January 17, 1895] 



NATURE 



28- 



THE FOUNDATIONS OF DYNAMICS} 



''pniS posthumous volume of Hertz's works, edited by Prof. 

 ^ Lenard, with a preface by von Helmholtz, has a doubly 

 melancholy interest. It is the last work of Hertz upon which 

 he was engaged until a few days before his death, and it con- 

 tains a preface which is almost the last work of von Helmholtz. 

 The pupil died shortly before his master, and by the departure 

 of such a pupil and of such a master, science, and with science 

 mankind, have lost many prospects of advances in the near 

 future. 



In his preface, von Helmholtz pays a touching tribute to the 

 genius of his favourite pupil, from whom he hoped most, and 

 who had drunk most deeply of his master's thoughts. In 1878 

 their intimacy began. At that lime difficulties connected with 

 various electrical theories of action at a distance were occupying 

 his thoughts, and he offered a prize for the best essay on in- 

 duction in non-induclively wound coils. Weber's theory would 

 have involved an inertia of the electric current di>iinct from 

 the magnetic inertia. The question is still interesting in con- 

 nection wiih discharges between two charged conductors, one 

 of which completely surrounds the other when a dielectric be- 

 tween them is suddenly made conductive. There is then no 

 magnetic force. Is there no inertia ? Can a medium become 

 jKt/cr't'w/)' conducting ? Is a conducting medium homogeneous? 

 Is there inertia 01 ionic charges which represent the non-homo- 

 geneiiy of the medium ? These questions still refjuire answer- 

 ing ; but in the seventies, in Germany, Maxwell'.* idea of mag- 

 netic force accompanying displacement currents was not 

 generally received, and Helmhollz's question as to the in- 

 duction in non-inductively wound coils really had reference to 

 these displacements. Hertz won the prize by showing that at 

 most only i 20th or i/3oth of the extra-current could be due to 

 electric inertia. By subsequent experiments on the possible 

 effect of centrifugal force on the current in rapidly rotating 

 plate=, he reduced this estimate to a very much smaller value. 

 Mr. Larmor has suggested that any centrifugal force may be 

 balanced by a tension in the length of the current, much in the 

 same way that the tension of a running rope will balance centri- 

 fugal force in the curves round which it may be running. In 

 every way the subject deserves further investigation, for it is 

 intimately connected with the most funlamenial questions as to 

 the nature of electricity and its connection with maiter. 



The next thing to which Hertz devoted himself was a prize 

 problem proposed, at von Helmhollz's suggestion, by the 

 Berlin Academy. The problem was to investigate .Mixwell's 

 postulate that changing electric displacement was an electric 

 current. This was the bud from which Herizs great work 

 sprang. Of it von Helmholtz says : " It is a pity we do not 

 possess more such histories of the inner psychological develop- 

 ment of knowledge. Its author deserves our sincerest thanks 

 for letting us see so deeply into the inmost working of his 

 thoughts, and for recording even his temporary mistakes. By 

 this work Hertz has settled for ever the question as to electro- 

 magnetic actions being propagated by a medium, and the only 

 outstanding question of the kind is as to gravitation, which we 

 do not yet know how to logically explain as other than a pure 

 action at a distance.' It thus appears that von Helmholtz to 

 the last was unconvinced as to the probahility of any hypothesis 

 like Le Sage's or Osborne Reynolds's. He seems, on the other 

 hand, to have been satisfied with the possibility of chemical 

 actions being explained cither by electromagnetic actions or by 

 actions not at a distance. This latter term, of course, requires 

 explanation as to what " al a distance " means. .\ny actions 

 other than those of absolutely rigid bodies, such, for instance, 

 as the fairly well-established forces of attraction of gaseous 

 molecules lor one another, and some of which can hardly be 

 explained either by electricity, magnetism, or gravitation, seem 

 to be actions at a distance that require explanation just as much 

 as gravitation. 



Following this short history of the work of his pupil which, 

 coming from such a master, must have a permanent interest to 

 all, von Helmholtz gives a. lisumt' oi the last work of Herlz. In 

 it there is attempted a continuously elabirated presentation of 

 a complete and self-dependent system of mechanics, in which 

 each particular applicali )n of this science is deduced from a 

 single fundamental law which can of course be itself only 

 assumed as a plausible hypothesis. In order to ex,)lain how 



1 'The Principles of Dvn.Tnics developed on ncv lines: — Hertz's Col- 

 lected Works," vol. iii. Pp. 310. (Leipzig : B.irth, 1594.) 



