and Bowista spores (0.0004 centimeter) 

come nicely within the range of the diffraction method.

(539)
36 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL.38.'

for such (small) quantities of dissolved salt as are enumerated in the 

tables is regular and uniform. The rate of subsidence appears to increase very slowly, almost imperceptibly at first, until a certain amount 

of solid is dissolved; further additions are accompanied by rapid acceleration in the rates of subsidence. But this inference is liable to error, 

inasmuch as at the critical stage in question, surfaces of deruarkation 

are no longer available.

My results on the relation of conductivity and sedimentation, when 

considered in the aggregate, may therefore be summarized thus: A similarity between corresponding data for electrical conductivity and rate 

of subsidence is roughly apparent when the change of internal energy 

of water is produced either by heat alone or by solution of different 

quantities of one and the same salt. Between the values of these variables obtained by dissolving different salts no relation is observable, 

except perhaps of a very general kind. In tbo case where precipitation takes place in different simple liquids (water, alcohol, other) the 

respective rates differ enormously from tbe values which the conductivity of these substances would lead us to infer. 1

In view of the fact that the degree of comminution of the particles 

under consideration is much smaller than the limit of microscopic visibility it is permissible to make this inference: The frictioual resistance 

experienced by the solid particle in its passage through the liquid, although apparently constant, is no longer so when regarded with reference to its value during a number of consecutive indefinitely small times. 

If, furthermore, wo admit that the limits within which this frictional 

force is comprehended increase with the degree of molecular agitation 

of the liquid, then the analogy between the phenomenon of electrical 

conductivity, as explained by Clausius, and the phenomenon of subsidence of extremely fine particles iu liquids is very nearly complete: in 

one case the ion is sensibly acted on by au electromotive force during 

the times when it is relatively in a state of freedom as regards the powerful chemical attraction of surrounding molecules; in the other, the 

tendency of gravity to urge the particle downward produces an effect 

when its weight is temporarily greater than the variable friction encountered during its motion through agitated molecules. The ultimate 

result in the electrical experiment is the appearance of free ions at the 

electrodes; in the other experiment a sediment collects at the bottom 

of the tube.

Particles of larger dimensions. I will introduce this, paragraph by 

the following random selection frem a large number of data. The table

_________________________________________5______________

1 Remarks of an analogous kind are made by those who have endeavored to express

the electrical conductivity, fc, iu terms of the quantity, p, of salt dissolved and the

viscosity, 77, of the solution. Grotrian (Pogg. Aim., CLVII, p. 250,18/6) obtains good

agreement (at 18° and 15°, respectively) by using the formula fc = c ^-, where c and

n are constants.

(540)
EFFECT OF TURBIDITY. 37

contains a comparison of the rates of subsidence in brine of 0 per cent., 

0.5 per cent, and 1 per cent, strength, respectively, when in one case 

the original mixtures ure densely turbid aud opaque, in the other only 

just opaque fading into translucent; tubes, 3 cm. in diameter and 20cm. 

long. In both sets of experiments I observe three different degrees of 

turbidity, in which the suspended material varies as 4: 2:1 for each of 

the stated percentages of salt solution, o. denotes opaque, tr. translucent, d. clear, as above. The depth of the opaque stratum is determined 

by noting the point of the tube at which a beam of the light of the sky 

reflected from a distant plane mirror and passing through the tube is 

extinguished. Depth is always given in millimeters below the meniscus as a datum; time, in hours (/*).

TABLE 11. Subsidence of opaque and of translucent mixtures in Irlnc.

Date.

Oct. 3, 1883...

Oct. 4, 1885... 

Get 0, 1885 . . .

Oct. 1,1885... 

Oct.!), 1885..'.

Oct4, 1885...

h

0 

5.3 

21 

CO

0

38

48 

03

Strength of brine =

Relative turbidity =

Densely opaque 

mixtures.

I

Dilute semi-translucent mixture.

. I

NaCI.O per, cent.

4

0. 

0. 

< 0.

? 15. 

i. n. 

) 50

2

0. 

0. 

0.

25

0.

90

1

0. 

0. 

0.)

50 5

0.

160

-Deiuiirkation indistinct.

0.

No dt 

ox a 

'tur 

Kit

0.

<> o.

) tr.

0. 0.

NaCl, 0. 5 per cent.

4

o. 

tr.

cl.

2

0.

tr. 

cl.

o. 

tr.

cl.

NaCl, 1 per cent.

4

0.

cl.

2

0.

cl.

1

0.

cl.

Particles full in the ratio of turbidity 

and concentration. leaving a filmy 

opalesoenco behind; sediment;, 

bulky aud flocculent, collects at 

the same rate. Precipitation ia 

complete in fractions of au hour.

0. 0. 0. 0. 0. 0.

iinarkation. Tubes approach translucency in tbo 

ct order of concontrutioii and turbidity, being 

)id still, although 1 per cent, is nearly clear. 

