OF WHICH IS MOVING ROTATIONALLY AND PART IRROTATIONALLY. 409 
Therefore the potential at the internal point x, y is 
c o — b , cab 
-- - -xy-\-— < 
2 a + b J 2 
• —] Ct> • —I 
sin 1 -.— — sm 1 - 
2 , o 
s/ +y 
9 1 
x y 
Thus if the density at the point x, y inside the elliptic cylinder - + 
a? ' b 
_c_( 1 1\ 
"4?rV& 3 W {*>£? 
W & 
then the potential at an internal point is 
c co —b cab 
2 '^Ti xy+ Y 
sm 
x 
—l a 
A A ?+t 
V a? + V 
sin 1 
y/x^+y* 
and the potential at an external point is 
cab / a 2 + 5 2 + 2e 
J-b ~ XlJ \VV + e)(6 2 + e)' 
0+ 2 i sm 
'— Sill 
v 7 x 1 + y i 
where 
J?L + J!L = i 
a 2 + e ' 5 3 + e 
3 a 
,= 1 be 
MDCCCLXXXIV. 
