of greatest: attraction. i 99 



being on one fide of a plane, and the particle at a given di- 

 ftance from the fame plane on the oppofite fide. The mafs of 

 matter which is to compofe the folid being given, it is required 

 to conftrucT: the folid. 



Let the particle to be attracted be at A (Fig. 3.), from A draw 

 AA' perpendicular to the given plane, and let EF be any ftraight 

 line in that plane, drawn through the point A' ; it is evident 

 that the axis of the folid required mull be in A A' produced. 

 Let B be the vertex of the folid, then it will be demonftrated 

 as has been done above, that this folid is generated by the re- 

 volution of the curve of equal attraction, (that of which 



the equation is y % zz a 3 x 3 — x 2 ), about the axis of which one 



extremity is at A, and of which the length muft be found from 

 the quantity of matter in the folid. 



The folid required, then, is a fegment of the folid of great- 

 eft attraction, having B for its vertex, and a circle, of which 

 A' E or A' F is the radius, for its bafe. 



To find the folid content of fuch a fegment, CD being zzy, 



and AC = x, we have y % zz a 3 x 3 — # 2 , and *y % x — na^x 3 x — 



* x z x — the cylinder which is the element of the folid feg- 

 ment. 



Therefore Jny 2 x, or the folid fegment intercepted be- 



2 — s 1 

 tween B and D muft be^srtf 3 * 3 — -*A; 3 -f-C. This muft 



5 3 



vanifh when x = a, or when C comes to B, and therefore C = 



It 3 

 — • z — a . 



J 5 



