ipo Of the SOLIDS 



will be no variation produced in the force which the folid exerts 

 on the particle A, in the direction AB. 



The curve ACB, therefore, is the locus of all the points in 

 whjch a body being placed, will attract; the particle A in the 

 direction AB, with the fame force. 



This condition is fufficient to determine the nature of the 

 curve ABC. From C, any point in that curve, draw CE per- 

 pendicular to AB ', then if a- mafs of matter placed at C be call- 



edw 3 , -TTTz will be the attraction of that mafs on A, in the di- 



m* X AE • • 



rection AC, and — ^-^ — will be its attraction in the direction 



711 ' 



AB. As this is conflant, it will be equal to 7^7, and therefore. 



AB J xAE = AC 3 . 



All the lections of the required folid, therefore, by planes 

 paffing through AB, have this property, that AC 3 =AB 2 xAE ; 

 and as this equation is fufficient to determine the nature of the 

 curve to which it belongs, therefore all the fections of the fo- 

 lid, by planes that pafs through AB, are fimilar and equal 

 curves \ and the folid of confequence may be conceived to be 

 generated by the revolution of ACB, any one of thefe curves, 

 about AB as an axis. 



The folid fo generated may be called the Solid of great eft 

 Attraction j and the line ACB, the Curve of equal Attraftion. 



II. 



To find the equation between the co-ordinates of ACB, the 

 curve of equal attraction. 



From 



