DEPARTMENT OF THE INTERIOR 

FRANKLIN K. LANE, Secretary 

UNITED STATES GEOLOGICAL SURVEY 

GEORGE OTIS SMITH, Director 

Professional Paper 95 

SHORTER CONTRIBUTIONS TO 

GENERAL GEOLOGY 

1915 

DAVID WHITE, CHIEF GEOLOGIST 

WASHINGTON 

GOVERNMENT PRJ;NTING OFFlCE 

1916 
PRELIMINARY REPORT ON THE DIFFUSION OF SOLIDS. 

By C. E. VAN 0RSTRAND and F. P. DEWEY.1 

INTRODUCTION. ; .0 

Although 19 years has elapsed since Roberts-Austen 2 published his c4ssical paper on the 

diffusion of solid metals, no attempt seems to have been made to verify hiB.i important results 

and conclusions or to extend the investigations to minerals and to the. great number of solids 

in which diffusion may be expected to occur. Progress has been made by means of chemical 

and electrical methods 3 in the detection of diffusion· in a number of metals in the solid state, 

some progress has been made in explaining the phenomena of diffusion on the basis of osmotic 

pressure and the kinetic theory, and recent measurements of the vapor pressures 4 of solids have 

contributed indirectly to the progress of t;he science, but investigators ha-ve not undertaken 

the difficult and essential task of making definitive determinations of the coeffidents of diffusivity 

at various pressures and temperatures. 

The investigation of which this paper is a preliminary note has for its first object the determination of the coefficients of diffusivity over a considerable range of pressures and temperatures for metals and minerals. The investigation was first undertaken in ·connection with some 

experiments on the elasticity and plasticity of metals. Although it-is-believed that the results 

are essential for the construction of a complete theory of .the physical properties of elastic and 

plastic bodies in the normal state or in a state of isostatic adjustment, it is realized that this is 

. only one of many fields in which the results are of fundamental importan{le. Roberts-Austen 

emphasized the importance of diffusion in its relation to the form11tion of;alloys and the more 

vital problem of the constitution of matter; the importance of the gener.aJ problem of diffusion 

in the ehicidation of geologic problems has been emphasized by Becker,5 wlio also prepared a 

table for the computation of diffusivities; Elsden 6 and Liesegang 7 give an--extended discussion 

of the subject in t1:.3ir textbooks; Desch 8 has pointed out the possibility of explaining secondary 

replacements of minerals, the formation of pseudomorphs, schiller inclusions, and other geo..:. 

logic features on the basis of the diffusion of minerals in the solid or molten state; and recently 

Gillette 9 has discussed a theory of ore deposition in which osmotic pressure is assumed to be 

one of the fun dam en tal factors. 

In their more general aspects the phenomena of diffusion are not confined to the inorganic 

world. It is well known that diffusive processes play an important part'· inliving matter, and 

1 Dr. Dewey is assayer to the Bureau of the Mint, United States Treasury Department, and thi.s paper is published with the permission of the 

Director of that bureau. .-· · 

2 Roberts-Austen, W. C., On the diffusion of metals: Roy. Soc. London Philos. Trans., vol.187 A, pp. 383-415, 1896; On thediffusionofgoldinto 

solid lead at the ordinary temperature: Roy. Soc. London Proc., 1900, pp. 435-441; also vol. 67, pp. 101-105. 

a Guillet, L., and Bernard, V., Local prevention of casehardening and diffusion in solids: Rev. metallurgie, vol. 11, pp. 752-765, July, 1914. 

Desch, C. H., Report on diffusion in solids: British Assoc. Rept., 1912, pp. 348-372. (As this report contains an excellent summary of the literature 

of the subject, the references need not be repeated in this paper.) . · 

~ Hulett, G. A., The distillation of amalgams and the purification of mercury: Phys. Rev., vol. 33, pp. 307-317, 1911. (Hulett made an approximate determination of the vapor pressure of platinum at a temperature of 200° C.) Langmuir; Ir~ing, The vapor-pressure of metallic tungsten: 

Idem, 2d ser., vol. 2, pp. 329-343, 1913. Langmuir, Irving, anq. Mackay, G. M. J ., The ~apor pressure of the m~tals :platinum and molybdenum: 

Idem, 2d ser., vol. 4, pp. 377-387, 1914. · Wartenberg, H. von, Uber Metalldampfdrucke: Zeitschr. Elektrochem'ie; vol.19, p. 482, 1913: 

s Becker, G. F., Note on computing diffusion: Am. Jour. Sci., 4th se.r., vol. 3, pp. 280-286, 1897. 

6 Elsden, J. V., Principles of chemical geology, Whittaker & Co., London, 1910. · 

7 Liesegang, R. E., Geologische Diffusionen, Theodor Steinkopff, Dresden and Leipzig, 1913. (An important.re:view of this. work is given by 

Adolph Knopf in Econ. Geology, December, 1913, pp. 803-806.) · ' · 

s Desch, C. H., op. cit. · 9 Gillette, H. P., Osmosis as a factor in ore formation, in Emmons, S. F., Ore deposits, pp. 450-454, Am. Inst. Min. Eng., 1913. 

83 
84 SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY, 1915. 

it will be interesting in this connection 1 to quote from the conclusion of the paper by RobertsAusten, already cited. Referring to Graham's great work on the diffusion of salts into liquids 

and of liquids into each other, he says: 

His work in experimental physics, more than that of any other investigator, taught the physiologist that tracing 

the relations of the phenomena of life as revealed in diffusion, transpiration, and osmosis will afford natural history its 

most precious records. 

The evidence gathered by the metallurgist of active atomi.c movement in fluid and solid metals may sustaht the 

hope of the physiologist that be will ultimately be able to measure the atomic movements upon which vitality and 

thought depend. 

THEORETICAL CONSIDERATIONS. 

The phenomenon of diffusion as exemplified by gases, salts, liquids, solids, and certain 

constituents of organisms is supposed to be a transfer of mass in a given direction due to the 

continuous haphazard motion of the molecules of which the substances are composed. A simple 

analogy is that of spheres moving over a smooth horizontal surface bounded on the edges by 

perfectly elastic walls. We may imagine one system to consist of white and the other of red 

spheres, and the two systems to be separated from eaeh other by a perfectly elastic partition. 