;ct of quantity of nalt not very readily obviouu.

f 0.

1 tr. 

1 tr.

tr. 

cl. 

5 tr. 

\cl.

(« 

0.

tr.

tr.

?" 

J tr. 

} cl. 

\ tr. 

id.

(cl. 

| cl.

cl. 

cl.

......

This table reproduces an exceedingly striking observation in an unavoidably coarse and imperfect way. The action of the precipitant is 

marked aud instantaneous when the solutions are densely turbid, I may 

add, in such a way as to contain relatively large corpuscles in suspension. When the turbidity is slight and the particles are fine, the tendency of salts to produce precipitation, however pronounced, is no longer 

quite so obvious.

Many of the particles here subsiding are probably too large to fall 

within the scope of the hypothesis enunciated in the preceding paragraph. But causes for the observed coherence of particles, the bulky 

and floccnlent precipitates and the rapid subsidence seem to me not far

(541)
38 , SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 36.

to seek. The view which I advance provisionally is based on a principle 

similar to that by which Lesage, of Geneva, endeavored to explain the 

mechanism of gravitation. Suppose for<a moment that the particles 

are without weight. If we regard any one of them individually, the 

effect of the molecular agitation would in general be nil so far as motion 

of the particle is concerned, inasmuch as this action is symmetrically 

distributed over the whole surface. If, however, there be given two particles, and if these be placed in sufficient proximity, then this symmetry 

of action is destroyed; the two particles will mutually screen or shield 

each other from impact on the paHs of their surfaces which face each 

other, whereas the external parts of the surfaces are left exposed in full. 

The result is a force tending to move the particles together in a line 

joining their centers. In some such way, I believe, the larger particles 

in the presence of precipitants, or at higher temperatures (i. e., under 

conditions of intensified molecular disturbance at the. surfaces of the 

particles), attract the finer particles, sweeping the greater number of 

them to the bottom of the tube at relatively large rates.

Subsidence and viscosity. In this place the results in Tables 7 and 

9, referring to ether, alcohol, and water, throw new light on the discussion. For the viscosities of these substances Poiseuille 1 found the 

relative data 0.3, 2.2,1, respectively where, however, the alcohol is 

not absolute, but an 80° (alcoholometer) spirit. Graham2 finds the viscosities of water and alcohol in the ratio of 1 to 1.2. These values are 

proportional to the times occupied by the liquids in passing through 

identical capillary tubes under identical circumstances (transpiration). 

Now it would appear that in the case of subsidence we have quite an 

analogous experiment. In the first instance, a fine thread of liquid 

moves through a fixed solid; in the second, a fine particle of solid 

moves through a stationary liquid. In both cases the two substances

move relatively to each other under conditions by which eddies are excluded, and the whole kinetic energy is at once converted into molecular kinetic energy or heat. Table 7, however, in connection with 

the results of Poiseuille and of Graham, shows conclusively that a relation between the rates of subsidence and the rates of transpiration is by 

no means apparent.. The necessary inference is either that the frictions 

encountered in the two cases are radically different, or that the dimensions and the density of the particles change with the properties of the 

liquid in which they are submerged, or both. Above (p. 15) I accepted 

the last as the most probable conclusion; but it is nevertheless difficult 

and unsatisfactory'to endeavor to make allowance for the observed enor 

nious variations of rate of subsidence by simple variations of density 

and dimensions of the subsiding particles. These remarks are further 

exemplified by the results obtained with saline solutions.

1 Poiseuille, Auu. de Cbim. et do Phys. (3), XXI, p. 104, 1847. 

*Graham, Phil. Mag. (4), XXIV, p. 239, 1862.

(542)
BAKU8.] CONCLUSION. 39

The effect of the solution of the salts CuSO4 , MgSO4 , ZnSO4 , Nad, 

and of the acids HC1, H2 ,SO4 in water, at' ordinary temperatures, 

is an increase of the viscosity of the liquid nearly proportional (where, 

as in the above tables, only fractious of a per cent, are dissolved) to the 

quantity of salt or acid in solution. 1

There are some salts,2 notably among them KI, the viscosity of whose 

weak solutions at low temperatures is less than the viscosity of 

water. But the value of the decrement produced by addition of 

quantities as small as 0.1 per cent, is in no case phenomenal or even 

large. Table 6, moreover, shows no marked difference between the respective rates of subsidence .in solutions of KI and of NaCl, whereas 

in the first instance the viscosity of water has been increased, in the 

second diminished, by the solution of like quantities of the two salts. 

To me it appears impossible that additions of small fractions of a per 

cent, of acid or of salt to water should be able to affect the mean or 

measurable viscosity of this liquid in. any marked degreej certainly 

not to such an extent as increases the rate of subsidence even many 

hundred fold.3

CONCLUSION.

