2^0 Mi\ Knight on the Attractions of such Solids 
Put 2’= ~ -f T*, whence T % = z % TT " zz\ by 
substituting these values we get 
A =/ 
a rz 
& I «*- ^ -<**+*’ 
— (because / 3 s — 1 — r ‘) /* ■ - 
which, if we multiply both numerator and denominator by 
B . 
becomes f 
(S a 
I + «* 
a z r x 
= arc (tang. = ~ z), and, by putting 
for z and /B their values, we have at last 
*A = arc (tang. = fs / 1 -f ^ 6 9 ) — arc (tang. = -]. 
In like manner, a first integration of B gives 
B =/ 
rT z t 
: = r 
i-\-r*)T % )* v' 1 4- r 2, fa 1 
rT'T 
Vi+r\f | /_£ 1_ 
_T a L T 1 
I+f ,+ r*)* (^+^>(7—,+ ^)"] 
Put T~ a tang. then T = a sect. Vir, a 1 4- r 1 = a* sect, 
•w ; by this means the last term under the sign of the fluent 
is changed to w — ^ ,+r 
{jk ? + ,ang ' 4 
r sin. zs 
( I -f r l sin. a w)i 
T 
wherefore, observing that tang. ©■ = ~, and consequently 
Sill. 75 
i , we find at last 
* This quantity can be put under another form, which may be better in some cases. 
b‘ 
If we denote by b 1 the side rv of the triangle, r “ and 
» b ^ a 1 +b x -\-b‘ l \ b \ 
A = arc (tang. --- I — arc (tang. — — h 
a 