If the spheres are set in motion and the air resistance is negligible, they will continue to collide 

with one another for an indefinite time. The mean kinetic energy of each system, corresponding 

in our analogy to the temperature of the system, may or may not be the same, but in either 

case if the partition is removed the red and white spheres begin to collide with one another 

and to occupy areas previously occupied by spheres of a single · color. A strip on each side of 

the line marking the original position of the partition will thus contain spheres of both colors, 

the greatest number of mixed colors being in the immediate vieinity of this line. It is conceivable 

that a very small number of spheres will reach the boundary wall parallel to the partition in a 

very short time, and that as the process continues spheres of the opposite color will accumulate 

in this region and there will th(m be reflection or resultant motion in the direction toward the 

partition, the tendeney being always for a sphere to move away from the region in which the 

nun1ber per unit area of spheres of its particular kind is greatest. Statistieal equilibrium in 

density will be attained when the number of red spheres per unit area is constant throughout 

the entire area, and similarly for the white spheres. The paths traced out by the spheres are 

of course very irregular, and even after equilibrium is established the spheres zigzag back and 

forth across the plane, but always in such a way that the average number of different spheres 

per unit area remains unchanged. It is evident that equilibrium of this kind implies that the 

average nu1nber of red or white spheres entering any fixed area of the surface over which the 

spheres are moving is the same as the number leaving the same area in a given interval of time. 

That the interdiffusion of gases, liquids, and solids and the diffusion of gases into solids 

and of gases and solids into liquids are mechanical processes analogous to the simple process 

just described may be inferred from the observations and verifieations with theory of the 

Brownian movements. A study of these phenomena has sufficed to establish Maxwell's fundamental laws for the equipartition of energy and the distribution of velocities about the average 

velocity for liquids and has thus provided a sound foundation on which the kinetie theory of 

matter in the three states-solid, liquid, and gaseous-may be constructed. The remarkable 

theoretical and experimental investigations of Perrin, 2 Einstein, and others leave no doubt as to 

the teality of molecules and molecular motion in liquids, and it therefore seems reasonable to 

infer that solids are mechanical systems of the same kind, in which the molecular displacements are much restricted, and in some solids, such as crystals, the law of restrietion varies 

from one form of crystal to another. It is eonceivable that molecules possess axes along which 

the attractive forces vary. In the liquid and gaseous states the molecules are in constant 

rotation, and the distance between centers is so great that the directional forces are inappreciable, but in the solid crystalline state these forces may predominate to such an extent that the 

1 See also, for example, Livingston, B. E., The role of diffusion ·and osmotic pressure in plants, Univ. Chicago Press, 1903. 

'Perrin, Jean, Brownian movement and molecular r<:ality, by F. Soddy, Taylor & Francis, London, 1910. 
PRELIMINARY REPORT ON THE DIFFUSION OF SOLIDS. 85 

strictly random rotations and displacements do not occur. The number of degrees of freedom 

of the system has been diminished. 

Attempts have been made to explain diffusion and osmotic pressure on the basis of chemical affinity, the formation of loose chemical compounds, and the influence of surface tension. 1 

Chemical affinity, however, is merely the potential energy of a dynamic system; the formation of 

loose compounds is simply aggregation and dissociation, and surface tension has long been 

known to be due to unequal molecular attractions. Each explanation is in reality the application of a special feature of dynamic theory, although it was apparently intended by the advocates of these hypotheses to obtain an explanation of the phenomenon which would be independent of mechanical systems. The fact that there is an observed transportation of matter 

would seem in itself to be a sufficient justification for the assumption that the system is mechanical, but the additional fact that solids possess a vapor pressure would seem to leave lttle doubt 

in regard to the validity of the hypothesis that solids 2 are composed of discrete articles .in 

a state of rapid oscillation, ~lthough restricted somewhat in their movements. 

In the consideration of the migration of the particles in the diffusion process, one of the 

simplest methods of procedure is to adopt a certain average value or constant which orresponds 

to a oertain type and state of molecular activity of the given substances. The quanti y selected, 

the coefficient of di:ffusivity (k), may be defined by considering the exchange of m lecules between two cylinders of different substances when the ends are placed in contact with eaoh other 

and the entire system is maintained at constant temperature. The principle of suffic ent reason 

suffices to show that the molecular transfer will take place in suoh a manner that the concentration, the mass of dissolving substance per unit volume of solution, is constant t oughout a 

layer of infinitesimal thickness perpendicular to the common axis of the cylinders. T e simplest 

assumption that can be made in regard to the interdiffusion of the two substances i to assume 

that the amount of diffusing substance which passes any plane perpendicular to the axis of the 

cylinder is proportional to the time, the area of cross section, and the rate of change of concentration per unit length, measured in the direction in which the solute is moving into e solvent. 

Expressed in the form of an equation, the assum.ption may be written 

wherein 

m. = mass of solute 

k = coefficient of diffusion 

a = area 

t = time 

m=ka (vl--v2) t ---------------------------------- (1) . ~X 

Ax= distance between two planes at which the concentrations are v1 and v2• 

Now put a, t, Ax, and (v1 -v2 ) eaoh equal t o unity; then k is the mass of sol te passing 

through a unit cube of the solvent in unit time when the difference between the con entrations 

at the opposite faces of the cube is equal to unity. It will be noted that equation (1) represents 

also the quantity of heat flowing through a plate of cross-sectional area a, thickness~ , in timet, 

when the temperatures of the respective surfaces are v1 and v2 • The quantity k is ere called 

the thermal conductivity of the substance. 

With this definition of the coefficient of diffusivity as a basis, we now proceed to find the 

amount of solute in any given volume of the solution whose center is at distance x fro the plane 

of contact, after a given time interval t has elapsed. If we imagine the two par llel planes 

which are perpendicular to the direction of flow of the solute to approach each oth r, we have 

in the limit, when the time interval also is infinitesimal, 

ov dm=ka0xdt 

1 For a discussion of these and other explanations, see Whetham, W. C. D., Theory of solution, Cambridge Univ. Press, 1902; 

der, Osmotic pressure, Longmans, Green & Co., 1913. · 

2 See also Nernst, Walther, The theory of the solid state, Univ. London Press, 1914. Bragg, W. H. and W. L., X rays and rystal structure, 

G. Bell, London, 1915. Magie, W. F., Relation of osmotic pressure to temperature: Phys. Rev., October, 1912, pp. 272-275. 
86 SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY, 1915. 

Here again it is evident that our assumption is the simplest possible, for it would not be unreasonable to assume that dm is a function of the higher powers of ovjox. Our equation merely 

amounts to stating that 

fx = k ~v-- -- --- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -(2) . uX . 

is the rate per unit time at which the solute flows through unit area of a plane which is perpendicular to the axis of the cylinder and at distance X from the plane of contact. The term flow 

is here used to designate the resultant motion of the solute in a given direction and is merely the 

summation in a given direction of the very irregular displacements of the molecules. The 

resultant at right angles to the direction of flow is zero, on account of reflection at the surface, 

but there is always a small resultant displacement. of the particles in the direction from higher 

to lower concentration. 

