THE statement that the familiar table jellies (gelatin gel) are typical representatives of the class to be discussed in the present paper will probably, at the outset, be found more useful than an attempt at strict definition. These systems exhibit immediately two of the most characteristic properties of the elastic gel stability of shape, notwithstanding a very high content of liquid (about 95 per cent in the case quoted) and perfect elasticity within certain narrow limits.

Only

The gel may be obtained in two opposite ways: either by transformation-which may be reversible or irreversible of a sol, e.g., by cooling a gelatin sol below a certain temperature; or by allowing the dry substance to "swell" in an appropriate liquid. Practically all substances from which elastic gels may be produced show this capacity of swelling, though to an extent which differs widely. certain liquids will cause a given substance to swell, and the relations between the constitution of the solid and the liquid, on which this property is based, are at present quite obscure. Thus gelatin and agar (the former a protein, the latter a mixture of carbohydrates) swell in water at ordinary temperature, but do not dissolve until the temperature is raised. Vulcanised indiarubber swells in various organic solvents such as benzene, toluene, or xylene, without dissolving. Finally, the processes of swelling and dispersion or solution may proceed pari passu, as with gum arabic at ordinary temperature. At low temperature, a definite stage of swelling may be observed to precede solution.

The elastic gel which can be most easily reproduced and has, accordingly, been studied most frequently and extensively, is that of gelatin. Bodies of any desired shape can be obtained by pouring the gelatin sol into suitable moulds and allowing it to set for a period of not less than 24 hours (cf. infra, E. Fraas). The procedure, once chosen, must be rigidly adhered to throughout, since all the properties of a gel depend, not only

* A General Discussion before the Faraday Society and the Physical Society of London, October 25, 1920.

on its composition, but also to a marked extent on its history, especially its "thermal history," i.e., the temperatures to which the sol has been exposed and the duration of such exposure. Some of the principal investigations will now be briefly summarised.

Elastic Properties.

These have been studied principally by R. Maurer (R. Maurer, Ann. d. Phys., 1866, xxviii., 628), P. v. Bjerken (P. v. Bjerken, ibid., 1891, xliii., 917), E. Fraas (E. Fraas, ibid., 1894, liii., 1074), and A. Leick (A. Leick, ibid., (Drude), 1904, xiv., 139). All these investigations date back some time, and were undertaken with a view to studying a material with very low modulus and sufficiently transparent for examination in polarised light, rather than with the intention of elucidating such problems as the structure of gels. Both Maurer and Leick determined Poisson's ratio for gels of various concentrations and find it 0.5 within the limits of error-a result which is not surprising in view of the large percentage of liquid. Maurer studied the elongation of gel cylinders of considerable diameter (2.21 cm.) with small loads, the extensions being measured microscopically. His figures for the modulus are in good agreement with those found by Leick, which range from 2:42 (grm./mm3) for 10 per cent to 29.4 for 45 per cent gels. Leick found the modulus E roughly proportional to the square of the gelatin concentration; the ratio E/c2, however, varies somewhat irregularly, and decreases with increasing c. All the investigators find that the modulus increases with increasing load.

Fraas studied the ageing of gels and found that a constant modulus was not reached until about 24 hours after apparently complete setting. These hysteresis effects are universal in colloidal systems, and the increasing modulus of a gel is paralleled by the increasing viscosity of the sol, when kept at a temperature above the setting point. In the following table one series of Fraas's results is given to illustrate the magnitude of the effect.

Cylinder of 20 per cent Gelatin Gel. Hours after re

I

2 3 4 5 6

7 24

5

moval from mould ... Extension produced by 50 grms. weight 12 5 7 5 7 7 6.5 6.5 6 Maurer, and more particularly Leick, also studied the effect of various substances dissolved in the water on the elastic modulus of gelatin gels; the results are of particular interest from the colloidal point of view, inasmuch as they can be co-ordinated with the well-known effects of such solutes on other properties of the system, e.g., maximum swelling, setting point of sol, &c. Leick finds that the addition of various chlorides action, while cane sugar and glycerine raise the lowers the modulus, sodium sulphate is without modulus considerably. Chlorides also lower the viscosity and setting temperature of the sol, while glycerine and cane sugar (generally substances containing hydroxyl groups) raise both constants.