In the above pages I have endeavored to throw light on the phenomenon of subsidence from three points of view. I adverted in the first 

place to the mechanical conditions of subsidence, i. e., to the dependence 

of rate of descent upon the figure and physical constants of a single particle or upon the constants of a stated group of particles. 1 then 

attempted to point oat certain possible analogies in'the sedimentation of very fine material with Clausius's interpretation of electrolysis to find some expression for the dependence of subsidence on the 

molecular conditions of the liquid. Finally, I called to mind the probability of certain permanent chemical effects of the liquid on the subsiding solid. The last of these subjects of inquiry is more nearly open 

to investigation, independently of the others, than either the first or 

second. This, therefore, seems to be the proper point of departure for

'Tbe literature of tlio viscosity of liquids since the original memoirs of Girard 

(M6m. do 1'Acad. Eoy. de I'lnst. do France, 1816) and by Poiseuillc (Ann. deu Cbim. 

et do Phys. (D), VII, p. 50, 1843; ibid., p. 76, 1847) has been steadily increasing, 

though the more important additions are of recent date. The reader desiring 

further information is«referred to the papers of Sprung, Pogg. Ann., CLIX, p. 1,1876; 

Grotrian, Pogg. Ann., CLII, p. 1, 187(5; ibid., CLX, p. 1, 1877; Wagner, Wied. Ann., 

XVIII, p. 259, 1883, and others. Grotriau studies the vibration about a vertical axis 

of a very large horizontal disk suspended in a liquid, the theory of which experiment 

is fully known. In other researches, however, Grotriau, in common with the remaining physicists, adopts the' more accurate method of transpiration. Sec Graham, " On 

liquid transpiration, etc.," Phil. Mag. (4), XXIV, p. 2.'58, 1861.

2 NH4Cl,NH4N03 ,NH.,Br, KI, KBr, KN03> KC1 (Sprung, 1. c.)f I3aN03 (Wagner, 1. c.).

3 Similar remarks may bo made with reference to the capillary and cohesion constants of liquids, those of Gay Lussac, for instance. Cf. Mousson, Physik, I, pp. 263, 

267, 1871-

(543)
40 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS.

further research 5 and I believe, if the relations in question are systematically studied, that the quantitative results will not only elucidate 

many obscure points of the chemical behavior of solids,1 but that they 

will even furnish data bearing directly upon the phenomenon of solution. Solution is here the limit of turbidity.2 Indeed, I know not 

whether the degree of extreme divisibility of subsiding particles, or 

even the mean size of the particles of an ordinary precipitate, has ever 

been systematically put into relation with the conditions, physical and 

chemical, under which subsidence takes place.

1 The tendency to liydration under varying conditions of mass per unit volume of 

liquid, for instance. *,

2 See above, page 12, and chapter II, p. 42. .

(544)
CHAPTER II.

THE DEPENDENCE OF RATE OF SUBSIDENCE ON ORDER OF SUR 

FACE, CONCENTRATION, AND TURBIDITY.

' EXPERIMENTAL EESULTS.

Introductory. In this chapter it is my object to begin a minute study 

of tbe conditions subject to which a column of turbid liquid must present a stratified appearance. The turbidity is assumed to be due to very 

finely comminuted insoluble matter which the liquid holds in suspension.

The strata in question are usually characterized by sharp upper surfaces, below which opacity decreases until <i depth is reached at which 

another surface juts out, as it were; from this point, downward, turbidity decreases again as far as the next consecutive surface, and so on 

for the remaining surfaces. Particles are thus aggregated on every surface and near it from below. If we suppose depth to be laid off verti- 

' caUy downward and opacity horizontally to the right, the appearance 

of the tube would be well given by a saw placed so that the cutting 

edges of the teeth may be upward on the right and nearly horizontal; 

in other words, the serrated outline of the diagram passes from left to 

right downward, indicating a general increase of opacity from top to 

bottom of the column. I need only add that the continuous decrease of 

opacity for parts of the column between the first and second, second 

and third surfaces, &c., is not so marked as between consecutive lower 

surfaces.

It has been stated above (p. 20) that in the case of fresh material the 

surfaces in question do not seem to appear until after the lapse of a 

large interval of time, say one to two hundred hours; but when the 

particles have just undergone subsidence, strata may be obtained sooner. 

Again, the occurrence of x^ronounced stratification is observable sooner 

with semi translucent than with very opaque mixtures; in the latter case 

they eventually appear in greater number than in the former. Finally, 

after the strata have come into distinct defiuitiou, they retain their individuality until they ultimately vanish,'or, at least, become too faint for 

measurement. Fluctuation of temperature interferes with sharpness of 

outline. In the present paper, however, some of the experiments have 

extended over 1,200 hours, so that the aggregated effect of temperature 

is probably nil.

The general method by which I hope to arrive at definite results on 

the ultimate cause of stratification consists in a minute study of the rate

(545) 41
42 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 36.

at which subsidence takes place considered in its dependence upon the 

order of the surface, the concentration, and the turbidity of the solution. 