NO. 1316, VOL. 5 l] 



this is required, von Helmholtz gives a short history of ihe 

 development of ihe science of mechanics. The first develop- 

 ments arose from the study of the equilibrium and motion of 

 solid bodies ;n direct contacts with one another, such as the 

 simple machines, the lever, the inclined plane, the pulley. 

 The law of virtual velocities gives the most fundamental general 

 solution of all such problems. Galileo subsequently developed 

 Ihe knowledge of inertia and of moving force as an accelerating 

 agent. It was, however, conceived by him as a succession of 

 blows. Newton was the first who arrived at the notion of force 

 acting at a distance, and its more accurate determination by the 

 principle of action and reaction. It is well known how 

 strenuously he and his contemporaries resisted this idea of pure 

 action at a distance. From this men developed the methods 

 of treating all problems of conservation forces with constant 

 connections whose most general solution is given by 

 DAlembert's principle. All the general principles of dynamics 

 have been developed from Newton's hypothesis of permanent 

 forces between material points and permanent connections be- 

 tween them. It was subsequently found that these laws held 

 even when these foundations could not be proved, and it was 

 thence deduced that all the laws of nature agreed with certain 

 general characteristics ol Newton's conservative forces of attrac- 

 tion, although it was not found possible to deduce all these 

 generalisations Irom one common fundamental principle. Hertz 

 has devoted himself to discovering such a fundamental principle 

 for mechanics, from which all the laws of mechanics hitherto 

 known as universally valid can be deduced ; and he has carried 

 out this with great acuteness, and by means of a very remark- 

 able presentation of a peculiarly general kinematic conception. 

 In working it out, he returns to the oldest mechanical theories, 

 and supposes all actions to be by means of rigid connections. 

 Of course he has to assume that there are innumerable imper- 

 ceptible masses and invisible motions of these, in order to ex- 

 plain the apparent actions upon one another of bodies that are 

 not in immediate contact. 'I'hough he has not given examples 

 of how this may be the case, he evidently builds his expectation 

 of being thus able to explain natural aclions upon the existence 

 of cyclical systems, rollers, &c., with invisible motions. The 

 justification of such an assumption can only be obtained by its 

 success. Von Helmholtz concludes this interesting preface by 

 remarking how English physicists have so often based their 

 work on dynamical and geometrical suppositions, as for ex- 

 ample Lord Kelvin and his vortex atoms. Maxwell and his cells 

 with rotating contents. These physicists, he says, "have 

 clearly been more satisfactorily helped by such illustrations, 

 than by the mere most general representations of the facts and 

 their laws as given by the system of physical differential 

 equations. I must confess that I have restricied myself to 

 this latter method of investigation, and have felt most con- 

 fidence therein ; and indeed I might not have arrived at any 

 important results by the methods which eminent physicists such 

 as the three mentioned have employed." 



Although so far it seems as if ihere were very little to choose 

 between the old methods of supposing that natural aclions can 

 be explained by conservative forces between molecules and by 

 s>stems of rigid connections, Hertz in bis introduction shows 

 that he is dissatisfied with the hypotheses, of these forces as 

 entities, while von Helmholtz, by his silence, seems to hold the 

 view that the old method was good enough for him. Hertz's 

 method has, however, the advantage of turning our attention 

 to something definite to be investigated and invented, namely, 

 the structure of these rigid connections It is apparently very 

 closely related to Osborne Reynolds's and " Waterdalc's, " sug- 

 gestions as to the structure of the ether, namely, that it consists 

 of perfectly rigid particles in almost complete juxtaposition 

 which, whether by their smoothness or by their rolling upon one 

 another, waste no energy in internal heat motions. 



In his own preface, Ileriz says that he has culled many 

 things from many minds, nothing particular in his work is new ; 

 what he presents as new is the arrangement and collocation of 

 the whole, and the logical, or rather philosophical, aspect 

 thereby attained. 



To these prefaces Ihere follows a long introduction, in which 

 Heilz reviews and criticises the present foundations of dynamics. 

 The great road by which this domain is now entered is one that 

 was laid by .\rchimedes, Galileo, Newton, and Lagrange. It is 

 founded on our notions of space, time, force, and mass. F'orce 

 is introduced prior to mot.ion, as the independent cause thereof. 

 Galileo's notion of inertia only involved space, time, and mass. 