The elasticity of gels is perfect only for small loads applied for a short time, but very little work has been done on relaxation in such systems. R. O. Rankine (R. O. Rankine, Phil. Mag. Ap.,

1906, 447) maintained gelatin gels of low concentrations (34 to 45 per cent) at constant strain and plotted the stress necessary to do this against time. The stress, within the limits of concentration and time investigated, never becomes zero. Breaks occur in the time-stress curves, which are taken to indicate that the elastic limit has been reached. The concentrations employed by Rankine are very much lower than those at which determinations of the modulus, &c. have been made.

Reiger (R. Reiger, Phys. Zeitschr., 1901, ii., 213) determined the relaxation time of gelatin gels by optical means (disappearance of the double refraction produced by strain). The invetigation was undertaken with the object of testing Maxwell's relation between modulus, viscosity and relaxation time, and was accordingly carried out at 29° C., i.e., at a temperature very near the "melting point" of the gel. In these conditions Reiger found a relaxation time of 10 minutes for 20 per cent, and about 41 minutes for 40 per cent gel.

That the conditions are entirely different at lower temperatures is shown by experiments by the writer, published here for the first time. Rectangular prisms of gelatin gel (10 per cent) with per cent of sodium fluoride, to prevent putrefaction, were cast and allowed to set for 36 these prisms was then bent between three stops fixed on a glass plate, the latter being covered with paraffin oil to prevent adhesion of the gel and consequent irregular deformation. The specimen was then photographed in polarised light (double plate glass as polariser, Nicol as analyser) within 10 minutes of the application of stress at room temperature, about 15° C. The glass plate with the specimen was then placed in a moist chamber for five days, being examined at intervals (visually) without any noticeable change showing itself. At the end of five days the stress had practically disappeared, so that the specimen could be removed without friction and without straightening itself appreciably. It was then again placed on an oiled glass plate and photographed as before. Considering the extreme sensitiveness of 10 per cent gel to deformation, it may be said that the appearance is substantially unaltered, and that at any rate the optical anisotropy caused by strain has not disappeared with the removal of the stress. The absence of relaxation in a system consisting to about 90 per cent of liquid is certainly remarkable and will be referred to again.

hours before removal from the mould. One of

Optical Properties.

The double refraction produced by deformation has been referred to incidentally in the preceding paragraph. Quantitative investigtion of this property has been carried out chiefly by Leick (l.c.). His principal results (obtained with gel plates in tension) are: (1) the double refraction `(D= ne — no) is, cæteris paribus, very approximately proportional to the strain, and (2) for equal relative elongations the double refraction is roughly proportional to the gelatin content.

The refractive index of both gelatin sols and gels has been shown by G. S. Walpole to be a linear function of the gelatin concentration G. S. Walpole, Koll. Zeitchr., 1913, xiii., 241). If the

refractive index is plotted against the temperature over a range containing the setting point, no discontinuity occurs at the latter, i.e., when the sol is tranformed into gel.

On the whole, our knowledge of the elastic and the related optical properties of gels must be pronounced slight. As in other branches of the subject, non-aqueous systems have received hardly any attention; their study is eminently desirable, as the enormous complications introduced in the case of a protein like gelatin by the formation of salts, and their electrolytic and hydrolytic dissociation, would be absent. There is a very large literature on the stress-elongation curve of indiarubber, which, however, refers only to the dry material and is not of immediate interest. The writer has found only one reference to a rubber gel in a paper by A. E. Lundal (A. E. Lundal, Ann. d. Phys., 1898, lxvi., 741), who determined the tensile modulus of rubber which had imbibed 133 per cent of paraffin oil and found it about onehalf that of the dry material.

Diffusion in Gels.

This phenomenon has, for various obvious reasons, received a considerable amount of attention. Thos. Graham already used dilute gelinstead of pure aqueous solutions in the study of diffusion, and found the rate approximately the same in both. This, however, only holds good of gelatin gels up to, say, 3 or 4 per cent and agar gels under 1 per cent. In more concentrated gels the rate of diffusion decreases markedly with the concentration, but no quantitative relations have, so far, been determined. The rate of diffusion for a given solution and gel concentration can be affected by various solutes in the latter. Among the earliest investigations on the point are those of H. Bechhold and J. Ziegler (H. Bechhold and J. Ziegler, Zeitschr. phys. Chem., 1906, lvi., 105), who found NaC and Na/ without effect; Na2SO, and several non-electrolytes as dextrose, glycerin and alcohol reduced the rate of diffusion of certain solutes. A certain though not exact-parallelism shows itself between the effect of solutes on the elastic modulus and the rate of diffusion : substances which increase the former reduce the latter. The experimental difficulties are very considerable and are explained in the literature. Among more recent papers on the subject are those by O. v. Fürth and F. Bubanovic (O. v. Fürth and F. Bubanovic, Biochem. Zeitschr., 1918, xc., 265; xcii., 139), and by W. Stiles (W. Stiles, Biochem. J., 1920, xiv., 58).

