G22 ItEPORT— 1900. 



the effective a(3aptatiou of abstract dynamics to such systems WeIs made iilde" 

 pendently by Kelvin and Routh about 1877 ; the more recent exposition of the 

 theory by Ilelmholtz has directed general attention to "what is undoubtedly the 

 most significant extension of dynamical analysis which has taken place since the 

 time of Lagrange. 



Returning to the molecules, it is now verified that the Action principle forms a 

 valid foundation throughout electrodynamics and optics ; the introduction of the 

 fether into the system has not a&ected its application. It is therefore a reasonable 

 hypothesis that the principle forms an allowable foundation for the dynamical 

 analysis of the radiant vibrations in the system formed by a single molecule and 

 surrounding 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 limited 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 generalised Maxwell-Boltzmann 

 principle 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 dynamics. In the demonstrations 

 usually offered the molecule is considered to have no permanent or constitutive 

 energy of internal motion. It can, however, be shown, by use of the generalisa- 

 tion aforesaid of the Action principle, that no discrepancy will arise on that 

 account. Such intrinsic kinetic energy virtually adds on to the potential energy of 

 the system ; and the remaining or acquired part of the kinetic energy of the 

 molecule may be made the subject of the same train of reasoning as before. 



Let us now return to the general question whether our definition of a dyna- 

 mical system may not be too wide. As a case in point, the single principle of 

 Action has been shown to provide a definite and sufficient basis for electro- 

 dynamics ; yet when, for example, one armature of an electric motor pulls the 

 other after it without material contact, and so transmits mechanical power, 

 no connection between them is indicated 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 

 element depends on the strain or other displacement occurring in that element 

 alone ; and the mechanical efi'ect 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 tractions until it reaches another place. We 

 have, however, to consider two atomic electric charges as being themselves some 

 kind of strain configurations in the tether ; each of them already involves an 

 atmosphere of strain in the surrounding sether which is part of its essence, and 

 cannot be considered apart from it ; each of them essentially pervades the entire 

 space, though on account of its invariable character we consider it as a unit. 

 Thus we appear to be debarred from imagining the sether to act as an elastic 

 connection which is merely the agent of transmission of a pull from the one 

 nucleus to the other, because there are already stresses belonging to and consti- 

 tuting an intrinsic part of the terminal electrons, which are distributed all along the 

 medium. Our Action criterion of a dynamical system, in fact, allows us to reason 

 about an electron as a single thing, notwithstanding that its field of energy is 

 spread over the whole medium ; it is only in material solid bodies, and in problems 

 in which the actual sphere of physical action of the molecule is small compared 

 with the smallest element of volume that our analysis considers, that the familiar 

 idea of transmission of force by simple stress can apply. Whatever view may 



