OP QH\\ 



penilicular* ore drawn on al 



art produced m a constant 



Uratgnt lines thus drawn equal particle* are placed: 



tniH' t/te crntr<- i/yrinVy f tin- 



tancc of t from u pcrnen- 



<r arc drawn from a fixed origin, and a the angle v. 

 listance makes wi* I Btraight line which coincides 



with one of the perpendiculars. Let n be the number of 



idea in th- polygon, and #- *" . Let p m denote the per- 



ir.m thf ori-in mi the m* side of the polygon; 

 Ucular from the assumed point 



is p m - c cos (mff a). Let r denote the constant ratio. 

 ... are the co-ordinates of the M" particle we 

 have 



r ;.- 



-a sn m + c sn a. 



ice proceeding as in Proposition MM. at the end of 



i. NM ..btain for the co-ordinates of the centre of 



cos a + ccos o, 

 jf-ij-^sin a-f csin o, 

 = p m cos m0, 17 = - /> sin m/9. 



4 Ft 



nee if r = 2 we have 



*-f, *; 



so that in tliis case the position of the centre of gravity is 

 the position of the assumed point 



proceed now to the analytical calculations. 



:i all the cases in which the Integral Calculus H 

 to ascertain the centre of gravity of a body the 



8 