It will be convenient to number the surfaces from the top downward, and 

distinguish them as surfaces of the first, second, third ...... order. Under concentration is to be understood the number of grams of dissolved 

precipitant per cubic centimeter of solution; under turbidity, similarly, 

the number of grams of insoluble dust of a given kind per cubic centimeter of solution. In the present experiments, however, it has been 

expedient to express ^turbidity arbitrarily.

Data. Tripoli suspended in distilled water or in weak brine subsides 

at rates of practically convenient magnitude. This mixture has therefore been used in the present work.

The first series of results refers to diluted, i. e., to semitranslucent 

mixtures. The degrees of concentration vary from 0 to 1 per cent, of 

salt. For each strength of brine, moreover, three degrees of turbidity 

in the ratio of 4:2:1 are observed. The following Table 12 is.a clear 

exhibit of the contents of the several tubes, the data indicating Iho 

number of cubic centimeters of turbid water, brine, and clear water 

mixed in each case.

TABLE 12. -Semitranslucent mixtures contents of tiibts.

Ingredients.

0 per cent.

4

40 

0 

10

2

20 

0 

30

1

10 

. 0 

40

0.1 percent.

4

40 

1 

9

2

 20 

1 

29

1

10 

1 

39

0.2 per cent.

4

40 

o

8

2

20 

2

28

1

10 

o

38

0.4 per cent.

4

40

4

G

2

20

4

 26

1

10

4

30

O.C per cent.

4'

40

G

4

o

20

C

24

1

10

G

34

0.8 per cent

4

40

8

2

o

20

8

22

1

10

8

32

1 per cent.

4

40

10

0

o

20

10

20

1

....

Ingredients.

Tripoli water............. .... cubic centimeters.

Brine............................ ..... do ..... 1..

Distilled water ...... ...... ..........do ........

Tripoli water used after standing three days.

Brine: 10 grams in 200 cubic centimeters.

Tubes (diameter, 25mm.; length, 200mm.) shaken up simultaneously October 1, 1S85,6 p. m.

Table 13 gives the results obtained with these mixtures; column 

first contains the date; column second, the time in hours elapsed since 

the beginning of the experiment; the remaining columns indicate the 

depth in millimeters of the surfaces of demarkation, for the condition 

of concentration and turbidity given at the column heading, below the 

surface of the liquid as a datum. Whenever the column shows a number of surfaces (surfaces of different orders), the depth of each is noted,

(540) -
TRANSLUCENT MIXTURES RESULTS. 43

the data being placed vertically above one another, in proper sequence; 

c. denotes clear.

TABLE 13. Semilranslucent mixtures consecutive positions of the surfaces ofdemarkalion.

Date. '

October 1, 1885............ 

October C, 1885............ 

Octobers, 1885............

October 9, 1885............

October 10, 1885...........

October 11, 1885. .......... 

October 12. 1885...........

October 13, 1885...........

Date.

 October 1, 1885............ 

October C, 1885............ 

Octobers, 1885............

October 9, 1885............ 

October 10, 1885...........

October 12, 1885...........

October 13, 1885...........

Time cu? day.

'C p. m ........ 

7 p. in........ 

10 a. m ........

10 a.m........

10 a.m........ 

12m..........

1 p. m ........

Time of day.

Cp. m........ 

7 p. m. ....... 

10a.m........

10 a. m.... .... 

10 a. m.... ....

12m ..........

1 p. m ........

h

0 

121 

100

184 

208

232

258 

283

h '

0 

121 

160

184 

208 

232 

258 

283

0 per cent.

4

0 

20 

26 

50 

70 

90 

32

58

80 

100 

35 

05 

90 

115 

. 40 

75

44 

80 

49 

89

0

0

40 

45 

90

54 

100

59 

110

65

72

77

0.4 per cent.'

4

0 

40 

50 

89 

60

( 

85 

'95 

105

2 1

0 0 

60 c. 

75 c.

83 o. 

c. c.

1

0 

70 

85

90

c.

c.

c.

c.

O.I per rent.

4

0 

23 

27 

45 

70

100

35 

53

115

38 

: 59

no

42 

67 

302 

45

'50 

82

2

0 

52 

65 

100

74 

120

82

95

102

110

0. 6 per ceii t.

4

0 

65

85

c. 

c.

2

0 

90 

110

c. 

c.

1

0 

f. 

c.

c. 

c.

1

0 

80 

97

112

c.

c.

c.

c.

'0.2 per cent.

4

0 

23

:i2

45 

01

90

35 

55

74

105

44

84

50 , 

98

57 

105

64

0.8 per cent.

4

0

too

c.

c. 

c.

2

0 

c. 

c.

c. 

c.

