452 



NA TURE 



[Sehtember 6, 1900 



detailed, though far from complete, analysis of the vibratory 

 motions that are going on in it ; these vibrations being in their 

 normal state characteristic of its dynamical constitution, and in 

 their deviations from the normal giving indications of the velocity 

 of its movement and the physical state of its environment. ' 

 Maxwell long ago laid emphasis on the fact that a physical 

 atomic theory is not competent even to contemplate the vast 

 mass of potentialities and correlations of the past and the future, 

 that biological theory has to consider as latent in a single organic 

 germ containing at most only a few million molecules. On our 

 present view we can accept his position that the properties of 

 such a body cannot be those of a "' purely material system," 

 provided, however, we restrict this phrase to apply to physical 

 properties as here defined. But an exhaustive discovery of the 

 intimate nature of the atom is beyond the scope of physics ; 

 questions as to whether it must not necessarily involve in itself 

 some image of ihe complexity of the organic structures i)f which 

 it can form a correlated part must remain a subject of specula- 

 tion outside the domain of that science. It might be held that 

 this conception of discrete atoms and continuous xther really 

 stands, like those of space and time, in intimate relation with 

 our modes of mental apprehension, into which any consistent 

 picture of the external world must of necessity be fitted. In any 

 case it would involve abandonment of all the successful traditions 

 of our subject if we ceased to hold that our analysis can be 

 formulated in a consistent and complete manner, so far as it 

 goes, without being necessarily an exhaustive account of phe- 

 nomena that are beyond our range of experiment. Such 

 phenomena may be more closely defined as those connected 

 with the processes of intimate combination of the molecules : 

 they include the activities of organic beings which all seem to 

 depend on change of molecular structure. 



If, then, we have so small a hold on the intimate nature of 

 matter, it will appear all the more striking that physicists have 

 been able precisely to divine the mode of operation of the in- 

 tangible sether, and to some extent explore in it the fields of 

 physical influence of the molecules. On consideration we 

 recognise that this knowledge of fundamental physical inter- 

 action has been reached by a comparative process. The mechan- 

 ism of the propagation of light could never have been studied 

 in the free aether of space alone. It was possible, however, to 

 determine the way in which the characteristics of optical propa- 

 gation are modified, but not wholly transformed, when it takes 

 place in a transparent material body instead of empty space. 

 The change in fact arises on account of the aether being 

 entangled with the network of material molecules ; but inasmuch 

 as the length of a single wave of radiation covers thousands of 

 these molecules the wave-motion still remains uniform and does 

 not lose its general type. A wider variation of the experimental 

 conditions has been provided for our examination in the case 

 of those substances in which the phenomenon of double refrac- 

 tion pointed to a change of the aethereal properties which varied 

 in different directions ; and minute study of this modifi- 

 cation has proved sufficient to guide to a consistent appreciation 

 of the nature of this change, and therefore of the mode of 

 ^ethereal propagation that is thus altered. In the same way, it 

 was the study and development of the manner in which the 

 laws of electric phenomena in material bodies had been 

 unravelled by Ampere and Faraday that guided Faraday him- 

 self and Maxwell — who were impressed with the view that the 

 oether was at the bottom of it all — in their progress towards an 

 application of similar laws to aether devoid of matter, such as 

 would complete a scheme of continuous action by consistently 

 interconnecting the material bodies and banishing all untraced 

 interaction across empty space. Maxwell in fact chose to finally 

 expound the theory by ascribing to the sether of free space a 

 dielectric constant and a magnetic constant of the same types as 

 had been found to express the properties of material media, thus 

 extending the seat of the phenomena to all space on the plan of 

 describing the activity of the tether in terms of the ordinary 

 electric ideas. The converse mode of development, starting 

 with the free tether under the directly dynamical form which 

 has been usual in physical optics, and introducing the influence 

 of the material atoms through the electric charges which are 

 involved in their constitution, ^ was hardly employed by him ; 



1 In 1870 Maxwell, while admiring the breadth of the theory of Weber, 

 which is virtually based on atomic charges combined with action at a 

 distance, still regarded it as irreconcilable with his own theory, and lelt to 

 the future the question as to why " theories apparently so fundamentally 

 opposed should have so large a field of truth common to both." — " Scientific 

 Papers," ii. p. 228. 



