ATTRACTION. SI'Iir.KK '\L SHELL. 



Tak litre of gravity of ti. y as the 



origin of co-orilin. 1 t a, />, c be the co-<>r.linat 



;>artiele. I>ivi<le tin- at t ractin^ Ixxly into inde- 

 finitely small elements; let x, y, z be the n>-<nlinate.s of an 

 element. ;// its mass, and / I;-* li-tan-.- tVoin the attr. 

 ]).irticle. r riien tho attraction nf this clement i I by 



resolving it parallel to the co-ordinate axes, we obtain 



a x * b y r z 



mr . , mr . , mr . , 

 r r r 



respectively. Hence, if A", )', Z denote the resolved parts of 

 irhole attraction, we have 



But, since the origin is the centre of gravity of the attr;< 

 body, we have 



0, Smy = 0, mz = ; 

 therefore A' = a2m, Y=b~m, Z=cm. 



But these expressions are the resolved attractions of i m.iss 

 placed at the origin, which establishes the ion. 



221. To find the attraction of a homogeneous spherical sin 11 

 on a particle without it; the law of attraction lein-j represented 

 Inj <}> (i/) , ichere y is the distance. 



If we proceed as in Art. 211, we find the resultant attrac- 

 tion of the shell on P along PC 



Suppose 



and y^ t (y) dy = + (y). 



Then, integrating by parts, we have 



. (y) Jy 



