607] 
A MEMOIR ON PREPOTENTIALS. 
325 
explanation. Taking cos a, .., cos y to be the inclinations of the normal at N, in the 
direction NP in which the distance « is measured, to the positive parts of the axes 
of (x, .., z), viz. these cosines denote the values of 
dS dS 
dx ’ '' ’ dz ’ 
each taken with the same sign + or —, and divided by the square root of the sum 
of the squares of the last-mentioned quantities, then the meaning is 
dW _dW 
ds dx 
dW 
cos a + ... + cos 7. 
7. The surface S may be the plane w = 0, viz. we have then the prepotential- 
where e (like «) is positive. In afterwards writing e = 0, we mean by 0 the limit of 
an indefinitely small positive quantity. 
The foregoing distribution-formulae then become 
(A), 
and 
which will be used in the sequel. 
It will be remembered that in the preceding investigation it has been assumed 
that q is positive, the limiting case q = 0 being excludedf. 
q = — Art. Nos. 8 to 13. 
8. I pass to the case q = — 2, we here have the potential-surface integral 
it will be seen that the results present themselves under a remarkably different form. 
The potential of the disk is, as before, 
2 (T^) s f P* 1 dr 
^ J (r 2 + ’ 
f This is, as regards q, the case throughout; a limiting value, if not expressly stated to be included, is 
always excluded.