218 Of th SOLIDS 
: xtNa+tx ‘ : 
the fluent is 24a L apres which, when x =7, gives the 
attraction of the femi-cylinder = 24 oe Ee 
Tuis expreffion is very fimple, and very convenient in cal- 
culation. It is probably needlefs to remark, that the loga- 
rithms meant are the hyperbolic. 
XVI. 
Let it be required to find the figure of a femi-cylinder gi- 
yen in magnitude, which fhall attrac a particle fituated in 
the centre of its bafe with the greateft force poflible, in the di- 
rection of a line bifeting the bafe. i 
Tue attraction of the cylinder, as juft demonftrated, is 
2aL someidh a 3 and haa the folid is fuppofed to be given 
; m3 is 
in magnitude, we may put 47°=m°>, ora= —— 5 fo that the formula 
m° 
r vr = 
2m? ‘i aN 2m3_ ri tNnret me 
above becomes —, ag bs ee 
7a 
Now we may fuppofe m=1, and then the attraction of the 
posi ie he 
cylinder = = L(r3+N7° +1). 
TuHIs 
