80 Mr GreenliiH, On Conjugate Functions [Mar. 21, 



As explained in Maxwell's Electricity, chapter XII., f and 77 

 may be taken to denote equipotential cylindrical surfaces and lines 



of force, and then J~* will represent the electrification at any 

 point. 



Thus a cylinder whose cross section is a Cartesian will if elec- 

 trified have a superficial density inversely proportional to the 

 square root of the product of the distances from the three foci; the 

 law for confocal conies being a particular case of this. 



3. The theory of quartics with four collinear foci A, B, C, D 

 may be considered as derived from the integral 



ch 



\j(z — a. z - b .2 — c.z — d)' 



and putting this 



2u 



*J(a — c.b — d)' 



then, using a notation employed by Clifford (Proceedings of the 

 London Mathematical Society, Vol. VII. p. 29), 



— a b — d 



sn ' t— •, 7 



2 — a — a 



_. z—d a—b 

 — en A / T ; 



V z-b a-d 



V 2-b a-c' 



where 



