Pa 
Of GREATEST ATTRACTION. 205 
the quantity that is to be a maximum or a minimum, and the 
line bounding the figure is defined by the equation Q — A. 
Att the queftions, therefore, which come under this defcrip- 
tion, though they belong to an order of problems, which re- 
quires in general the application of one of the moft refined in- 
ventions of the New Geometry, the Calculus Variationum, form 
a particular divifion admitting of refolution by much fimpler 
means, and direétly reducible to the conftruion of loci. 
In thefe problems alfo, the fynthetical demonftration will be 
found extremely fimple. In the inftance of the folid of great- 
eft attraction this holds remarkably. Thus, it is obvious, that 
(Fig. 1.) any particle of matter placed without the curve 
ACBH, will attra the particle at A in the direction AB, lefs 
than any of the particles in that curve, and that any particle of 
matter within the curve, will attra@ the particle at A more 
than any particle in the curve, and more, d fortiori, than any 
particle without the curve. The fame is true of the whole 
fuperficies of the folid. Now, if the figure of the folid be 
any how changed, while its quantity of matter remains the 
fame, as much matter muft be expelled from within the fur- 
face, at fome one place C, as is accumulated without the fur- 
face at fome other point H. But the action of any quantity of 
matter within the fuperficies ACBH on A, is greater than the 
action of the fame without the fuperficies ACBH. The folid 
ACBH, therefore, by any change of its figure, muft lofe more 
attraction than it gains ; that is, its attraction is diminithed by 
every fuch change, and therefore it is itfelf the folid of great~ 
eft attraction. Q. E. D. 
Cec 2 XII. 
