July 6, 191 1] 



NATURE 



3* 



receives striking confirmation from a recent interesting 

 investigation of Griineisen ' concerning the small effect of 

 low temperatures on the compressibility of metals. The 

 average compressibility of aluminium, iron, copper, silver, 

 and platinum falls off only 7 per cent, between the 

 temperature of the room and that of liquid air. Extra- 

 polation of the curves indicates that at the absolute zero 

 very little further diminution should occur. So far as 

 we can guess, therefore, the hard metals are almost as 

 compressible at the absolute zero as at room tempera- 

 tures. But at the absolute zero all heat-vibration is sup- 

 posed to stop; hence this remaining compressibility must 

 needs be ascribed to the atoms themselves. 



If the atoms are compressible, all mathematical reason- 

 ing which assumes them to be incompressible rests upon 

 a false basis. The kinetic theory of gases remains un- 

 molested by these considerations, except as. they indicate 

 the changeability of b in the equation of van der Waals, 

 but the new views affect seriously the application of this 

 equation to solids and liquids. 



Let us proceed to trace a few of the outcomes of our 

 hypothesis. If atoms may really be packed closely 

 together, the volumes of solids and liquids should afford 

 valuable knowledge concerning the relative spaces occupied 

 by the atoms themselves under varying conditions. The 

 densities of solids and liquids then assume a significance 

 far more interesting to the chemical philosopher than 

 before, because they have a more definite connection with 

 the fundamental nature of things. 



An apparent objection at once suggests itself ; if the 

 particles in condensed material are really touching one 

 another, how can we account for heat within the material? 

 Would such closely packed atoms be able to vibrate? 



The theory of compressible atoms supplies as one of its 

 own corollaries the immediate answer to this question. If 

 atoms are compressible throughout their whole substance, 

 they may contract and expand, or vibrate within them- 

 selves, even when their surfaces are prevented from moving 

 by being closely packed together. It is thus possible to 

 conceive of a vibrational effect, even in contiguous atoms, 

 provided we can conceive of these atoms as being elastic 

 throughout all their substance. Agitation sufficient to pro- 

 duce even the Brownian movement might easily exist in 

 such a system. 



Clearly there is nothing impossible or obviously contra- 

 dictory to experimental knowledge in the notion that atoms 

 are compressible ; indeed, the old idea of small, hard 

 particles far apart is really more arbitrary and hypothetical 

 than the new conception. The obvious simplicity of the 

 latter is rather in its favour than otherwise, as in Dalton's 

 atomic theory. In general, the more simply a hypothesis 

 interprets the phenomena of nature, the more useful the 

 hypothesis is likely to be, provided, of course, that the 

 interpretation is adequate. The modern philosophy of 

 pragmatism is a good guide in such matters ; a theory 

 not obviously illogical should be judged by its usefulness. 

 Let us, then, test the new hypothesis by applying it to 

 other aspects of physical chemistry. 



If pressure produces a change in the sizes of the atoms 

 and molecules themselves, may not the actual volumes of 

 liquids and solids be used as a guide to the unknown 

 internal pressures within them? Cannot we thus discover 

 whether or not chemical affinity exerts pressure in its 

 action ? To follow this clue, the simplest possible case 

 was chosen at first, namely, the comparison of the con- 

 tractions taking place on combining several elements in 

 succession with a single very compressible one. The 

 changes of volume occurring during the formation of oxides 

 were first computed ; later, chlorides and bromides were 

 studied. According to the theory of compressible atoms, 

 we should expect to find greater contraction in cases of 

 greater affinity. A diagram depicting typical data con- 

 cerning certain nearly related chlorides strongly supports 

 this inference. 3 One line shows the total change of 

 volume which occurs when a grain-molecule of chlorine 

 combines with the equivalent weight of metal ; the other 



1 E. Griineisen, Ann. Physik. iqio, [iv], xxxii!., 1235. The relative 

 values for the compressibilities recorded in this investigation ate doubtless 

 trustworthy, although the absolute magnitudes are somewhat 

 because they depend on the rather inadequate theory of elasticity. 

 Richards, Proc. Amer. Acad., 1002 



Chem. So 



IQOQ 



, 399 ; also especially J. Amer. 



