512 On the Theory of the Magnetic Influence on Spectra. 



At a very great distance the electric force (as well as 

 the magnetic force) is thus perpendicular to r, and is equal 

 to — r~ l sin 9f(t — r/c); and the flow of energy is thus by 

 Poynting's principle radial. For the case of an ion e moving 

 with velocity v,f(t) is equal to ev; and in f(t — r/c) the value 

 of the function / belongs to the position of the molecule at a 

 time r/c previous, where r is its distance at that time. The 

 rate of loss of energy by radiation may be computed by 

 Poynting's formula as (4:7r) -1 times the product of the above 

 electric and magnetic forces integrated over an infinite sphere : 

 it is thus 



{±m'*c)- l {f \t -r/c)} 2 j sin 2 6 d$, or f^c-'u 2 . 



In the process of getting up a velocity v of the ion from rest, 

 there is a loss of energy equal to §0 2 g' -1 \v 2 dt. In motion 

 with uniform velocity there is no loss; during uniformly 

 accelerated motion the rate of loss is constant. 



As the electric and magnetic forces at a great distance are 

 each proportional to the acceleration of the ion and do not 

 involve its velocity, and as we can combine the components 

 of its motion in fixed directions, it follows generally that the 

 rate of loss of energy by radiation is §e 2 c -1 x (acceleration) 2 . 



The store of kinetic energy belonging to the ion is § e 2 a _1 u 2 . 

 Thus the loss of energy by radiation from an undisturbed 

 vibrating molecule would not be sensible compared with its 

 whole intrinsic kinetic energy, when the velocities of the ions 

 are not of the order of magnitude of that of radiation : while 

 for higher velocities the importance of the radiation is, in 

 part at any rate, counteracted by the increase of the inertia 

 coefficient. 



11. Finally, it is to be observed that the law of the mag- 

 netic vibration excited by a moving ion is stated in § 9 only 

 for the case in which r is small compared with the wave-length. 

 Further away from the ion the law of variation of the mag- 

 netic force with distance is ev/r* + ev/cr instead of evjr*. 

 Thus at a distance of a large number of wave-lengths, the 

 vibration-curve of the radiation proper is similar to the pro- 

 jection of the hodograph of the orbit of the ion on the wave- 

 front, instead of the projection of the orbit itself. 



It would thus appear that when the steady orbital motions in 

 a molecule are so constituted that the vector sum of the accele- 

 rations of all its ions or electrons is constantly null, there will 

 be no radiation, or very little, from it, and therefore this steady 

 motion will be permanent. But this is just the condition 

 which holds good so long as the molecule is free from 

 extraneous disturbance. 



St. John's College, Cambridge. 

 Nov. 8, 1897. 



