ATTRACTION OF BODIES. 



267 



of Ee/F is proportional to its surface multiplied by F/, and 

 the angle D E r being equal to D P E (because P E r is a right 



angle by the property of the circle), therefore E r = =--r; , 



JJ Jjj 



and if we callPE,or PF = r, ED = y, and DF = x, Drfwill 



V U X 



be d x, and E r = ; and the ring generated by the revo- 



%j 



lution of r E is equal to r E x E D, or r E x y ; therefore this 

 ring is equal to re? a?, or the attraction proportional to the 

 whole ring Ee will be proportional to the sum of all the 

 rectangles P D x D d, or (a #) d x ; that is, to the integral 



2 (L T* - _ <>" 



of this quantity, or to ; which by the property of 



2 



V a 

 the circle is equal to -. Therefore the attraction of the 



t 



solid E e/F will be as y* x F/, if the force of a particle F/ 



Kg .16. 



on P be given ; if not, it will be as y* x F/ x / that force. 



PS v dx 

 Now d x : F/ :: r : P S, and therefore F/ = - , and the 



attraction of E e/F is as 



; or taking / = r 



(as any power of the distance PE), then the attraction of 

 Ee/F is as PS . r*~ l y*dx. Take DN ( = u) equal to 