NO. 2175, VOL. 87] 



gives the heat evolved during combination. The lines 

 show distinct parallelism ; that is to say, reactions evolving 

 much heat manifest great contraction. In cases of this 

 kind, the heat of reaction is usually not very different 

 from the change of free energy; therefore we may infer 

 that greater affinity is associated with greater contraction ; 

 and it is but a small leap in the dark to guess that the 

 change of volume is caused by the pressure of affinity. 

 Since chemical affinity holds two elements firmly together, 

 why should it not exert pressure? And if it exerts 

 pressure, why should not the volume of the system be 

 diminished by this pressure? 



Evidently the change of volume in any case must depend 

 not only on the intensity of the pressure exerted by the 

 affinity, but also, among other things, on the compressi- 

 bility of the substances concerned. The greater the com- 

 pressibility, the greater should be the change of volume 

 caused by a given pressure of affinity. Before any definite 

 conclusion can be drawn, the differences in compressibility 

 must be taken into account. 



These thoughts led to the measuring of the compressi- 

 bilities of a large number of elements and simple com- 

 pounds. The previously employed methods for solids and 

 liquids being unsatisfactory, a new and highly satisfactory 

 method was devised for the work done at Harvard. The 

 compressibilities of thirty-five elements and many single 

 compounds were studied by this method with sufficient 

 care to leave no doubt as to their relative values. It 

 became at once manifest that the formation of a compound 

 of a compressible element was attended with greater 

 decrease of volume than the formation of a similar com- 

 pound of a less compressible element, other things being 

 equal. 1 This is just what the theory leads us to expect, 

 and is a fact inexplicable by any other hypothesis as yet 

 known to me. 



Another essential aspect of the theory of compressible 

 atoms is that which concerns cohesion. 2 If the pressure 

 of chemical affinity causes atomic compression, may not 

 the pressure of cohesive affinity also have the same effect? 

 Traube suggested this possibility, but looked at the whole 

 question from a different point of view. 3 The affinity 

 which prevents solids and liquids from vaporising is gener- 

 ally admitted to produce great internal pressure ; must it 

 not tend to compress the molecules into smaller space? 

 Molecules with high cohesive affinity (those of substances 

 hard to volatilise) should be much compressed and possess 

 small volume, whereas molecules with a slight cohesive 

 affinity should be more bulky. Moreover, those molecules 

 already much compressed by their own self-affinity would 

 naturally be but little affected by additional pressure. 

 Thus, as regards two substances otherwise similar, the less 

 volatile one would be less compressible, denser, and possess 

 greater surface tension. 1 These outcomes of the theory 

 correspond with the facts in a majority of cases thus far 

 studied ; for example, o-xylene is denser, less volatile, less 

 compressible, and possesses a greater surface tension than 

 either m-xylene or p-xylene. Differences of structure and 

 differences of chemical nature sometimes conceal these 

 relations ; the parallelism appears most strikingly among 

 isomeric compounds. In brief, the bulk of evidence 

 strongly indicates that cohesiveness as well as chemical 

 affinity exerts pressure in its action, and hence that each 

 plays a part in determining the volumes occupied by 

 molecules. 



Thus the computation of the space occupied by either a 

 solid or a liquid becomes a very complex matter. Not 

 only must the various chemical affinities at work be taken 

 into account, but also the cohesive attraction of both 

 factors and products, and the compressibilities over a very 

 wide range of all the substances concerned. Discoverable 

 parallelism in volume changes is to be expected only when 

 one alone of these forces is the chief variable. 



The exact mathematical working out of the consequences 



1 Richards, Proc. Amer. Acad., 1904, xxxix., 1 2 IMd. 



3 See especially Traube, Ann. Physik., 1897, [iii], Ixi., 383 ; 1901, [tv], v., 

 548; 1902, viii., 267; 1907, xxii., 519: Zeitsch. physikal. Chem., 1910, 

 ixviii., 2S9 ; also Walden, Zeitsch physikal. Chem., 1909, lxvi., 385 Their 

 interpretation depends largely on the application of van der Waals's equation 

 and the complicating assumption of a co-volume: however, Walden s very 

 recent paper presents a number of interesting and important relations con- 

 cerning internal pressure, which seem to demand the assumption of atomic 

 compressibility for their expl.i nation. 



* Richards and Mathews, Zeitsch. physikal. Chem., 1908, Ixi., 449. 



