as are terminated by Planes , &c. 
and, if we put zz = x, the last term becomes 
— 2 nfz 2 arc ( tang. = -^ ( 1 r*) 
2 n f - — = r = =r. — = 2 n 
•2 n 
V zk ( i -f r 2 ) — r 2 
[ — arc (sine : 
z“z 
rz 
V zk (i + r0 
or by putting its value for 
znk (i -fr 1 ) 
^ r z 
- i * v/SS3 
rV) 
this fluent is 
/ . rV' .r \ -r L ) 
arc ( sine = -===- — n k/ — L ~ — - j; — a:*. 
' v^2k (i + r 2 )/ r 
Collecting all the parts of A, we have at length 
A == 2 nx arc (tang. = — s/ zk (i + ?*) x — — • 
rx 
znk (i-J-r 3 ') 
arc (sine 
-V' 
V zk ( i 4 - r 1 ) 
s/ zk ( i -f- r a ) x — r s x 2 -J- 
(rc — 2) ttx -f- corr. 
But it is easy to see that each of the arcs in this expression is 
the complement of the other ; put then A = arc (tang. = — 
s/ zk ( 1 ~j-r 2 ) x — fx 1 ) and the expression becomes 
A= 4" n {k—x) } (tt — 2A) zxtt — nx . tang. A -|- corn 
When x — 0, A = so that, if the fluent is to begin when 
X = 0, no correction is necessary. 
(n — 2) tt 
When x — zk, A == arc (tang. = ■—) = and 
zk ( 1 -4- ) x — r 2 x 2 = zk, 7r — - 2 A = 7 r — — — • 
' 1 ' n n p 
whence we have for /Vz<? attraction of the whole solid 
znk 
r 
(«)• 
This will appear to be an expression of great simplicity, if we 
reflect what very different solids it belongs to, from that whose 
section is a triangle, to the sphere whose section is a circle. 
N n a 