' Now imagine a parallelepiped whose edges are 2dx, 2dy, 2dz, and whose center is at distance 

x from the plane of contact. The change in concentration per unit volume . at x in time dt is 

(ovjot) dt and the increment in the mass of the solute in this elementary volume is therefore 

represented by the equation 

volume X change in concentration = 8 dxdydz~~dt_ ___ . _______________ (3) 

We can obtain another expression for the same quantity, for the :r;ate at which the solute is 

flowing into the parallelepiped across the plane nearest to the plane of. contact is 

4 dydz(fx+~)dx 

Similarly the rate of outflow across the plane farthest from the plane of contact is 

4 dydz ( fx- Of;) dx 

and the total gain to the parallelepiped in time dt is therefore 

8 dxdydz ofxat 

ox . 

Equating this expression to (3) and making use of (2) we get the result 

An integral of ( 4) is 

in which 

ov ofx 02V 

ot = ox = k ox2 - - - - - - - - -- ~- - - - -- - - - - - - - - - - -- - ( 4) 

[ 

2 fq . J . v=v0 1--{;Jo e-q2

dq ----------------------------(5) 

V0 =constant 

q =x/2-J'kt 

This result may be established by expressing the integral as a function of the limits of integration and performing the necessary differentiations. 1 

1 For other methods of integration, see, for example, Carslaw, H. S., Fourier's series and integrals, Macmillan & Co., 1906; Ingersoll, L. R., 

and Zobel, 0. J., Mathematical theory of heat conduction, Ginn & Co., 1913; Byerly, W. E., Fourier'sseriesandsphericalharmonics, Ginn &Co., 

1895; Woodward, R. S., A new method of integrating one of the differential equations of the theory of heat diffusion: Phys. Rev., vol. 16, pp. 

176-177, 1903; On t:p.e free cooling of a homogeneous sphere: Annals Math., vol. 3, pp. 75-88, 1887 
PRELIMINARY REPOR1' ON THE DIFFUSION OF SOLIDS. 87 

If lc is replaced by 

h K=-

pC 

where p, h, and c are respectively density, conductivity, and specific heat of th substance, 

equation (5) will then represent the distribution of temperature in an insulated ar of great 

length, initially at a uniform temperature of 0° throughout the mass, and subjecte at one end 

to a constant temperature v0 for the time interval t. Similarly, equation (5) re resents the 

distribution of concentration in a cylinder of initially pure substance .in the sold or liquid 

state when a layer of constant concentration 'Vo is maintained at the base of the cylinder for 

a ti1ne t. When t = 0, equation (5) gives v = 0 for all values of x, thus expressing the fact that at 

the beginning of the experiment the cylindrical mass contained no solute. For all nite values 

oft other than zero, equation (5) gives v=v0 for x=O, which agrees with the cof.dition that 

constant concentration is maintained at the plane of contact; and for other values 9f x, v diminishes as x increases until for x= oo, v=O. These results agree with the general for of the observed curve indicated in figure 32 (p. 94). As tin1e proceeds, the curves cont." ue to rise, 

and when an infinite time has elapsed, v =v0 for all values of :c. In other words, c nstant concentration is attained in.a cylinder of infinite length in an infinite time. Stefan 1 a sumed that 

reflection occurs at the ends of a cylinder of fmite length and that the concentr 

point is the sum of the concentrations at corresponding points in a cylinder of eat length, 

the long cylinder being supposed to be cut into lengths equal tQ that of the short ylinder and 

then folded backward and forward upon itself until the extreme portion contain· g solute is 

contained within the short lel)gth. The correctness of the assumption has been abundantly 

verified by the experiments of Roberts-Austen on molten metals. 

EXPERIMENTAL METHODS. 

Roberts-Austen determined the coefficients of diffusion of solid gold into solid ead at temperatures of 100°, 165°, 200°, and. approximately 18° C. In some experinients a god plate was 

fused to the end of the lead cylinder; in others a gold. plate . or a 5 per cent alloy of gold and 

lead was pressed against the surfaced end of the lead cylinder by means of bin ing screws. 

The specimens were maintained at constant temperatures for various time inter als ranging 

from 10 to 41 days for the high temp_eratures and 4 years for the ordinary tempe, atvre., after 

which they were sliced and .the gold content of each section determined to a hi h degree of 

precision by means of a careful assay. · 

We have conducted similar experiments at temperatures of 100°, 150°, 180°, and 197° C., 

using for some of the specimens 0.5-millimeter. gold plates clamped to the end of the lead 

cylinders, and for others a gold electroplate on one or both ends of the lead cylinde , in accordance with a suggestion of Dr. N. E. Dorsey, of the Bureau of Standards. After t e specimens 

were heated for a number of days in an air thermostat controlled by a mercury re~ulator, they 

were cut into sections by means of a sharp bevel-edged wheel attached to a turn~p lathe. 

The distances from the planes of contact to the boundary planes of the sectj. n were first 

determined with a micrometer attached to the lathe, but this method proved to be unsatisfactory on account of the necessity of shifting the specimen in the lathe chuck. more satisfactory method consisted in marking the begibning and end . of each section wit a dividing 

engine. A slight error results from inaccuracYii in. setting the cutting tool, but su h errors are 

accidental and are therefore not of a serious chl racter. The method of determininJ the lengths 

from the densities will be used in . connection with th~ preceding method for d~ erminations 

of the very highest precision. , 

As the edges of the electroplate must be turned off to obtain a perfect cylind r, the plates 

frequently tend to curl, and it is therefore necessary to clamp the ends lightly in or er to insure 

perfect contact 'throughout the plane surface. None of the electroplated specimens f iled to show 

1 Stefan, J., Uber die Diffusion der Flussigkeiten: K . .Akad. Wiss. Sitzungsb., Band 79, Abt. 2, pp. 161-214, 18 9. 
88 SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY, 1915. 

diffusiOn when heated to a temperature above the normal, but in some of our trials with 0.5-

:millimeter gold plates only 20 per cent of the specimens showed diffusion at temperatures of 

100° and 180° C. In another experiment, however, in which five pairs of gold and lead were 

heated to a temperature of 150° C., each specimen was found to contain a sufficient quantity 

of gold for the determination of the coefficient of diffusion (k). We have no explanation to 

offer for the cause of failure other than the possibility of oxidation and imperfect mechanical 

treatment. The ends of the lead cylinders were carefully surfaced on a lathe. Oil was used 

in the surfacing process and afterward removed by the use of caustic soda and a 10 per cent 

solution of nitric acid. The 0.5-millimeter gold plates (20 millimeters in diameter) require no 

preparation other than cleansing in dilute nitric acid and distilled water. 