1

0 

c. 

c.

c, 

c.

o

0 

42

90

60

70

82

89

08

1

0 

72 

02

105

c.

c.

c.

c.

1 percent.

4

0 

c. 

c.

c. 

c.

o

0 

c. 

c.

c. 

c.

1

Table 14, finally, contains data for the rates of subsidence of each of 

the divers orders of surfaces, degrees of concentration and degrees of

 * 711.7)2' turbidity given in Table 13. Rates are expressed in -T-. To derive

these results I used graphic methods. The accuracy thus obtainable is 

fully in keeping with the accuracy of the other work.

(547)
44 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 30. 

TABLE 14. Semitranslucent mixtures rates of subsidence.

Order of surface. 

1 ............................................

2 ............................................ 

3............................................

^.. ..........................................

Order of surface.

1....... ..................................... 

2............................................

3.. ..........................................

4.. ......................... 1................

0 per cent.

4

0. 1C 

0.32 

0.44

0.50

o

0.28 

0.54

1

0.54

0.4 per cent.

4

0.35 

0.5C

.2

0.4G

1

0.1 per cent.

4

0.18 

0.28 

0.44

0. C2

2

0.40 

0. 04

1

0.03

0. C per cent.

4

0.54

2

0.71

1

......

0.2 per cent.

4

0.23 

0.30

0.57

2

0.35 

0.50

1

0.57

0.8 per cent.

4

0.82

o

......

1

......

The next three tables are constructed on a plan identical with that 

pursued in the cases of Tables 12, 13, and 14. Time, h, is given in

AlJilJ}

hours, depth in millimeters, rate of subsidence in -j In addition to

the experiments with water, it was found convenient to compare the 

rates of subsidence in pure water and in water charged with alcohol and 

with ether, respectively, in the proportions specified in the last four columns of Table 15.

TABLE 15. Opaque mixtures contents of tubes.

Ingredients,

Tripoli water .... cubic centimeters . .

Distilled water.. ............do......

0 per cent.

4

CO 

0 

1C

2

30 

.0 

40

1

15 

0 

Cl

0.5 per cent.

4

GO 

8 

8

o

30 

8 

38

1

15 

8 

53

1

1 per cent.

4

CO 

1C 

0

2

30 

1C 

30

1

15 

1C 

45

Alcohol.

w.

CO

20

A.

CO

%

Ether.

w.

70

10

E.

70

10

Tripoli water, densely opaque.

Brine, 10 grains in 200 cubic centimeters.

Tubes (diameter, 25 mm.; length, 200 mm.) shaken up simultaneously October 3, 1885, 12 ra.

.(548)'
BAKUB.1 , OPAQUE MIXTURES RESULTS. 45 

TABLE 16. Opaque mixtures consecutive positions of the surfaces of demarkatioit.

Date.

Octobers, 1885 .............

October 10, 1885............

October 11, 1885 ............

 October 12, 1885............

October 13, 1885 ............

October 11, 1885 ............

October 16, 1885...........

October 17, 1885 ............

October 19, 18S5 ............

Time of 

day.

12 m ....

10 a. m..

10 a. m . .

12m....

1 p.m..

5 p. in . .

9 a. m.

2 p.m..

9 a. m . .

h

0

166

190

216

241

269

309

338

381

0 per cent.

4

0

10

13

....

15

19

(a)

22

25 

38 

50 

63 

73

85

105 

29 

44 

56 

C9 

81

95

112 

33 

53 

66 

80

90

107

120

2

0

17 

(a)

GO

75

95 

27 

70

85

104

30

52

65

80

100

125

35

55

70

90

110

140 

38 

65 

78 

100 

125

42 

70 

85 

110 

138

49 

80 

90 

124

1

0

25 

65

90. 

110 

30 

C7

100

120 

31 

80

110

145

40

87

120

45

97

140

111

60 

123

C8 

135

0.5 per cent.

4

0

Sub 

ii

ti

Ml

ii

2

0

side 

Uio 

atioi 

id is 

frac 

o de

1

0

 v 

ICO

rati« 

i .an 

almo 

tion 

uavl

1 pc 

4

0

take 

>of 

I tin 

st ci 

jof'a 

jatio

r cei t.

2

0

s pi; 

uonc 

 bidi 

inpl 

n ho 

n.

1

0

CO

only, 

ut:o

Mcoliol.

\f.

0

30 

50 

63'

77

41

50

74

88

45 

65

84

A.

0

(6)

i

60

72

35th

W.

0

34

25 

37

111 

44

;r. 

E.

0

m

(b)

a Incipient stratification. b Column turbid.

(549)
.46 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [uuLL.36. 

TABLE 16. Opaque mixtures consecutive positions pf the surfaces, <fc. Contiaued.

Date.

October 20, 1885 ............ 

October 21, 1885............ 

October 22, 1885 ............

October 23, 1885 ............ 

October 24, 1885 ............ 

October 25, 1885 ............

