/ 
Of GREATEST ATTRACTION. 203 
: ., or making AE =x, EC=y, and AB=g, as before, 
m+ 
== = or a"x= (x+y) 7, and x+y = 
ey he Ted 
qret KP+ts or y* — ae ari xt, 
Ir m=1, or m+ 1=2, this equation becomes y* = a x — x’, 
being that of a circle of which the diameter is AB. If, 
therefore, the attracting force were inverfely as the diftance, the 
folid of greateft attraction would be a fphere. 
Ir the force be inverfely as the cube of the diftance, or 
= Ba a) ? 
m = 3, and m-+- 1= 4, the equation is y* = a? x* — x’, which 
‘ belongs to a line of the 4th order. 
oO 
2 
Ir m= 4, and m+ 1 = 5, the equation is y*=a* x* — x’; 
which belongs to a line of the roth order. 
In general, if m be an even number, the order of the curve 
is m-+1 X23; but if m be an odd number, it is m + 1x fimply. 
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 leaft 
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. ; 
Vou. VI.—P. IL. © 10-09 CE Ler 
