Of GREATEST ATTRACTION. 203 



1 



, or making AE = x, EG = y, and AB zz a, as before, 

 AB M 



* 1^= -£ or *"* = «+/) S f t , and x % -f f = 



^^T+T #« + 1 , or y 1 zz a ™+i x m +~ l — x\ 



If «=i, or»i+iz:2, this equation becomes y 1 zz a x — a?% 

 being that of a circle of which the diameter is AB. If, 

 therefore, the attracting force were inverfely as the diffcance, the 

 folid of greateft attraction would be a fphere. 



If the force be inverfely as the cube of the diftance, or 



m zz 3, and z» -f- 1 = 4, the equation is y 1 zz a 2 at * — a? a , which 

 belongs to a line of the 4th order- 



If mzz 4, and m + 1 — 5> the equation is y = « y * J — x* , 



which belongs to a line of the 10th order. 



In general, if m be an even number, the order of the curve 



is »z + iX2j but if m be an odd number, it is m -f r limply. 



XI. 



In the fame manner that the folid of greateft attraction has 

 been found, may a great class of fimilar problems be refolved. 

 Whenever the property that is to exift in its greateft or leafh 

 degree, belongs to all the points of a plane figure, or to all the 

 points of a folid, given in magnitude, the queftion is reduced to 

 the determination of the locus of a certain equation, juft as in 

 the preceding example. 



Vol.VI.—P.II. Ce Let 



