Septembee 21, 1900.] 



SCIENCE. 



431 



tion of all the details of the special case of 

 motion, were occasionally slow to appre- 

 hend the advantages of a procedure which 

 stopped at formulating a description of the 

 nature of the interaction between various 

 typical groups of motions into which the 

 whole disturbance could be resolved. 



The new train of ideas introduced into 

 physics by Faraday was thus consolidated 

 and emphasized by Helmholtz's investi- 

 gations of 1858 in the special domain of 

 hydrodynamics. In illustration let us con- 

 sider the fluid medium to be pervaded by 

 permanent vortices circulating round solid 

 rings as cores ; the older method of analysis 

 would form equations of motion for each 

 element of the fluid, involving the fluid 

 pressure, and by their integration would 

 determine the distribution of pressure on 

 each solid ring, and thence the way it 

 moves. This method is hardly feasible 

 even in the simplest cases. The natural 

 plan is to make use of existing simplifica- 

 tions by regarding each vortex as a perma- 

 nent reality, and directly attacking the 

 problem of its interactions with the other 

 vortices. The energy of the fluid arising 

 from the vortex motion can be expressed in 

 terms of the positions and strengths of the 

 vortices alone; and then the principle of 

 Action, in the generalized form which in- 

 cludes steady motional configurations as 

 well as constant material configurations, 

 affords a method of deducing the motions 

 of the cores and the interactions between 

 them. If the cores are thin they in fact 

 interact mechanically, as Lord Kelvin and 

 Kirchhoff' proved, in the same manner as 

 linear electric currents would do ; though 

 the impulse thence derived towards a direct 

 hydro-kinetic explanation of electro-mag- 

 netics was damped by the fact that repul- 

 sion and attraction have to be interchanged 

 in the analogy. The conception of vortices, 

 once it has been arrived at, forms the 

 natural physical basis of investigation, al- 



though the older method of determining a 

 distribution of pressure-stress throughout 

 the fiuid and examining how it affects the 

 cores is still possible ; that stress, however, 

 is not simply transmitted, as it has to main- 

 tain the changes of velocity of the various 

 portions of the fluid. But if the vortices 

 have no solid cores we are at a loss to know 

 where even this pressure can be considered 

 as applied to them ; if we follow up the 

 .stress, we lose the vortex ; yet a fluid vor- 

 tex can nevertheless illustrate an atom of 

 matter, and we can consider such atoms as 

 exerting mutual forces, only these forces 

 cannot be considered as transmitted 

 through the agency of fluid pressure. The 

 reason is that the vortex cannot now be 

 identified with a mere core bounded by a 

 definite surface, but is essentially a config- 

 uration of motion extending throughout 

 the medium. 



Thus we are again in face of the funda- 

 mental question whether all attempts to 

 represent the mechanical interactions of 

 electro-dynamic systems, as transmitted 

 from point to point by means of simple 

 stress, are not doomed to failure ; whether 

 they do not, in fact, introduce unnecessary 

 and insurmountable difficulty into the 

 theory. The idea of identifying an atom 

 with a state of strain or motion, pervading 

 the region of the sether around its nucleus, 

 appears to demand wider views as to what 

 constitutes dynamical transmission. The 

 idea that any small portion of the primor- 

 dial'medium can be isolated, by merely in- 

 troducing tractions acting over its surface 

 and transmitted from the surrounding parts, 

 is no longer appropriate or consistent; a 

 part of the dynamical disturbance in that 

 element of the medium is on this hypothe- 

 sis already classified as belonging to, and 

 carried along with, atoms that are outside 

 it but in its neighborhood — and this part 

 must not be counted twice over. The law 

 of Poynting relating to the paths of the 



