232 OUTLINES OF NATURAL PHILOSOPHY. 



twice the area ABED is equal to the square of 

 the velocity at B, ( 100. vol. i.). Let this velo- 

 city = 0; having bisected AC in G, let the velo- 

 city in G be == c. Draw the perpendicular b e 

 indefinitely near to BE. Then t>* : c* : : 



2 ABED, therefore 2 ABED = c* X ~, or 



since AB=AC CB, 2ABED=c*X 



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= c *r^P i\ 



VBQ j 





xAC \ 

 For the, same reason, 2 A e D=e* X ( 1 ), 



and therefore the area 2 B & * E=c* ( - 



wherefore, 2 B 6 X BE = c , and 



dividing by B *, 9 BE = c X =c X . 



AG 



therefore, BE sr c* X . But BE represents 



the centripetal force at B any point in the line 

 AC, and both c and AG are given, therefore the 

 centripetal force at B is inversely as the square 

 of BC, the distance from the centre of force. 



Therefore, 