Pure gold was obtained from Mr. Jacob B. Eckfeldt, of the United States Mint at Philadelphia. Lead was obtained from the Pennsylvania Smelting Co., Pittsburgh, in the form of 

bars 1 by 3 by 6 inches. It was found to be free from gold and silver but contained a trace of 

copper. 

The thermostat is provided with two heating coils, one consisting of insulated resistance 

tape attached to a cylinder of coarse wire screen .and placed just within the inside wall, and 

the other consisting of 20 nickel coils wound on soapstone cylinders (2 by 3! inches) and placed 

on the bottom of the thermostat. The insulation powder (Silox) was obtained from the General 

Electric Co. 

Temperatures were measured with standardized mercury thermometers placed at various 

points. The temperature gradients were found to be so slight that no errors could have arisen 

from this source. 

METHODS OF EVALUATION OF CONSTANTS. 

In the evaluation of the coefficient k, investigators frequently use Stefan's tables/ which 

are very convenient when an alloy or concentrated solution of known height and concentration 

diffuses into pure solvent. In order to apply the tables it is necessary to make the height of the 

section selected for analysis equal to one-half the height of the alloy or solution from which 

diffusion emanates. Such tables are not adapted to our needs, and we have used instead some 

manuscript tables of the probability integral which have been prepared especially for the computation of diffusivities. 

The observed concentrations require no correction for the differences in density of the two 

metals, but the observed distances (x') from the plan~ of contact must be corrected for the 

expansion of the solvent over .the temperature interval (T-T0) where T0 is the temperature at 

which the specimen is sliced and Tis the temperature at which diffusion takes place. · If a is 

the coefficient of expansion of the solvent, the value of x to be used in the formula for q is 

x=x' [1 +a(T-T0 )]. 

With q_ as an argument the values of the probability integral are taken frDm the special 

tables for points which correspond to the upper, middle, and lower planes of the section, and in 

accordance with the approximate formula of Cotes, the average value of the integral for the 

entire section may be taken to be · 

~[sum ofend ordinates+4Xmiddle ordinate]. 

Designating the difference between unity and th~s value of the integral by i, equation (5) may 

be written 

V = V0i-- - -- - -- - -- - -- - -- - -- -- -- ~- _- _- -- _- _- (6) 

1 Stefan, J., op. cit. 
PRELIMINARY REPORT ON THE DIFFUSION OF SOLIDS. 89 

·Equation (5) contains two unknown constants, v0 and lc. Numerous soluti ns may be 

{)btained by adopting different methods of procedure or by assigning different we ghts to the 

observation equations. As the different methods lead to slightly different values of the constants, it is essential that the method adopted should be theoretically correct. 

For the data of this paper the maximum error in the determination of the gol content of 

each section is of the order of magnitude of 0.005 milligram. The probable erro of a single 

determination is of course less than this quantity, and there is no reason for assumi g it to vary 

for the different sections. The weight of each point on the concentration curve is therefore 

equal to unity for sections of normal height and one-fourth for sections of one-half the normal 

height. 

Roberts-Austen determined the value of 'Vo by extending the concentration urve backward until it intersected the axis of ordinates. This method is not entirely sat sfactory on 

.account of the rapid changes in curvature of the concentration curve in the vicinity f the origin. 

_For this reason we have adopted the linear equation 

• 2 v0 idv0 + qe-q {~lc dlc = dv _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ______ (7) 

idv0 + qe-q2dk' = dv _____________________________ - __ (8) 

which enables us by the method of least squares to determine both constants at th same time. 

'The approximate values necessary for the computation of dv were determined by selecting at 

]east three v&.lues of 7c at equal intervals apart and over a sufficient range to includ the correct 

·value. Substituting each value of 7c in (6) and solving in the form 

"f-piv 

Vo = !-piz - - -- - - - - - - - - - - - - - - - - - - - - - --- - - - - - - - - - - ( 9) 

-wherein weights are designated by p, we obtain the corresponding weighted values of v0 • The 

:sum of the· weighted squares of tlie residuals was then computed in the usual anner and 

·plotted with the values of 7c as abscissas. The value of 7c which corresponds to a minimum 

value of the sum of the weighted squares of the residuals was ascertained by drawi g a tangent 

·to the curve parallel to the 7c axis. The corresponding value of v0 was . determin d by inter-

:polation, using 7c as an argument. A rough check on the computation consists in plotting 

the sum of the weighted squares of the residuals for the new values of v0 and 7c on the original 

.diagram. · The new point should of course fall at the vertex of the curve. A more satisfactory 

·Check is obtained by solving equations (7) and (8). The coefficients and absol te terms of 

-the observation equations are computed from one of the original pairs of values of v0 and 7c 

·that are adjacent to but do not coincide with the minimum point of the curve whiof represents 

·the sum of the weighted squares of the residuals. 1 

In order to show the influence which the data from the various sections ex rt in fixing 

·the final values of the constants, and at the same time to illustrat e the method of c mputation, 

-.the observation equations for the data of Table 1 are tabulated below. 

0.68722 dv0+0.14949 dk'=+0.00059 

.44324 .27868 - .. 00005 

.26730 .37185 - .00037 

.15024 .42083 - .00053 

.07850 .42608 - .00040 

.0::1802 .39519 + .00009 

.01704 .34005 + .00015 

.00706 .27351 + .00014 

.00269 .20665 + .00009 

.00095 .14715 + .00008 

. . 00031 .09899 - .00023 

.00009 .06302 . - .00006 
90 SHORTER' CONT'RIBUTIONS TO GENERAL GEOLOGY, 1915. 

The normal equations are 

from which we obtain 

As 

we have 

and 

The approximate values 

1.69266 dv0 + 0.94621 dk' = -0.0000016 

0.94621 dv0 + 1.02166 dk' = -0.0003281 

dk' = - 0.000664 

dv0 = + 0.00037 

Vo 

-v'1rk = 1.54386 

dk= -0.00043 

k = 0.0080 - 0.0004 = 0.0076 

V0 = 0.02189 + 0.00037 = 0.02226 

k=0.0080 

V0 =0.02189 

were determined as explained above from the following quantities: 

lc 

0 . 0070 

.0075 

.0080 

Vo 

0.02283 

.02234 

.02189 

~(residuals) 2 

126 

84 

105 

The numbers tabulated in the third column are the first two or three digits only of the actual 

sums. If these numbers are plotted with the values of k as abscissas, it will be found that the 

minimum point of the curve falls at k = 0.0076. With this value of k as argument, the corresponding value of v0 is found by interpolation to be v0 = 0.02230. These values agree almost 

identically with those just ·found by solving the above system of observation equations. · The 

number .found for ~(residuals) 2 is 82, which is practically the same as the value found by the 

graphic method. . As the coefficients and absolute terms of the normal equations are summations 

of squares and products of coefficients and products of coefficients and absolute terms of the 

observation equations, it. is evident that the equations at the bottom of the list exert but little 

influence in the determination of the constants. The final values would remain practically 

unchanged if the last two or three equations were omitted. The weights of v0 and k are each 

finite and may be determined in the usual manner. The respective weights of these quantities 

resulting from the use of equation (9) are ~pi2 and oo. Another solution consists in assigning 

an infinite weight to v0 , and then taking the weighted mean of the resulting values of k. It is 

thus evident that the relative weights of v0 and k must be taken into account, . as well as the 

relative weights of the observation equations. These distinctions may be of practical Importance when the deviations from the theoretical curve are of considerable magnitude. 