The fact that both the swelling and the drying of gels are controlled by diffusion involves some consequences which, considering that they may have an important bearing on histology and related subjects, have not yet received adequate attention. If a body of a gel is bounded by a surface in which the radius of curvature changes very quickly or (as in polyhedra cylinders bounded by plane ends, &c.) discontinously, diffusion to or from regions adjacent to tracts of surface with low or zero-radius takes place more rapidly than from the rest. The result is that a body of gel does not remain similar to itself during swelling or drying, but undergoes successive deformations which may be considerable. The effect is particularly marked in drying; thus, cylinders with plane ends at first dry more rapidly

round the circular edges, which contract, the profile becoming that of a barrel with convex ends. As the material forming the edges becomes less permeable, the large surfaces dry more quickly, and the final shape is, approximately, a singleshell hyperboloid with concave ends. On allowing such a body of dry gel to swell again, the original shape is not necessarily restored; the reason for this alteration in the capacity of absorbing water is obscure (E. B. Shreve, Science, 1918, xlviii., 324; Il. Frank. Inst., clxxxvii., 319).

The foregoing summary-though necessarily restricted by considerations of space-may give the reader unfamiliar with the literature some idea of our present knowledge. The two great problems to be solved must now be set forth briefly. They are (1) the elucidation of the structure of elastic gels, and (2) the explanation of the phenomenon of swelling. As regards the former, there is at present a fundamental divergence of opinion, inasmuch as some authors (H. Procter, W. Pauli, and J. R. Katz) maintain that elastic gels are homogeneous systems, i.e., solid or (H. Procter) "semi-solid" solutions. The evidence for this view is set forth at length in a very exhaustive monograph by Katz (J. R. Katz, die Gesetze der Quellung, Koll. Reib., 1917, ix.). The other school (W. B. Hardy, Wi. Ostwald, Wo. Ostwald, S. C. Bradford, Dorothy J. Lloyd) consider gels to be heterogeneous systems, but differ regarding the state of aggregation of the phases. Ostwald, in particular, considers gels to be systems of two liquid phases having an interfacial tension, while some of the other investigators incline to the view that the properties of gels are best accounted for by assuming some sort of network or cellular arrangement of solid phase permeated by liquid. Speaking generally, these rival theories are based on the consideration of a limited number of selected properties, and a great deal of further work is required, probably on quite novel lines, before a definite conclusion commanding universal acceptance can be reached. The author feels, in particular, that the elastic properties have received insufficient attention, and has attempted, as a first step, to examine whether they are compatible with the assumption of two liquid phases possessing interfacial tension (E. Hatschek, Trans. Faraday Soc., 1916, xii., Part 1), the result being negative if the assumptions necessary to allow of mathematical treatment are granted.

THE CONSTITUTION AND STRUCTURE
OF THE RADIO-ACTIVE ELEMENTS.
By HAWKSWORTH COLLINS.

ALL the deductions in preceding papers have been obtained by observing and then reasoning upon batches of concordant coincidences in numerical facts. When these facts are fairly numerous. it is possible to take into consideration all available facts and find out by the theory of mathematical probability whether the apparent coincidences are merely coincidences or whether they involve absolute truths. But when the number of facts is limited as in the case of the radio-active elements, it is not possible to employ the theory of mathematical probability, so that there is no claim that the following matter is proved to be true.

In mathematics the word "theory" is used in its original meaning of "something that is seen (to be true)"; and is not employed at all in the sense of "hypothesis" or "guesswork"; e.g., the Theory of Quadratic Equations does not contain anything of the nature of hypothesis. But in Chemistry the words "theoretical" and "hypothetical" are used synonymously, so that unfortunately a mathematical theory may be spoken of as "a piece of theoretical work," an expression which is entirely misleading. All the deductions in previous papers have been proved to be true mathematical theories, and if anyone were to speak of them as "theoretical conclusions" he would be employing an expression which has a meaning exactly opposite to that which he intends

to convey.