October ?0, 1885 ......:..... 

October 27, 1885 ............

Time of 

day.

8 a. ra.. 

8 a. m . .

12 in.... 

2 p.m..

8 a. m . . 

8 a. in..

h

404 

428 

452

480 

500 

525

548 

572

0 per cent.

4

34 

55 

70 

85 

08 

11.7 

138 

38 

59 

75 

00 

103 

122 

1.45 

39 

62 

80 

95 

108 

128 

152 

40 

05 

85 

104 

117 

137 

45 

70 

89 

109 

122 

145 

45 

72 

92 

113 

125 

147 

40 

74 

95 

119 

130 

50 

78 

100 

125 

135

2

50 

84 

100 

130

55 

90 

111 

13C

59 

95

CO 

100

CO 

107

08 

110

70 

118

74 

120

1

74

75

80

85

90

93

99

101

0.5'percent.

4 2 1

1 per cent.

4 2 1

Alcohol.

W.

50 

70

90 

51

71 

92

54 

75

100

57 

84

04

90

C5

92

05 

95

70 

98

A.

75

82

87

91

95

90 

100

Ether.

W.

32

45

38

39

54

40 

00

44 

65

45

47 

50

E.

(a)

a Column turbid.

(550)
OPAQUE 

TABLE 10. Opaque'mixtures 

MIXTURES RESULTS. 47 

consecutive positions of the surfaces, <J-c. Continued.

Date.

October 28, 1885 ,

October 29,1885............

October 31,1885............

November 2,1885 ..........

'Novembers, 1885...........

November 5, 1885.

November 9,1885...........

November 13,1S85..........

November 23,1885..........

Time of 

day.

8 a. in.

1 p.m.

9 p.m.

10 a. m.

8 a. m.

7 a. m.. 

12 m...

9 p. m. 

G p. m.

h

590

625

681

718

740

787

888

993

0 per cent.

4

51

80

102

128

141

55

85

108

134

149

59

01

118

141

G2

97

125

03

99

120

103

133

07

79

118

149

87

129

104

150

2

75

125

80

131

85

140

91

149

91

99

110

127

145

1

110

112

118

124

120

133

147

(a)

(a)

0.5 per cent.

4 - 1

1 per cent.

4 2 1

Alcohol.

7:

I-*

102

74

100

fin oU

83

80

90

A.

103

107

113

118

120

124

<&)

Ether.

\V. K.

51

51

50

59

,5,

a Clear. b Column turbid.

TABLE 17. Opaque mixtures rates of subsidence.

1...... ..........

2...... ..........

3................

4................

5

0................

7

0 per cent.

4

0.08

0.13

0.17

0.21

0.28

n. as 1

2

0.12

0.20

0.25

0.32 

0.40'

0.51

1

0.17

0.30

0.51

0.05

Water.

W.

0.12

0.17

0. 22

0.25

|

A.

0. 17

El her.

AV.

0.08

0.12

E.

......

......

(551)
48 SUBSIDENCE OF FINE SOLID PAETICLES IN LIQUIDS. [HULL. 30.

A few remarks on these tables are in place here. The observation 

that distinct stratification is an earlier occurrence in translucent solutions than in very opaque solutions is well shown by the data in Table 

1C. The alcohol and the ether solutions remain turbid during,the 

whole of the 1,230 hours within which subsidence is in progress. The 

descending surface in alcohol (very dense) must therefore be of an 

order higher than the first. Possibly the persistent turbidity may be 

connected with slow evaporation of alcohol or of ether out of the solvent 

water. Where subsidence'takes place too rapidly for the formation of 

surfaces, no data are given, since these results would not bo comparable with the other data, and the qualitative character of the phenomena has already been fully given in Chapter I.

The term translucent solution is used interchangeably with diluted 

mixture, opaque solution interchangeably with dense mixture. The extreme members of the dilute and of the opaque series differ largely in turbidity; but the degrees of turbidity of the intermediate members (i. e., 

high degrees for translucent solutions and low degrees for opaque solutions) probably overlap.

DEDUCTIONS.

The discussion may expediently be made to conform with tile general 

plan pursued in the experiments. Eate of subsidence is therefore to be 

studied with regard to its dependence on order of surface, on concentration, and on turbidity.

Surf aces'of different orders. Turning first to the data for diluted mixtures, Table 14,1 find three series of results available for comparison. 

In these there appears a distinct tendency of rate of subsidence to augment by nearly the same increment on passing each of the consecutive 

surfaces of demarkation. In the case of one and the same column, therefore, like differences of order correspond approximately to like differences of rate. This deduction is'nearly true for the 0 per cent, solutions, and true to a smaller extent for the 0.1 per cent, and 0.2 per cent, 

solutions.

