Dispersion in Relation to the Electron Theory. 235 



diainagnetic polarization. I£ in addition the molecules 

 contain rotating masses of finite magnetic moment, a pre- 

 cessional motion will be set up in these, the extent and 

 duration of which will depend upon the disturbing effect of 

 collisions and therefore upon the temperature, but will be 

 capable of developing a mean paramagnetic polarity. It 

 may also be expected that the applied field may in many 

 cases produce a molecular distortion, which, reacting on the 

 vibrators, will influence their free-periods. 



Sir J. Larmor's treatment of the problem of magnetic 

 rotation * from the point of view of the first of the above 

 effects is based on general dynamical principles and gives a 

 result independent of the actual mechanism of dispersion. 

 The formula obtained, namely (in symmetrical units f ) 



?• e ^ dn ,.. 



is equivalent to the empirical formula of Becquerel, involves 

 no adjustable constants, and agrees with experiment in 

 giving rotations of the same sign on the two sides of an 

 absorption band. It involves the assumption that the 

 constant e/m is the same for all the resonators concerned. 

 If we take formula (2) for the dispersion we obtain 



dn h{\, /> 2 X 



— n ^ = 7^ — r -5w ~r 



dX (V — V) 2 (x 2 -V) : 

 Hence 



8=- 



2mC 2 nX, 2 



h{ h {^w)~ +b (w^' 



\ 



a summational formula of the same type as that obtained by 

 Drude. If we assume that the summation holds good in this 

 form with different values of e/m, we may write 



d ~ -2C 2 ^ 2 t^iU 2 -V/ m 2 \\*-\ 2 y + '" J w 



If the infra-red bands are attributed to vibrators of atomic 

 mass, the value of ejm for these is so small that the corre- 

 sponding term vanishes from the summation, and this very 

 completely in the visible and ultraviolet where the X factor 

 is very small also. If, however, any such band is due to a 

 comparatively small number of electrons, the term must be 

 retained. Also referring to equation (3) we see that ndnjdX 



* '^Ether and Matter; App. F. p. 352. 

 + See note infra. 



