402 Sir J. J. Thomson on the Scattering oj 



suppose that when the force X cos qt acts on the electron 

 x and y are still represented by equations of this type, 

 but that the parameters are variable and are functions 



of the time which it is our object to determine. If ^~ 



ot 



denotes differentiation with regard to the time onty so far 



as the time enters into these parameters, and if we take 



the more general case where the electron is acted on by 



disturbing forces X', Y' parallel to the axes of x and y 



respectively, we have by the principle of Instantaneous 



Orbits 



*? = o ^ = o 



where #' = -=-, y=-^, the parameters being considered 



constant for these differentiations ; the mass of the electron 

 has been taken as unity. From the equation 'dx/'dt = 

 we get 



0—-rr cos<£ — -j- a sin (j)---j(ae). {k 1 cos-v/r — k 2 cos %} 



— ae-j~ {hi sin t]t — & 2 sin %). 



In the coefficient of de/dt terms which are small compared 

 with <xsin(/> have been omitted. 



From ^ = we get 

 ot 



r, da • , de d . . , . . _ . . 



u= t $m<p + a cos 9 . — + -r;{ae)(ki sin y-f-A^ sin %) 



— ae-j- (k] cos Y -f k 2 cos y). 



From |^ = Y'. 

 dt 



dt 



v , da f J??,~ x , . 6?6 



Y= *i" +a ^| cos *- a ' ism *^ 



+ -, (a* )((/; — l)n£x cos -v/r + (p + 1)t?& 2 cos %) 

 + ae ^ ( (P — 1) ? ^'i sin if 1 + } + 1) n ^2 sm %)• 