It is remarkable that as far as the O.G per cent, brines, the lowest surfaces for all turbidities and concentrations have like rates. This, however, may be merely accidental, so that if the tubes had been of greater 

length the result would no longer hold. Any rate in turbidity 1 is, as 

a rule, repeated in turbidity 2; rates in turbidity 2 are repeated in 

turbidity 4. When turbidity decreases, greater rates are more frequently repeated than smaller rates. We are thus inclined to infer 

that for continued dilution the column of finer material eventually becomes so nearly transparent that the surfaces escape detection; but 

this explanation is not valid, as will be shown presently in the case of 

opaque mixtures. For brine of greater strength than 0.6 per cent, the 

observations lose in accuracy, and we begin to encounter marked evi-
BARUS.] SURFACES OF DIFFERENT ORDERS. 49

dences of the effect of salt. Finally the increment of rate from surface 

to surface is augmented in marked degree in proportion as the turbid 

column approaches trauslucency.

With these suggestive results in hand it is well to turn for further 

corroboration to the experiments upon opaque solutions given in Table 

17. The three degrees of turbidity of the 0 per cent, solutions, as well 

as the water of the* alcohol and the ether series, are here available for 

comparison. The evidence given by all of these corroborates the deductions made above in a very satisfactory manner, viz : for one and 

the same turbid column the rate of subsidence tends to increase, step 

by step, in regular order, downwards. If mere dilution were of moment 

here, the upper layers would subside fastest. The column, which at the 

outset is continuously opaque, splits up into periods of nearly the same 

value. Again, the increment of rate of subsidence corresponding to two

consecutive surfaces is manifestly smaller for opaque than for translucent solutions, and varies quite regularly with the degree of turbidity. This result is fully confirmed by the data for dilute solutions. 

The very satisfactory accordance of all data in hand may be shown 

graphically by regarding rate of subsidence as a function of order of surface arid constructing the linear loci on which the isolated points of observation approximately lie. This has been done in the annexed Fig. 

3. If these lines taken as a whole be prolonged in the direction of

3:0

FIG. 3. Relation of rate of subsidence to order of surface for different degrees of turbidity.

order decreasing, we infer from the positions of the divers points of 

intersection with the axis X, that probably only one or at most two surfaces of very slow rate have escaped detection. Whether or not such 

prolongation be permissible remains to be seen, but the particles belonging to one of these surfaces are probably the cause of the permanent 

opalescent turbidity which frequently remains after measurable subsidence is complete.

Concentration. In the case of dilute mixtures turbidity 4, surfaces 1 

and 2, and turbidity 2, surfaces 1, are available. It appears that rate 

of subsidence as a function of concentration varies at a gradually accelerated rate, almost imperceptibly between 0 per cent, and 0.2 per 

cent.; more rapidly from 0.2 per cent. on. Surfaces are obtainable even 

as far as 1 per cent. In the case of very opaque solutions surfaces are

(553) 

Bull. 3G 4
50 SUBSIDENCE OF FINE SOLID PARTICLES IN LIQUIDS. [BULL. 88.

no longer obtainable even for brine of a few tenths per cent, of strength. 

Here, therefore, rate of subsidence increases with concentration much 

more rapidly than holds for dilute mixtures.

Turbidity. In the case of opaque solutions the six consecutive surfaces of the 0 per cent, series are available. The data show that 

velocity of subsidence diminishes at a gradually decreasing rate as turbidity increases. This diminution is more pronounced for the upper 

rapidly-falling surfaces than for the lower surfaces of slower descent. 

Begarded as a whole, therefore, the curves converge more and more

o.o

6 1 £ 3

FIG. 4. Relation of rate of subsidence to turbidity for consecutive orders of surfaces.

nearly in proportion as the original coJumn is more opaque (Fig. 4). 

Hence for very opaque solutions, cseteris paribus, the curves probably 

converge in the rate of subsidence zero. In other words, the tendency 

is toward permanent opacity without stratification.

All these inferences are sustained by the data in hand for translucent 

solutions, where first surfaces of the 0.0, 0.1, 0.2, 0.4 per cent, solutions, 

and second surfaces of the 0.0, 0.1, and 0,2 per cent, solutions have been 

compared. Unfortunately, the results for opaque and for dilute solutions are on .a different scale of turbidity. It is a question, moreover,

whether surfaces of like order can be at once co-ordinated, so that 

further inquiry into this subject will be desirable and fruitful.

Temperature. It has already been pointed out, as a result of the error 

introduced by temperature, that the actual locus does not necessarily 

pass through the origin. This assumption, therefore, is only partially 

correct. It is, however, the only method of representation which may 

be consistently applied throughout. I may add, that, columns of liquid 

placed side by side, show parallel variations of temperature discrepancy. If the surfaces observed above were due to temperature only, 

then we ought to find traces of a daily effect. In the 1,230 hours of 

examination, therefore, fully fifty such surfaces should be anticipated. 

The phenomenon observed is essentially different from this.

