M i:vl 1'BOI'ERTlEf. 1 V.i 



''-I* be acted an by a number ' 



*iny through a fixed j* . proportional to // 



m th'i( ix'int, t/ lt n-stiltnnt /,* "-ill y<,/ v thr--i-j', //."/ 



' <i w/ fc proportional to the distance from that j> 



Take any position of the particle as the origin; let 

 be the co-ordinatca of a fixed point ; r, the distance 



M which acts on 

 3 niilarly / * f , 



i<3 co-ordinates of a second ti\<-<! ]...int; /_ i:> : -tancc 

 . tin* corresponding force on the 



parti so on. Lei whole force 



along the axes of or, y, *; then, by 







Similarly 1" - /AJT, + /Ajf t 4 

 and *-** 



Let o-nnlinatcs of the centre of gr:i 



of a system of particles, whose masses are proportion 



/ z i . ^ ....... placed at the respective fixed points ; t 



tore JT-^./. )' =>/?.?, Z~'~ 



These equations shew that the resultant force is equal to 



the distance of the centre of gravity from 



i. and that its din ct ion passes through tre of 



i the particle is situated at tre of 



gravity the resultant force vanishes and the particle is in 



equilibrium. 



placed on a horizontal plane, to find tchcn 

 ill be supported. 



ly force acting on it besides the resistance of the 

 t* own weight, and this act) in A v. rtical dir* 

 ;.;h the centre of gravity of the body. Hence, by 



