434 



NA TURE 



{Sept. 5. 1889 



attraction at the same distance more than a thousand 

 million billion billion times, the atoms being regarded as 

 spheres oppositely electrified each to about the potential 

 of a volt, the gravitative attraction between two worlds 

 the size and density of our earth exceeds their electrical 

 attraction when likewise oppositely charged each to a volt 

 in just about the same ratio. The ratio of the forces de- 

 pends, in fact, on the fourth power of the linear dimensions 

 of the bodies concerned — other things being fixed. For a 

 couple of smiU bullets the two forces would be approxi- 

 mately equal. 



Again, if every atom be regarded as separately charged, 

 and able to combine with each other, we get the maximum 

 possible energy of combustion, which may be put down as 

 at the most 20,000 therms per gramme. The heat of for- 

 mation of our moon by combustion is on this estimate very 

 comparable to that -developed by the falling together of 

 its materials from infinity under gravitation. But whereas 

 tha energy of combustion is simply proportional to the 

 masses concerned, the energy of gravitation is propor- 

 tional to the product, i.e. to the second power of the 

 masses ; and so we find that when a body is as big as the 

 sun the gravitative energy of its mere earthquake sub- 

 sidence as it shrinks is enormously greater than that 

 which could be afforded by the combustion of an equal 

 mass. So also it is shown to bs greater than could be 

 caused by any reasonably permissible hail of meteorites 

 from infinity : meaning by "reasonably permissible," such 

 a hail as would not introduce planetary perturbations of a 

 conspicuously non-existent amount. 



Returning now to the beginning of the volume, we find 

 an altogether admirable, but rather stiff discourse on 

 capillarity. How it can help being stiff when it enters 

 into problems usually treated by the higher mathematics, 

 and hitherto reserved for specialists, I do not know. It 

 is a serious mathematical essay done into ordinary 

 language. The diagrams of the precise shape of liquid 

 surfaces are beautiful, and such as are nowhere else to be 

 found. To a reader who will concentrate his thought 

 upon this discourse, it will gradually become luminously 

 clear, but perhaps the conscientious person who always 

 reads books from cover to cover, may run the risk of being 

 choked off by the accident of its coming first. 



Appended to it are three notes, one on the " tears of 

 strong wine," as explained by Prof. James Thomson ; one 

 on the author's remarkable and beautiful discovery of 

 the reasons why mist globules cannot form without a 

 nucleus, why big rain-drops form at the expense of little 

 ones, and why put-away clothes get damp ; and lastly, a 

 note on the sufficiency of Newtonian gravitation to ex- 

 plain cohesion. This latter is a highly ingenious piece of 

 special pleading. It is so easy to prove that gravitation 

 will not explain cohesion, on any of the commonly current 

 mental ideas of what atoms are like ; but here, by assum- 

 ing a sufficiently violent concentration of substance in 

 certain regions, and sufficient absence of all substance 

 from other regions of an atom, it is shown that cohesion 

 may be explained by gravitation. At least, it can be seen 

 that different atoms can cling to each other, but it is not so 

 clear how the various parts of the atoms themselves hang 

 together. No-how, it seems to me, unless they are 

 exaggeratedly fibrous structures, and unless the ends of 

 the fibres of one atom cling on to the next, and thus build 



up a body like a cobweb. Nothing but cobweb can cohere 

 by gravitation, so it seems to me (perhaps wrongly, of 

 course) ; and although one has gradually learnt that no 

 hypothesis concerning reahty is a prioj'i absurd or un- 

 likely, yet this does not feel, nor indeed is it intended, as 

 anything final or satisfactory. 



Then comes a long lecture on electrical units of 

 measurement, wherein the foundations of the conventional 

 " absolute " systems of electrical measurement are ex- 

 plained and illustrated by showing how by means of 

 electrical observations the fundamental standards of 

 length, mass, and time might, if lost, be conceivably 

 recovered. The subject is rather technical, and scarcely 

 of sufficient general interest to repay the unelectrical 

 reader, though there are here, as everywhere, numerous 

 suggestive remarks. One might, perhaps, suggest that 

 the distinction between the conventional and the 

 essential is not always sufficiently borne in mind and 

 enforced. 



The lecture on the size of atoms is intensely interest- 

 ing to everybody. Physicists know by how many 

 different lines of argument a limit of smallness for the 

 spice occupied by an atom can be fixed, or an actual 

 estimate of the number of molecules in a given lump of 

 matter can be made. A number of these methods 

 suggested by the author are here stated, and, with many 

 illustrations, explained. But, besides this, there are 

 instructive mechanical models or images illustrating 

 Prof. Stokes's theory of phosphorescence, Cauchy's 

 theory of dispersion, and the polarization of light by 

 small particles. 



The remaining subjects dealt with in this volume — 

 elasticity regarded as a mode of motion, and a kinetic 

 theory of matter — are closely related to each other, are 

 wholly the author's own, and are among the most brilliant 

 speculations of the century. But a small inkling of the 

 great field thus opened up is given here — enough, however 

 to afford to the reader some glimpse of the possibilities 

 of development lying in this direction. 



Such are the contents of the volume before us, and a 

 more comprehensive collection of scientific addresses 

 has seldom been published. They do not, of course, 

 really represent Sir William Thomson at his best : 

 neither they nor any other intelligible production of his is 

 able to convey to the general reader an adequate notion 

 of the magnitude of his solid work, or of the grounds for 

 the veneration with which his contemporaries regard him. 



Such as they are, however, every physicist will be glad 

 to read these papers again in this handy form, and every 

 intelligent and educated man who feels an interest in the 

 strong thought of physical science during this eventful 

 century will do well to make a serious effort to grasp at 

 least the main outlines of the profound studies shadowed 

 forth in this small volume. Oliver J. Lodge. 



THE MATHEMATICAL THEORY OF 

 POLITICAL ECONOMY. 



Elements d'Aconojnie Politique Picrc. Par Ldon Walras. 

 (Lausanne: F. Rouge, 1889.) 



THE appearance of a new and enlarged edition affords 

 us a wished-for opportunity of calling attention to 

 this original work. Its author is one of the favoured few 



