MR. J. H. MICHELL ON THE THEORY OF FREE STREAM LINES. 
429 
Thus each singular point gives a factor 
n Tl [iv — iVq — 27nl — ink}^{w — Wq— 2ml — (2n + 1) 
— 00 — 00 
or, what is the same thing, 
@ \a (iv — H [a (w — 
where @, H are Jacobi’s functions so indicated, and, therefore, 
~^ = U{@[a {iv - H [a {lu - 
where 
al=^ 
2ak = K' 
K, K' being the complete elliptic integrals usually so denoted. 
If oio be the internal angle of the figure corresponding to iVq, we have, as before, 
M = 1 , 
IT 
so that, finally, 
^ = IT,. {®\a{w — [iv — 
(B) Suppose now that one conductor is outside the other, and that the potential at 
infinity is zero, that of the conductors being — k and k. We suppose equal and 
opposite quantities of electricity on the conductors, 2l being the cyclic constant, as 
before. 
The terms corresponding to angles of the polygon will be the same as in (A). 
But there is now in addition a singular point in the field which we proceed to 
determine. 
At a great distance from the prisms the potential will be the same as for two line 
distributions at the centres of mass, say at 2 = a, z = — a. 
So that 
ultimately, and 
= M loof 
— a 
^ z + a 
= - 2 
Ma 
dw 
dz 
= 2Ma2“^ = 
w~ 
2Ma 
or 
dz _ 2Ma 
dw ’ 
and, therefore, there is a point of order — 2 at the point in the w rectangle 
corresponding to the potential at infinity. 