COMPARISON OF OBSERVATION WITH THEORY. 

The data on the diffusion of gold into solid lead under atmospheric pressure are presented 

in Tables 1 to 11 inclusive. The values in the first columns are the observed distances at· 

temperature T0 from the plane of contact to the center of the section. The !-millimeter section 

adjacent to the. plane of contact was always rejected. Column 6 gives the percentage of gold 

computed from the weight of the· alloy and the weight of the gold contained in the alloy as 

tabulated in columns 2 and 3 respectively. Columns 4 and 7 contain the computed theoretical. 

values, and columns 5 and 8 contain the residuals or the differences between the observed and 

computed values. It will be noted that in each case equation (5) represents the observed facts 

to a high degree of precision. 
• 

Distance 

'(x') from 

plane of 

contact 

( centimeters). 

1 

0.2 

.4 

.6 

. 8 

1.0 

1. 2 

1.4 

1.6 

1.8 

2.0 

2.2 

2.·4 

0.2 

.4 

.6 

.8 

1.0 

1.2 

1.4 

1.6 

1.8 

2.0 

2.2 

2.4 

0.2 

.4 

.6 

.8 

1.0 

1.2 

1.4 

1.6 

1.8 

2.0 

2.2 

2.4 

0.2 

.4 

. 6 

.8 

1.0 

1.2 

1.4 

1.6 

1.8 

2.0 

2.2 

2.4 

Weight 

of 

alloy 

(grams). 

2 

6. 7250 .6.6105 

6.6680 

6.6600 

6.6310 

6.6535 

6.6510 

6.5785 

7.3140 

6.6850 

6.7030 

6.5480 

5.5255 

5.4750 

5.4775 

5.5130 

5.4940 

5.4935 

5.5250 

5.4880 

5.4590 

4.8595 

5.5080 

5.4915 

5. 5980 ' 

5.5200 

5.5645 

5.5695 

5.4845 

5.5590 

5.5120 

5.6080 

5.5655 

5.5620 

5. 8775 

5.5470 

7.8865 

7.8200 

7.8140 

7.8295 

7.8225 

7.8310 

7.6505 

7.8265 

7.8235 

7. 7865 

7.8535 

7. 7580 

PRELIMINARY REPORT ON 'l:HE DIFFUSION OF SOLIDS. 

TABLB 1. 

I Weight of gold (milligrams). ! I P<;Jrcentage of gold (v). I 

Ob- 11 

Ob- Com- served- Observed. puted. com- served. 

3 

1.26 

. 96 

.73 

. 53 

. 38 

• 29 

. 20 

. 13 

.09 

.05 

.01 

.01 

0.71 

.53 

.37 

.25 

.18 

.12 

.08 

.04 

.02 

.02 

Trace. 

Trace. 

0.80 

.59 

.44 

. 31 

. 22 

.15 

.10 

.04 

.03 

. 02 

Trace. 

Trace. 

1.03 

. 74 

.54 

. 39 

. 26 

.17 

.11 

.07 

.05 

. 01 

. 01 

. 01 

1.23 

. 97 

. 75 

.56 

.40 

. 27 

.18 

.11 

.08 

.04 

.02 

.01 

0.70 

.53 

.39 

. 27 

.18 

,11 

.06 

.04 

.02 

. 01 

. 004 

. 002 

0.79 

. 60 

.45 

. 32 

. 21 

.14 

.08 

.05 

.03 

. 01 

.008 

.003 

1. 00 

. 76 

. 56 

. 39 

. 26 

.16 

.10 

.05 

. 03 

. 01 

. 01 

.003 

puted. 

5 j I 1. 6 

+0.03 

- .01 

- .02 - .03 

- .02 

+ .02 

+ .02 

+ .02 

+ .01 

+ .01 - .01 

.oo I 

0.0187 

. 0145 

. 0109 · 

.0080 . .0057 ; 

.0044 

.0030 

.0020 

. 0012 

. 0008 

. 0002 

. 0001 

TABLE 2. 

+O. 01 0. 0129 . 00 . 0097 - . 02 . 0068 - .02 .0045 . 00 . 0033 

+ . 01 .0022 + .02 .0015 

.00 .0007 

.. .:-~~-- _1_ _:_~~~; .. 

·········-'lir········ 

TABLE 3. 

+0. 01 - . 01 - . 01 - . 01 

+ . 01 

+ .01 

+ .02 - .01 

.00 

+ .01 

j 

0.0143 

. 0107 

. 0079 

. 0056 

. 0040 

.0027 

. 0018 

.0007 

.0005 

.0004 

TABLE 4. 

+0.03 

- .02 - .02 

.00 

. 00 

+ .01 

+ .01 

+ .02 

+ .02 

.00 

. 00 

+ .007 

I 

I 

0.0131 

.0095 

.0069 

.0050 

.0033 

. 0022 

. 0014 

.0009 

. 0006 

.0001 

.0001 

. 0001 

Computed. 

7 

0.0184 

. 0146 

. 0113 

. 0084 

. 0060 

. 0041 

.0027 

. 0017 

.0010 

.0006 

.0003 

.0002 

0.0127 

.0097 

.0070 

.0049 

.0032 

.0020 

. 0012 

.0007 

.0003 

.0002 

. 0001 

.0000 

0.0141 

. 0109 

. 0081 

.0057 

. 0039 . 

. 0025 

. OQ15 

. 0009 

. 0005 

. 0003 

. 0001 

. 0001 

0.0127 

.0098 

. 0072 

. 0050 

. 0033 

. 0021 

. 0013 

. 0007 

.0004 

. 0002 

. 0001 

.,0000 

Observedcomputed. 

