1895.] of the Electric and Luminiferous Medium. 227 



without intrinsic inertia, in a rotationally elastic fluid sether, is 

 entertained, the null result of the Michelson-Morley second-order 

 experiment on the effect of the Earth's motion on the velocity of light 

 becomes included in the theory ; in fact, according to a suggestion 

 thrown out by FitzGerald and Lorentz, and developed somewhat in 

 this manner by the latter, the second-order optical effect is just com- 

 pensated by a second-order effect on the lengths of the moving arms 

 of Michelson's apparatus, which is produced by its motion along with 

 the Earth th rough the aether. 



As mixed dynamical and statistical theories of electrons or other 

 objects require delicate treatment, especially when pushed, as here, to 

 the second order of small quantities, the formulae of this part of the 

 paper are deduced independently by two very different analytical 

 methods. In the first place, there is the usual process of extending 

 the fundamental circuital relations of the free ffither which express its 

 dynamical relations as differential equations of the first order, by 

 suitable modification of the significance of the vectors involved in 

 them, so that the same equations shall apply to ponderable media as 

 well, the vectors then representing averages taken over the element 

 of volume. The other method consists in working out the dynamics 

 of a single electron, and applying the results statistically to the 

 inclusion of the various ways in which the electric current arises 

 from the movements of the electrons in ponderable media. 



The theory as thus developed from the electron as the fundamental 

 element, may be stated in a form which is independent of the 

 dynamical hypothesis of a rotational aether. Maxwell's formal equa- 

 tions of the electric field may take the place of that hypothesis, 

 though it may, I think, be contended that an abstract procedure of 

 that kind will neither be so simple nor so graphic, nor lend itself so 

 easily to the intuitive grasp of relations, as a more concrete one of 

 the type here employed. 



The exact permanence of the wave-lengths in spectra, under various 

 physical conditions, may be ascribed to the influence of radiation ou 

 the molecule, which keeps it in, or very close to, a constant condition 

 of steady motion, of minimum total energy corresponding to its pre- 

 determined constant momenta. It is also pointed oat, from the 

 analogy of physical astronomy, that the harmonic oscillations into 

 which the spectroscope divides the radiation from a molecule, may 

 be far more numerous than the co-ordinates which specify its relative 

 motions ; that, therefore, relations of a semi-dynamical character may 

 be discovered among the spectral lines, without its being rendered 

 likely that we can ever penetrate from them back to the actual con- 

 figuration of the molecular system. 



Reverting finally to matters relating purely to a rotational tether 

 theory, with electrons as the sole foundation for matter, it is possible to 