Sedimentation lattery. The experiments made suggest the following 

scheme for researches of a final kind: The tubes for subsidence should 

be 50 cm. long and about 3 cm. wide. This will give assurance not only 

that all surfaces have been detected, but will enable the observer to 

follow each one through a large interval of descent. These tubes (36 to

(554)
BAUDS.] - SEDIMENTATION BATTERY. 51

s

100) are to be conveniently arranged in tiers of say 6 to 10 in each horizontal row and the same number in each vertical row. Where brine and 

tripoli, for instance, are the ingredients, the degrees of concentration 

0.0, 0.1, 0.2, 0.4, 0.6, 0.8, 1 per cent, (horizontal row) and the degrees 

of turbidity 1, 2,4, 6, 8,10 (vertical row) will probably suffice to enable 

the observer to follow all the essential phenomena closely. It is highly 

desirable that each tube be provided with a millimeter scale (etched). 

It is necessary that the battery be placed in a room whose temperature 

is constant. Great pains must be taken to detect and observe all surfaces, and even to seek for such as are apparently invisible, by some such 

method as that described in the text, page 49. The experiments must, 

of course, be extended to a variety of subsiding solids. They must frequently be repeated to exhibit the time effect of the action of the liquid 

on the suspended solids.

(555) , '

INDEX.

Page. 

Battery for sedimentation work.............................................. 50

Brewer, experiments of ...................................................11,12,13

Capillarity, effect of ........................................................ 39

Clausius, electrolysis explained by........................................... 25,36

Concentration denned....................................................... 42

effect of................................................................. 49

Demarkatiou, sharpness of.................................................... 20

Discussion of experimental results. ...... .................................... 33

Durham, experiments of...............'.............................. .^...... 13

Ether, subsidence in......................................................... 15

Fog phenomena in liquids ................................................... 16

Fraunhofer, vesicles of mist in air measured by ............................... 35

Graham, viscosity of alcohols ............................................... 34,38

Grotrian, viscosity of liquids ................................................ 39

Helmholtz, smallest visible length as stated by ................ ...... ........ 14

Helmholtz and Piotrowski, experiments of ................................... 13

Hunt, experiments of ....................................................... 13

Hydration, effect of ..................................... ................... 12

Kohlrausch, conductivity of water .......................................... 25

Kundt and Warburg, external friction'....................................... 13

Maxwell, viscosity of air given by........................................... 14

equation of ............................................................. 17

Meyer, size of molecule given by............................................ 21

Molecules, size of............................................................ 21

velocity of.............................................................. 22

Opacity denned............................................................. 17

Packing .................................................................... 31

Particles, size of ............................................................ 21,34

Poiseuille, viscosity of liquids as found by ................................... 23,39

viscosity of ether found by .............................................. 34,38

Precipitants, effect of........................................................ 24

Sedimentation work, battery for ............................................. 50

SI otte, viscosity of water as found by......................................... 23,34

Solution, how understood ................................................... 40

Sprung, viscosity of liquids.................................................. 39

Stokes, viscosity of air....................................................... 14

- reflection from motes...... .............................................. 18

Stratification ............................................................... 15

Stuntz, experiments of ...................................................... 13

Subsidence, general relations of ............................................. 11

mechanical relations of ................................................. 33

electrical relations of ................................................... 35

larger particles ......................................................... ,36

^Subsidence and viscosity .................................................... 38

Surfaces of demarkation, order, of, denned and discussed...................... 42,48

(557) 53
54 INDEX.

	Page. 

Table 1. Subsidence at 15° andat 100°...................................... 23'

2. Subsidence in. distilled water ...... ................................ 26

3. Subsidence in salt solutions........................................ 27

4. Subsidence in salt solutions........................................ 28

5. Subsidence in salt solutions........................................ 29

6. Subsidence in salt solutions........................................ 30

7. Subsidence in divers liquids ........................................ 3ft

8. Bulk of sediment after subsidence.................................. 31

9. Bulk of sediment after subsidence ................................. 31

10. Digest of rates of subsidence....................................... 32

11. Subsidence of opaque and of translucent mixtures in brine.......... 37

12. Semitranslucent mixtures contents of tubes ...................... 42

13. Semitranslucent mixtures.......................................... 43

14. Semitranslucent mixtures rates of subsidence..................... .44

15. Opaque mixtures contents of tubes............................... 44

16. Opaque mixtures consecutive positions of surfaces of demarkation. 45

17. Opaque mixtures rates of subsidence............................. 47

Temperature,effect of....................................................... 20,50

Turbidity, effect of........................................................... 19,37

defined................................................................. 42

relations of subsidence to varying ....................................... 50

Viscosity, literature of....................................................... 39

Viscosity of air.............................................:............... 14

Wagner, viscosity of liquids................................................. 39

White, aid of ............................................................... 13

Williamson, etherification explained by...................................... 25

(558)

c

o

p

ct

s

I

31 

ttt