NO. I 6 10, VOL. 6':>] 



in part, perhaps, because, owing to the necessity of correlating 

 his theory with existing electric knowledge and the mode of ib 

 expression, he seems never to have reached the stage of mould 

 ing it into a completely deductive form. 



The dynamics of the aether, in fact the recognition of tli 

 existence of an tether, has thus, as a matter of history, beei 

 reached through study of the dynamical phenomena of mattei 

 When the dynamics of a material system is worked up to i 

 purest and most general form, it becomes a formulation of the 

 relations between the succession of the configurations and states 

 of motion of the system, the assistance of an independent idea 

 of force not being usually required. We can, however, only 

 attain to such a compact statement when the system is self- 

 contained, when its motion is not being dissipated by agencies 

 of frictional type, and when its connections can be directly 

 specified by purely geometrical relations between the co- 

 ordinates, thus excluding such mechanisms as rolling contacts. 

 The course of the system is then in all cases determined by 

 some form or other of a single fundamental property, that any 

 alteration in any small portion of its actual course must produce 

 an increase in the total " Action " of the motion. It is to be 

 observed that in employing this law of minimum as regards the 

 Action expressed as an integral over the whole time of the 

 motion, we no more introduce the future course as a determining 

 influence on the present state of motion than we do in drawing 

 a straight line from any point in any direction, although the 

 length of the line is the minimum distance between its ends. 

 In drawing the line piece by piece we have to make tentative 

 excursions into the immediate future in order to adjust each 

 element into straightness with the previous element ; so in 

 tracing the next stage of the motion of a material system we have 

 similarly to secure that it is not given any such directions as would 

 unduly increase the Action. But whatever views maybe held as 

 to the ultimate significance of this principle of Action, its import- 

 ance, not only for mathematical analysis, but as a guide to physical 

 exploration, remains fundamental. When the principles of the 

 dynamics of material systems are refined down to their ultimate 

 common basis, this principle of minimum is what remains. 

 Hertz preferred to express its contents in the form of a principle 

 of straightness of course or path. It will be recognised, on the 

 lines already indicated, that this is another mode of statement of 

 the same fundamental idea ; and the general equivalence is 

 worked out by Hertz on the basis of Hamilton's development 

 of the principles of dynamics. The latter mode of statement 

 may be adaptable so as to avoid the limitations which restrict 

 the connections of the system, at the expense, however, of 

 introducing new variables ; if, indeed, it does not introduce 

 gratuitous complexity for purposes of physics to attempt to do 

 this. However these questions may stand, this principle of 

 straightness or directness of path forms, wherever it applies, 

 the most general and comprehensive formulation of purely 

 dynamical action : it involves in itself the complete course of 

 events. In so far as we are given the algebraic formula for the 

 time-integral which constitutes the Action, expressed in terms 

 of any suitable co-ordinates, we know implicitly the whole 

 dynamical constitution and history of the system to which it 

 applies. Two systems in which the Action is expressed by the 

 same formula are mathematically identical, are physically pre- 

 cisely correlated, so that they have all dynamical properties in 

 common. When the structure of a dynamical system is largely 

 concealed from view, the safest and most direct way towards an 

 exploration of its essential relations and connections, and in 

 fact towards answering the prior question as to whether it is a 

 purely dynamical system at all, is through this order of ideas. 

 The ultimate test that a system is a dynamical one is not that we 

 shall be able to trace mechanical stresses throughout it, but that 

 its relations can be in some way or other consolidated into 

 accordance with this principle of minimum Action. This 

 definition of a dynamical system in terms of the simple principle 

 of directness of path may conceivably be subject to objection as 

 too wide ; it is certainly not too narrow ; and it is the conception 

 which has naturally been evolved from two centuries of study of 

 the dynamics of material bodies. Its very great generality may 

 lead to the objection that we might completely formulate the 

 future course of a system in its terms, without having obtained 

 a working familiarity with its details, of the kind to which we 

 have become accustomed in the analysis of simple material 

 systems ; but our choice is at present between this kind of 

 formulation, which is a real and essential one, and an empirical 

 description of the course of phenomena combined with explan- 



