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SCIENCE. 



[N. S. Vol. xn. No. 299. 



ently 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 Eether of free space a dielectric con- 

 stant and a magnetic constant of the same 

 tj'pe as had been found to express the prop- 

 erties of material media, thus extending 

 the seat of the phenomena to all space on 

 the plan of describing the activity of the 

 sether in terms of the ordinary electric 

 ideas. The converse mode of develop- 

 ment, starting with the free aether under 

 the directly dynamical form which has 

 been usual in physical optics, and intro- 

 ducing the influence of the material atoms 

 through the electric charges which are in- 

 volved in their constitution,* was hardly 

 employed by him ; in pai't, perhaps, be- 

 cause, owing to the necessity of correlating 

 his theory with existing electric knowledge 

 and the mode of its expression, he seems 

 never to have reached the stage of mould- 

 ing it into a completely deductive form. 



The dynamics of the sether, in fact the 

 recognition of the existence of an sether, 

 has thus, as a matter of history, been 

 reached through study of the dynamical 

 phenomena of matter. When the dynamics 

 of a material system is worked up to its 

 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 such a compact statement when the 

 system is self-contained, when its motion 

 is not being dissipated by agencies of fric- 



* In 1870 Jlaxwell, 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 left 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. 



tional type, and when its connections can 

 be directly specified by purely geometrical 

 relations between the co-ordinates, thus 

 excluding such mechanisms as rolling con- 

 tacts. 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 

 may be held as to the ultimate significance 

 of this principle of action, its importance, 

 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 recognized, on 

 the lines already indicated, that this is 

 another mode of statement of the same 

 fundamental idea ; and the general equiva- 

 lence is worked out by Hertz on the basis 

 of Hamilton's development of the prin- 

 ciples of dynamics. The latter mode of 

 statement may be adaptable so as to avoid 



