428 



SCIENCE. 



[N. S. Vol. XII. No. 299. 



our dynamical systems have long been em- 

 phasized by Lord Kelvin ; * the effective 

 adaptation of abstract dynamics to such 

 systems was made independently by Kelvin 

 and Eouth about 1877 ; the more recent 

 exposition of the theory by Helmholtzr has 

 directed general attention to what is un- 

 doubtedly the most significant extension of 

 dynamical analysis which has taken place 

 since the time of Lagrange. 



Eeturning to the molecules, it is now 

 verified that the Action principle forms a 

 valid foundation throughout electrodynam- 

 ics and optics ; the introduction of the 

 sether into the system has not affected its 

 application. It is therefore a reasonable 

 hypothesis that the principle forms an al- 

 lowable foundation for the dynamical analy- 

 sis of the radiant vibrations in the system 

 formed by a single molecule and surround- 

 ing sether; and the knowledge which is 

 now accumulating, both of the orderly 

 grouping of the lines of the spectrum and 

 of the modifications impressed on these 

 lines by a magnetic field or by the density 

 of the matter immediately surrounding the 

 vibrating molecule, can hardly fail to be 

 fruitful for the dynamical analysis of its 

 constitution. But let it be repeated that 

 this analysis would be complete when a 

 formula for the dynamical energy of the 

 molecule is obtained, and would go no 

 deeper. Starting from our definitely lim- 

 ited definition of the nature of a dynamical 

 system, the problem is merely to correlate 

 the observed relations of the periods of 

 vibration in a molecule, when it has come 

 into a steady state as regards constitution 

 and is not under the influence of intimate 

 encounter with other molecules. 



It may be recalled incidentally that the 

 generalized Maxwell-Boltzmann principle 



* For a classical exposition see his Brit. Assoc. Ad- 

 dress of 1884 on ' Steps towards a Kinetic Theory of 

 Matter, ' reprinted in ' Popular Lectures and Ad- 

 dresses,' vol 1. 



of the equable distribution of the acquired 

 store of kinetic energy of the molecule, 

 among its various possible independent 

 types of motion, is based directly on the 

 validity of the Action principle for its dy- 

 namics. In the demonstrations usually 

 offered the molecule is considered to have 

 no permanent or constitutive energy of in- 

 ternal motion. It can, however, be shown, 

 by use of the generalization aforesaid of 

 the Action principle, that no discrepancy 

 will arise on that account. Such intrinsic 

 kinetic energy virtually adds on to the po- 

 tential energy of the system ; and the re- 

 maining or acquired part of the kinetic 

 energy of the molecule may be made the sub- 

 ject of the same train of reasoning as before. 

 Let us now return to the general ques- 

 tion whether our definition of a dynamical 

 system may not be too wide. As a case in 

 point, the single principle of Action has 

 been shown to provide a definite and suffi- 

 cient basis for electrodynamics ; yet when, 

 for example, one armature of an electric 

 motor pulls the other after it without ma- 

 terial contact, and so transmits mechanical 

 power, no connection between them is in- 

 dicated by the principle such as could by 

 virtue of internal stress transmit the pull. 

 The essential feature of the transmission of 

 a pull by stress across a medium is that 

 each element of volume of the medium 

 acts by itself, independently of the other 

 elements. The stress excited in any ele- 

 ment depends on the strain or other 

 displacement occurring in that element 

 alone; and the mechanical effect that is 

 transmitted is considered as an extraneous 

 force applied at one place in the medium, 

 and passed on from element to element 

 through these internal pressures and trac- 

 tions until it reaches another place. We 

 have, however, to consider two atomic elec- 

 tric charges as being themselves some kind 

 of strain configurations in the sether ; each 

 of them already involves an atmosphere of 



