446 Mr. J. H. Jeans on the 



spectral lines. In addition to this, the actual periods of 

 vibration of the atom are altered by its velocity in space. It 

 has been shown by Lorentz that the effect of a uniform 

 velocity of translation (u, 0, 0) is to decrease the components 

 along the axis of x of all the electrical forces involved, in 

 the ratio 1 : (1 — ^ 2 /V 2 )^, where u is the total velocity of the 

 atom relatively to the asther. 



The result of this is that the spherical symmetry of the 

 atom is destroyed, and the lines in the spectrum which have 

 been supposed to be superposed and indistinguishable will 

 become separated. It is, however, easily verified that this 

 separation will be much too small to be capable of observation. 



The view which we have taken up compels us to suppose 

 that the linear dimensions, not only of atoms, but of complete 

 bodies, depends upon their orientation in space. It has 

 been pointed out by Lorentz"*, Larmor f, and Walker f, that 

 this supplies the only satisfactory explanation of Michelson's 

 aberration experiments. 



§ 34. The influence of the rotation of the atoms will, like 

 that of the translation, be two-fold. There is, first, a purely 

 kinematical effect, already discussed in § 2, and, second, a 

 dynamical effect, as follows : — 



We can allow for a rotation iv, by supposing a force 

 iv 2 r sin 6 to act per unit mass, perpendicular to the axes of 

 the atom. The effect of this, regarded as a steady force, will 

 be to produce a new equilibrium configuration, each element 

 being moved a slight distance from its old position. 



The vibrations will now be vibrations about this displaced 

 position of equilibrium, under the influence, partly of the 

 displacement-potential, and partly of the centrifugal force 

 which is supposed to act. 



The periodicities will therefore be slightly changed, and the 

 amount of change for every vibration will contain w 2 as a 

 factor. 



Remembering that w* varies from atom to atom, it appears 

 that the effect upon the spectrum of the whole gas, which is 

 produced by allowing for the rotation of the atoms, will be 

 to change each line into a band. The centre of the band will 

 not coincide with the original line ; the position of this line 

 will now be occupied by the extreme edge of the band, 

 corresponding to iy = 0, and since the probability of zero 

 rotation is nil for each atom, this line will be of zero 

 intensity. 



* Lorentz, Versuch einer fheorie ... p. 120. 

 t Adams Prize Essays, 1900. 



