Conway — The Dynamics 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 



We get at once the vis viva equation 



mr- + 1 (h + h) r' = - 2cT-W, 

 so that approximately 



onr^- = - 2c . T-W - 2chn-' {k, + h) ^'"r, 



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 



m -J- I /iy I + kJlySi-T = 0, 

 so that y is fixed and 



^- I log /?• ) = - — Stt. 



dt \ ^ J 111 



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

 plane. 



K.I.A. PEOC, VOL. XXVII., SECT. A. [26] 



