107, 108] ATTRACTION OF ELLIPSOIDS. 205 



In like manner 



2 dq dy 2 \dy> dq 2 ' 

 dq dz 2 \dz) dq 2 ' 



Accordingly 



^F 



d 



dq 



Now since F is a function of q only, the expression on the right 

 must be a function of q only, say </> (q). Consequently, that 



may represent a set of equipotential surfaces, the parameter q must 

 be such that the ratio of its second to the square of its first differ- 

 ential parameter is a function only of q, 



If this is satisfied, we have 



d , dV 



dq 



There must be one value q such that the level surface is a sphere 

 of infinite radius, and for this V must vanish. 



