2iB Of the SOLIDS 



• X "T~ » ^? ~f~ X 



the fluent is 2 a L — ! ■ — , which, when x zz r. gives the 



a ° 



attraction of the femi-cylinder = 2flL- 



a 



This expreflion 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- 

 ven in magnitude, which fhall attract a particle fituated in 

 the centre of its bafe with the greateft force poflible, in the di- 

 rection of a line bifecting the bafe. 



The attraction of the cylinder, as jufl demonflrated, is 



r _|_Vr 2 +a 2 



2 a L — — j and becaufe the folid is fuppofed to be given 



a 



in magnitude, we may put a r 2 =m*, or a = — r ; fo that the formula 





2» 3 T r 4 2 m 3 T r 3 -fVr 6 -f- m 6 

 above becomes — — JL — s: —-5— 1-. —, . 



Now we may fuppofe m = 1, and then the attraction of the 



cylinder = — L (> 3 + W + 1). 



This 



