Co'NW AY— T/ie DijnamicB of a Rigid Electron. 



181 



As an example, consider the case of a sphere which moves about a centre 

 of force under the law of nature, there being no rotation. We have 



mi- + JcitStt + l\T . T^ = - cr . T'h. 



We get at once the vis viva equation 



mr- + i (/h + h) t' = - 2cT-\, 



so that approximately 



mf- = - 2c . T-'t - 2c-m-' (k, + h) T-h, 



so that the motion is the same as if, in addition to the original force, we 

 had a force varying inversely as the cube of the distance ; and the effect of 

 such a force is, as is well known, to cause a motion of rotation of the orbit 

 if this is one plane. If we put Vrf = hy, where Ty = 1, we find 



d 



so that y is fixed and 



on -^ 1 % ) + kJiySTT = 0, 



-|-fl0g/2.U- ^ Sir. 

 df \ ^ m 



Hence the average value of h is zero, and the motion takes place in one 

 plane. 



R.I.A. PRon., VOL. XXVII., SECT. A. 



[26] 