The observation of the following coincidences with regard to numerical facts concerning radioactive elements is due to the preceding mathemaatical theories, s that the probability of the truth of the matter is much greater than it would be if it were an entirely independent investigation. The main characteristic constituent of the radioelements is a portion represented by hexadic titanium.

No one could possibly have guessed or hypothesised this and then made the facts fit into his hypothesis.

In Table I. the atomic weights of the radioelements are split up in different ways into parts which happen to represent nearly all the characteristic elements with which they are associated in mineralogy, so that there is a very great probability that the radio-elements and their associated elements are interrelated.

=

TABLE I.

U CbYFe = TaFe
ThCbZrTi = CbLa
Io = CbYTi
Ra = ZrBa

This is

=TaTi

=238 =WTi =: =232

= CbBa=230

=ZrYTiLaY = 226

where Cb= Na, Ti

Y = CaTi Ba=CaTi,

La=ZrTi

Radium=ZrBa

The constitution and structure of Zr has been

Ca-Na-Na-H-H,

ᎫᎴ

If these become active, i.e., become valency electrons as the disintegration proceeds, there will finally be left the four valences of Pb.

The manner in which two slightly different products of equal mass can be produced may be illus trated by the above formula for niton. If the two helium-portions were given off from one Tiportion, they would be followed immediately by two B-particles; but if one helium-portion were given off from each of the Ti-portions, there would be no emission of 8-particles until after the expulsion of a third atom of helium.

There is no doubt that the theory is in almost exact agreement with observed facts with regard to the disintegration products of radium.

Uranium=CbYFe

As iron is the main constituent of meteorites, it is probable that this element is readily formed from more elementary matter; and this probability is increased by the following facts: If he.ium could be given off from Fe (56) a product of the same mass as Cr (52) would be left; and if helium could be given off from the latter a product of the same mass as Ti (48) would be left; and if another helium could be thrown off, Sc (44) would be left; and if one more, then Ca (40) would remain; so that it is reasonable to expect that Fe may produce Ca by giving off four helium-portions,

Pb Ca,Na, Cu,Ca2

This is a very suitable formula, since Pb is especially connected with Ca, its ultimate matrix being limestone.

In order to demonstrate the way in which the theory accounts for the emission of the negative B-particles, the following facts must be mentioned Al is monobasic and diacidic, i.e., it has a single electro-negative valence free for combination with a base, and a pair of electropositive valences free to combine with the two electro-negative valences of an atom of oxygen. The theory shows that if Al (Na-H-H,) could give off H-H, with its two positive charges, the single negative charge emanating from Na would be left. But since this negative charge is only due to the presence of the free H-H,, it becomes, what it potentially is, a positive charge by throwing off the negative 6particle.

Similarly, if Si (Na-H-H,-H) were to throw off its helium-portion, two negative -particles would follow of necessity. And if Ti (=K—H—H,—H-H,-H) were to throw off its two helium-portions one after the other, there would again be two 6-particles to follow.

Consequently it may reasonably be expected that if a triadic portion (like Al) of a radio-active element were being disintegrated, a 8-particle would follow the emission of a single a-particle; and if a tetradic portion (like Si) were being disintegrated, two 6-particles would follow an aparticle, and if a hexadic portion (like Ti) were being disintegrated, two 6-particles would follow two a-particles.

When this reasoning is considered in relation to the observed facts regarding Ra, there is no 6particle to come off (as previously shown) after the expulsion of the first atom of helium. In the structure given for Nt the twelve quiescent charges represent the twelve metastasic electrons.

of four begins with Ca and ends with Fe, for there are no elements of atomic weights 36 and 60.

Then since U=CbYFe, and Cb=Na,Ti, and Y=CaTi, there are altogether eight heliumportions to come off from U (238) before Pb (206) is left, and the different order in which they may come off causes the production of isobares.

According to the theory there would be six 6particles to come off, and this is in accordance with the observed facts.

Ionium=CbYTi

According to the theory there are six helium atoms available, two from the Cb-portion, two from Y and two from Ti. There are also six Bparticles to come off before Pb (206) is left.