8 

i 

I 

+O. 0003 II 

- . 0001 II 

- . 0004 

- . 0004 - . 0003 

+ .0003 + .0003 

+ .0003 + .0002 + .0002 - . 0001 

- . 0001 II 

+0.0002 ! 

.0000 i! 

- . 0002 

- . 0004 

+ . 0001 

+ . 0002 + . 0003 

.0000 

+ . 0001 '.+ .0002 

+O. 0002 - . 0002 - . 0002 

- . 0001 

+ . 0001 + . 0002 

+ . 0003 - . 0002 

. 0000 

+ . 0001 ............ 

············ 

+O. 0004 - . 0003 

- .0003 

I 

Cons ants. 

a=0.00~0293 . T=197' C . t=53. 9 days . v0=0.m226 . k=O. 00176 . 

T=197' C. 

t=53.92 days. V0=0.01p87. 

k~O.OO~ 7. 

T=197°C. 

t=53.92 days. v0=0. 0 739. 

k=0.00t3. 

.0000 

.0000 

+ . 0001 + .0001 + .. 0002 

+ . 0002 - . 0001 

T=197° C . 

't=53.92 days. ·V0=0.0lr>88. 

k=0.0059. 

. 0000 

+ . ooo1 I 

II 

91 

i 
92 SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY, 1915. 

TABLE 5. 

Distance Weight of gold (milligrams). Percentage of gold (v). 

(x') from Weight - plane of of Ob- Ob- Constants. contact alloy Ob- Com- served- Ob- Com- served- (centi- (grams). served. puted. com- served. puted. com- · meters). puted. puted. 

1 2 3 4 5 6 7 8 

0. 2 7.9530 1.04 1. 02 . +0.02 0. 0131 0.0128 +O. 0003 

.4 7.8310 . 76 .78 - .02 . 0097 . 0099 - . 0002 

. 6 7.8025 . 55 . 58 - .03 .0071 . 0074 - . 0003 - .8 7. 8530 .41 .41 .00 . 0052 . 0053 - . 0001 

1.0 7.8180 . 29 .28 + .01 . 0037 . 0036 + . 0001 T=197° C. 1.2 7. 7710 .19 .18 + .01 . 0024 . 0023 + . 0001 t=53.92 days. 1.4 7. 7970 .13 .11 + .02 . 0017 . 0014 + . 0003 

1.6 7. 7950 . 07 . 07 . 00 . 0009 . 0008 '+ 0 0001 V0=0.01580. 

1. 8. 7. 7780 .04 .04 . 00 0 0005 . 0005 . 0000 k=0.0064 . 

2.0 7.8805 .01 . 02 - . 01 . 0001 . 0003 - . 0002 

2.2 7. 7940 Trace. . 010 ............ ... .... .................... . 0001 ................ .. .. ... . 

2. 4 8.0590 . 01 . 005 + .005 . 0001 . 0001 . 0000 

2.6 7. 6385 Trace. ................ ................. .. .. ..................... .. .................. ........ .. .. .. .. .. .... .. 

l 

TABLE 6. 

0.2 7.8095 0.99 0.98 +0.01 0.0127 0.0125 +0.0002 

.4 7.8490 . 74 . 75 - .01 . 0094 . 0095 - . 0001 

.6 7.8385 .51 .54 - .03 . 0065 . 0069 - . 0004 

.8 7.8175 . 38 . 38 . 00 . 0049 . 0048 + . 0001 

1.0 7.7950 .25 . 25 . 00 . 0032 . 0032 .0000 T=197° C. 1.2 7.8280 .17 .16 + .01 . 0022 . 0020 + . 0002 t=53.92 days. 1.4 7.7425 .11 .09 + .02 . 0014 . 0012 + . 0002 V0=0.01554. 1.6 7.8155 . 06 .05 + .01 . 0008 . 0007 + 0 0001 k=0.0058. 1.8 7.R160 .03 .03 .00 . 0004 . 0003 + 0 0001 

2.0 7.8210 . 01 .01 .00 . 0001 . 0002 - 0 0001 

2. 2 9.2530 .01 . 01 .00 . 0001 . 0001 0 0000 

2. 4 7.8790 Trace. . 003 ......... .. .......... ....................... ........... .. ........ ....................... 

2. 6 7.8350 Trace. .................. ........ .. .......... .............. .. .... ........ .. .......... ................... .. ... 

TABI.E 7. 

0.15 3.7347 0.29 0.28 +0.01 0.0078 0.0074 +O. 0004 

. 3 7. 7415 .46 .47 - .01 . 0059 . 0060 - . 0001 

. 5 7. 8412 . 33 , 34 - .01 . 0042 . 0044 - . 0002 

. 7 7.8305 .................. .24 ................. -- --- ----- . 0030 ....................... T=150° C . 

. 9 7. 9955 .18 .16 + . 02 . 0023 0 0019 + . 0004 t=63.29 days. 

1. 1 7. 9550 . 09 . 09 .00 . 0011 . 0012 - . 0001 v0=0.00878. 

1.3 8.0085 . 05 0 05 . 00 . 0006 0 0007 - 0 0001 k=0.0043. 

1.5 7. 9655 . 03 . 03 . 00 . 0004 . 0004 .0000 

1.7 8.0165 . 005 .02 .'015 . 0001 . 0002 - . 0001 

1.9 8.0818 Trace. . 007 ........ .. ......... ..................... . 0001 ............................ 

TABLE 8. 

0. 15 4.0910 0.46 0.42 +0.04 0.0112 0.0103 +O. 0009 

.3 7.7562 . 63 . 65 - .02 . 0081 . 0084 - . 0003 

.5 7.7805 .46 .48 - .02 . 0059 . 0061 - . 0002 

. 7 7.8545 .34 ·. 33 + .01 . 0043 . 0043 . 0000 T=150° C . 

.9 7.9800 .24 .22 + .02 . 0030 . 0028 + . 0002 t=63.29 days. 

1. 1 8.0210 . 14 .14 .00 . . 00l7 . 0017 . 0000 v0=0.01223 . 

1.3 8.0762 . 09 . 08 + . 01 . 0011 . 0010 +. 0001 k=0.0044. 

1.5 7.9545 . 02 . 04 - .02 . 0003 . 0005 - . 0002 

1.7 8. 0075 . 01 .02 - .01 .0001 . 0003 - . 0002 

1.9 7.9967 .01- .01 .00 ... .. .. .. .. .. .. .. . . . 0001 ...................... 
DiBtance 

(x') from 

plane of 

contact 

( centimeters). 

I 

PRELIMINARY REPOR.T ON THE DIFFUSION OF SOLIDS. 

Weight 

of 

alloy 

(grams). 

'l'AJJlLE 9. 

