202 Of the SOLIDS 



This equation alio belongs to a curve of equal attraction; 

 the plane in which that curve is being parallel to AB, the line 

 in which the attraction is eftimated, and dirtant from it by the 

 fpace b. 



Instead of reckoning the abfcifla from K, it may be made 

 to begin at C. If AL or CK = b, then the value of b is deter- 



mined from the equation b % — a 3 b 3 — b% and if x = b -J- u, u 



being put for CF, v = £ {h -f »)f — (b -f- u) z — J b% + //, or 



w* + (A + »)' + A* = « T (b + uy, or (V-f- (£ + *)* + £ 2 ) 3 = 

 a' (b + u)\ 



When b is equal to the maximum value of the ordinate EH, 

 (iv. 2.) the curve CGD goes away into a point ; and if b be fiip- 

 pofed greater than this, the equation to the curve is impoffible. 



X. 



The folid of greater!; attraction may be found, and its pro- 

 perties inveftigated, in the way that has now been exemplified, 

 whatever be the law of the attracting force. It will be fuffi- 

 cient, in any cafe, to find the equation of the generating curve, 

 or the curve of equal attraction. 



Thus, if the attraction which the particle C (Fig. I.) exerts on 

 the given particle at A, be inverfely as the m power of the di- 



ftance, or as -r-^, then the attraction in the direction AE 



Ad'" 



AF t AF 

 will be -7- , and if we make this = -, we have 3- 



m -+- 1 t 111' in •+• r 



AG AB AG 



1 



— m> 



AB 