Thorium CbZrTi

According to the theory there are only five helium-portions available as disintegration products, leaving a mass of 212 composed of Na2 Ca from Cb, Na,Ca from Zr, and Ca from Ti, i.e., Na,Ca, altogether. This remnant would evidently be something like lead but would not be lead. As it appears to be impossible to separate ionium and thorium chemically, the observed facts with regard to their disintegration products are probably confused; and the variable atomic weights found experimentally for the end-products of disintegrating radio-elements are probably due to mixtures of elements represented by 206 and 212.

INSTITUTION OF MINING AND METALLURGY.-The Gold Medal of the Institution of Mining and Metallurgy, the highest distinction in the power of the Council to bestow, has been awarded to Sir Thomas Kirke Rose, D.Sc., Assoc. R. S.M., M. Inst. M. M., "in recognition of his eminent services in the advancement of Metallurgical Science with special reference to the Metallurgy of Gold." "The Consolidated Gold Fields of South Africa, Ltd." Gold Medal and Premium of Forty Guineas have been awarded to Mr. H. Livingstone Sulman for his paper, "A Contribution to the Study of Flotation" (Transactions, 1919-1920, vol. xxix.).

DETERMINATION OF MOLYBDENUM.

By J. P. BONARDI and EDWARD P. BARRETT. (Continued rom p. 233.)

Effect of Sulphuric Acid.

IN order to determine the effect of sulphuric acid on the precipitation of molybdenum by lead acetate, the molybdenum was determined in samples taken from a solution of ammonium molybdate when no sulphuric acid was present, and in the presence of 15 cc. of concentrated sulphuric acid in samples containing amounts of molybdenum equal to those of the first samples. The concentration of the solutions and the procedure were the same as outlined in the detailed gravimetric method.

15 cc. of sulphuric acid was used because that volume represents approximately 27.60 grms. of acid, a greater weight than that of the sulphates that would be present in a sample taken for analysis, even after fuming with io cc, of acid.

The following table shows the results, which indicate that sulphuric acid does not interfere with the precipitation of molybdenum by lead acetate if precautions are taken as described in the details of the gravimentric method, especially as given under "Precipitation." As the solution containing molybdenum is titrated with a lead acetate solution and only 2 cc. excess is added, the amount of lead sulphate that might form would be readily soluble in the hot acetate solution.

TABLE I.-Results of Precipitation of Pb MoO, with and without sulphuric acid, first series of

were

As a further test two 1-grm. and two o'25-grm. samples of a high-grade molybdenite ore weighed. The 1-grm. samples were decomposed with aqua regia and the molybdenum precipitated with lead acetate. The o25-grm. samples were decomposed with aqua regia and one was fumed with 5 cc. of concentrated sulphuric acid and the molybdenum precipitated with lead acetate. The results, given in Table II., justify the conclusion that sulphuric acid does not interfere with the precipitation of lead molybdate if this is conducted as given under "Precipitation."

No sample ever taken for analysis and decomposed by aqua regia would contain as much sulphates as is produced by 5 cc. of concentrated sulphuric acid, consequently the amount of lead sulphate formed by the small excess of lead acetate (2 cc.) added to the molybdenum solution when titrating would be rendered soluble in the acetates present. If lead sulphate should be carried down mechanically with the lead molybdate this would, under the vigorous boiling after precipitation, be rendered soluble during the change inform of the bulky lead molybdate to the granular form.

Effect of Lime.

In order to test the effect of lime on the gravimetric method two samples representing 6.31 per cent molybdenum on a 1-grm. basis were prepared. To each was added 3 grms. of precipitated calcium carbonate just acidified with hydrochloric acid. The molybdenum was then determined in the samples by the procedure given for the gravimetric method. The results, presented in Table III., show that a large excess of lime will slightly lower the percentage of molybdenum obtained.

TABLE III. Results of precipitation of PbMoO. in the presence of Lime.

However, as the 3 grms. of precipitated calcium carbonate present in these tests lowered the percentage of molybdenum only 0.21, probably the small proportion of lime present in the ordinary run of molybdenum ore does not cause any appreciable difference.

If the ore should be high in lime the molybdenum can be determined by the volumetric (KMnO) method, or the lime can be removed from the alkaline solution by means of sodium carbonate before precipitating the lead molybdate. Molybdenum remains in solution. Two precipitations should be made, washing the precipitate well each time.

As calcium molybdate is partly precipitated from a solution slightly acidified with acetic acid only when the solution is boiled vigorously for a prolonged period, it is essential that the directionsgiven under "Precipitation" be followed closely.