Weight of gold (milligrams). Percentage of gold (v). 

Observed. Computed. 

Ob111! Observed- Ob- Com- served- com- served. puted. computed . puted. 

Cons ants. 

1--1--1--2--1---a--1 --4--l--s ___ lt ___ 6-- l---7--l---s---l---+---l 

0. 15 

.3 

. 5 

. 7 

.9 

1.1 

1. 3 

1. 5 

1. 7 

1.9 

0. 15 

. 3 

. 5 

.7 

.9 

1. 1 

1. 3 

1.5 

1. 7 

1.9 

0. 15 

. 3 

. 5 

.7 

3. 7090 

7. 7700 

7. 8110 

7. 8028 

7.8800 

7.9560 

7.8985 

7. 7985 

7.8360 

7. 7175 

4.0060 

7.7520 

7. 7710 

7.8545 

7. 9950 

8. 1765 

7.9370 

7.8960 

7.8355 

7.8320 

3. 9050 

8. 1800 

8.0000 

8. 1380 

0.22 

. 40 

. 29 

. 21 

. 13 

. 09 

. 04 

. 02 

.01 

. 005 

0.45 

. 63 

. 46 

. 33 

. 23 

.15 

. 06 

. 03 

. 02 

. 01 

0.04 

. 03 

. 01 

.01-

0. 23 

. 39 

. 29 

. 20 

.13 

. 08 

. 05 

. 03 

. 01 

. 006 

0.41 

. 65 

. 47 

. 33 

. 21 

.13 

. 07 

. 04 

. 02 

. 01 

0.04 

. 03 

.00 

. 002 

--0.01 

+ .01 

. 00 

+.01 . 00 

+ .01 

-.01 

-.01 

. 00 

- . 001 

0.0059 

. 0051 

. 0037 

. 0027 

. 0017 

. 0011 

. 0005 

. 0003 

. 0001 

. 0001 

TABLE 10. 

+0. 04 

_:_ . 02 

- . 01 

. 00 

+ .02 

+ .02 - .01 

_ .01 I . 00 

. 00 

0.0112 

. 0081 

. 0059 

. 0042 

. 0029 

. 0018 

. 0008 

. 0004 

. 0003 

. 0001 

TAJJLE 11. 

0. 00 0. 0010 . 00 . 0004 

+ . 01 . 0001 •••••• •••• II• • 0001-

1 

0.0062 

. 0051 

. 0037 

. 0026 

. 0017 

. 0010 

. 0006 

. 0003 

. 0002 

. 0001 

0.0103 

. 0084 

. 0061 

. 0041 

. 0027 

. 0016 

. 0009 

. 0005 

. 0002 

. 0001 

0.0011 

. 0004 

. 0000 

•. 0000 

-0.0003 . 0000 

. 0000 

+ . 0001 

. 0000 

+ . 0001 - . 0001 

. 0000 - . 0001 

.0000 

+O. 0009 - . 0003 - . 0002 

+ . 0001 + . 0002 + . 0002 - . 0001 - . 0001 

+ . 0001 

. 0000 

-0.0001 

. 0000 

+ . 0001 

T=150 ' C. 

t=63.2! days . V0=0.0( 738. 

k=O.OO 4. 

T=150 C. 

t=63.2! days. 

t'0=0. 01~31. 

k=O.OO 2. 

T=100° C. 

t=103.4l days . 

V0=0.0023. 

k=0.00(2+ . 

93 

The agreement of theory with observation is further shown in figure 32, in which the heavy 

line represents the theoretical and the dotted line the observed concentrations of Talle 1. The 

short vertical lines drawn perpendicular to the x axis mark the points at which the le~ d cylinder 

was sliced. The remarkable agreement between the different determinations of k i shown In 

Table 12. - t_ ,, · 

Temperature. 

(o C.). 

197 

197 

197 

197 

197 

197 

150 

150 

150 

150 

100 

Time 

(days). 

53.92 

53.92 

53.92 

53.92 

53.92 

53.92 

63.29 

63.29 

63.29 

' 63. 29 

103.43 

Vo 

(per 

cent). 

0.0223 

. 0159 

. 0174 

. 0159 

. 0158 

.0155 

.0088 

. 0122 

. 0074 

.0123 

.0023 

TABL 12. 

k 

0. 0076 

.0057 

.0063 

.0059 

.0064 

.0058 

.0043 

.0044 

.0044 

.0042 

.0002+ 

Mean. 

0.0076 

0.0060 

0.0043 

0.0002+ 

Remarks. 

Gold cylinder. 

Electroplate. 

Do. 

Do. Do 

Do. 

0.5-millimeter gold plate. 

Do. 

Do. 

Do. 

Do. 
94 SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY, 1915. 

o.ozzo 

o.ozoo 

0.0180 

0.0160 

~ 0.0140 

'oO 

_!g · 

~ 0.0120 u 

.. 

()) 

~0.0100 

> 

0.0080 

0.0060 

0,0040 

o.oozo 

r-.. ~-

l 

o.L~ I 

l 

I 

I 

I 

I 

I 

0 

> 

I 

I 

I 

t 

ll 

----

o.o/87 

\ -

o.o;J p.0145 

\ ,\ r!;...0/13 o.o;o~ \ 

'\ \ 

o.ooac 

I J I 

0.0084 

' 0.006£ 

0.0057 

~ ~~0049 

. ?.0041 

~ >?_-003 ") 

').0027 ~-- o:oo27 "'¢ ~ II.. 

?.oo,? 

~ f:_?0/2 ()I) o·o· ::loAoov 

Lo~ Y

0

0 

I I I I ~ o· p: c91 

O.a 0.'2 0.4 0.6 0.8 1.0 I.Z 1.4 1.6 1~6 2.0 Z.2 2..4 

x (centimeters) 

FIGURE 32.;-Comparison of observed and theoretical concentrations in experiments on diffusion of 

solids. rhe latter are represented by the continuous line; the former by the dott.~d line. 

The value k = 0.0076 

at 197° agrees well with 

Roberts-Austen's values 

0.007 and 0.008 at 200°. 

The fact that all the values determined from electroplates are low is suggestive, but the deviation 

of the highest value 

(0.0076) from the mean 

of the entire set is less 

than five tin1es the pro bable error of a single observation, consequently it 

must be inferred that the 

distribution of values is 

accidental. The valuek = 

0.0043 at 150° is in close 

agreement with RobertsAusten's values 0.004 and 

0.005 at 165°, but our 

value 0.0002 + at 100° is 

ten times his value at the 

same temperature. 

VARIATION OF THE COEFFICIENT OF DIFFUSIVITY WITH PRESSURE. 

