302 Mr. Knight on the Attraction of such Solids 
APPENDIX TO §. III. 
Of the Attraction of an infinitely long Prism, whose Base is any 
right lined Figure whatever. 
Prop. A. 
Let the rectangle bb' c'c, fig. 20, be the section or base of 
a prism, infinitely extended on both sides of it, and let the line 
psu bisect the opposite sides bb', cc' of the rectangle. 
It is required to find the attraction of the infinitely long 
solid, on the point p, in the direction psu. 
Let C be the centre of the rectangle, put k = sC, a — bs, 
u — pC ; draw rm perpendicular to .sCu, and put x = Cm. 
Now it appears, from Cor. 2, Prop. 1 of the paper (putting A 
for the required attraction ) that 
A = 4/pm x arc (tang. = ^) = 4/* arc 
= 4,x arc (tang. = -—Oj - 4/* 333 (tang. = ^ ) the last 
term of which is 4 - ; put u -f- x == z, x = z, x = % 
— u, and it becomes 4 which is q/zL. (a* + £ 2 )£ 
— 4 u arc (tang. = -jJ so that 
A = yx arc (tang. — — 4 u arc (tang. = + ^aL . 
(T-h ( a -j- x) s )Z, or A = 4 (x + u) arc (tang. = — 
2 u 7r -j— 41? L . (a — p (zz -j- x ) ) 2 , 
which fluent being taken from x = — k to x = k gives 
A — 4 (zz + A’) arc (tang. = — 4 (zz — k) arc (tang. = 
j—j) "h ~b ( u Hr k')% — 4«L . ( a*-p (zz — t)L 