Only a few preliminary attempts have been made to determine the effect of pressure on 

the diffusion process. The lead cylinders used for this purpose were about 20 millimeters in 

diameter an~ 5 or 6 ce~timeters in length. The ends of each cylinder were ~lectroplated with gold. 

A small hole was drilled from one end to the center of 

the cylinder for the insertion of .a thermo1element. 

Pressures wer~ applied by means of oil. The observations and the constants obtained from them are summarized in Table 13. The data are barely sufficient for 

the determination of the two constants, as in most of 

the experiments there were only two . observed ·values. The results obtained from A and C are quite as 

trustworthy as those obtained from B. The latter 

shows a very large increase in the rate of diffusion; the 

former practically none at all. Each end of specimen D 

was melted during the progress of the experiment. This 

may have been due to a slight variation in the temperature gradient within the bomb, or to some other accidental 

irregularity of which we have no knowledge. Specimens 

E and F were subjected to high pressures at ordinary 

temperature. No gold was found in either of these specimens. Figure 33 is a photograph of specimen F. The 

double system of fractures was probably produced by 

differential stresses resulting from the increased viscosity 

of the oil at high pressures. A small portion only of the FIGURE 33.----:-Lead fractured by small differential stresses 

I b f I

. when subjected to a hydrostatic pressure of 10,200atmos- tota num er 0 lnes On the surface of the lead cylinder pheres to the square inch. 
was rep 

Luder's 

' l 

. PRELIMINARY REPORT ON THE DIFFUSION OF SOLIDS. 95 

roduced in the photograph. Markings of a somewhat similar character ar« known as 

lines.1 

TABLE 13. 

I 

I 

Distance Weight Pressure 

(x') from Weight of Percent- (atmos- TernSpeci- plane of of gold age of pheres pera- Time Constants. men. contact alloy (milli- gold. per ture (days). 

( centi- (grams) · (grams). square (o C.). 

meter). inch). ; 

0.15 4.7125 0.09 

--~:-~;~ -) { v0=0, 006 . 25 ,3. 4570 .02 1,000 150 2.00 

. 35 3.0780 Trace. k=O. 006 

A .... .15 4. 9690 . 09 

___ :_~~~-) { v0=0. 007 . 25 3.6800 . 01 1,000 150 2.00 

. 35 3.2115 Trace. 

k=O. 004 

.2 6.8120 .19 

___ :_~;~_) { v0=0. 012 

.4 6.3735 .01 1,650 150 1. 229 

.6 6.3985 None. k=O. 010 

B .... 

___ :_~~~ _'} 

. 2 6.8725 .18 { V0=0. 010 

.4 6.8900 . 02 1,650 150 1.229 

. 6 6.8970 None. 

k=O. 013 

.15 3.2125 .07 

::i:~~~u . 25 4.3400 . 03 1,900 150 2.00 { V0=0. 006 

. 35 3. 8350 Trace. k=O. 007 

. 45 3. 6270 Trace. 

c .... 

:::::~~~: } .15 3.5480 . 09 

. 25 3.6375 .02 1,900 150 2.00 { V 0=0. 008 

. 35 4.1900 Trace. k=O. 005 

.45 3.0655 Trace. 

.05 5.2525 147.04 ··j=·j .15 3:4670 1.40 

. 30 7. 1680 1. 19 1,650 190 1. 250 { V 0=0. 079 

.50 7.1479 . 26 . 00364 k=O. 022 

. 70 7.1808 .02 .00028 

. 90 7.1964 None. ..... . .... . D ..... 

.05 3.1250 93.14 

.15 3.6390 ---:~r) 1. 54 

. 30 7. 1850 1.19 1,650 190 .... · .... { V 0=0. 079 

. 50 7.4616 . 22 . 00295 k=O. 023 

. 70 7.4728 .01 . 00013 

. 90 7.5469 None. ........ .... 

E ..•• { 

.15 3.8075 None. 

··········} . 30 7.2725 None. ........ ...... 7,200 20 2.825 

.50 7.1885 None. ..................... ................. ...... 

• 70 7.1700 None. ........ .. ........ .. 

F ..... { 

.2 8.5932 None. . ....... .. } . 4 8.3433 None . .................. ... .. 10,200 17 2.94 

. 6 8.4005 None . ............................ .......... ............ 

. 8 8.3940 None . ........... ........ 

h 

CONCLUSIONS AND INFERENCES. 

Roberts-Austen's values of the coefficients of diffusion of gold into solid lead are practically 

correct except for the value at 100° C., which is probably too small. The close agreement of 

the values of the coefficients obtained from specimens subjected to the same temperature 

indicate that a higher degree of precision may be attained in their determination. The value 

of the coefficients probably increases with pressure. 

1 Mason, W., The Luder's lines on mild steel: Phys, Soc. London Proc., vol. 23, pp. 305-333, 1911. 
96 SHORTER CONTRIBUTIONS TO GENERAL GEOLOGY, 1915. 

. The observed values tabulated in Table 1 and shown graphically in figure 32 represent the 

diffusion into lead from a gold cylinder 20 millimeters in diameter and 10 millimeters in height. 

A very sensitive test failed to detect the diffusion of the lead into the gold at depths greater 

than 0.2 millimeter, but the methods of detecting lead under these conditions are far less precise 

than those for detecting gold in lead. 

The tendency of molecules to diffuse must always exist when there is a heterogeneous 

distribution of concentration and the temperature of the masses is above the absolute zero. 

Considered as a dynamic system operative at all times, the transportation of matter by diffusion 

in the solid crust of the earth may be very extensive. The possible effects of these persistent 

motions may be indicated by considering the migration of gold into pure lead at a temperature 

of 200° C. If we accept the lower value of the coefficient k = 0.007 and put the initial concentration v0 = 0.02 per cent, particles of gold would have passed through 6.4 centimeters (2.5 

inches) of lead in one year and 64 centimeters (25 inches) of lead in 100 years in sufficient 

quantities to have produced a concentration of 0.0001 per cent at these points. 

If a portion of the materials constituting the crust of the earth are capable of diffusing 

into one another under pressure, it would seem that the argument for isostatic adjustment is 

greatly strengthened, for a substance in which the particles glide over one another possesses one 

of the essential characteristics of a liquid and may therefore be expected to yield slowly when 

subjected to small stresses operating during geologic epochs. 

ACKNOWLEDGMENTS. 

The electroplates used in these experiments were prepared by Mr. R. C. Wells, of the 

United States Geological Survey. The pressure tests were conducted by Drs. John Johnston 

and L. H. Adams, of the Geophysical Laboratory of the Carnegie Institution. We are greatly 

indebted to these gentlemen for their suggestions and cooperation.