286 Theorems and Problems 
Sotution. Put d= the diameter of the 
sphere and height of the cube; j=314159, Ke; 
also let F, f, R and r denote the quantities, 
which they represent in theor. 2. Then the 
masses of the cube and sphere are as d? to 
= or as 6 toj; therefore as Fi: f'::6: 7, 
by theor. 1; but as F:'f:: Rs 7, by ax. 4. 
hence as 6:7:: R:r; ‘but R is as nd, the 
matter removed by the cube; therefore as. 
6 Ht YY n d*: int = the matter removed by 
the sphere. Now if J ae be less than? 2 or 
“half the sphere, the depression made by the 
globe is a segment less than a hemisphere, the 
perpendicular height of which is =; ; but if 
jn 4* be greater than ie that is, if m be 
6 
greater than Ly the depression made by the 
globe is a cylindrical pit, having a hemispheri- 
cal bottom, the perpendicular height of which 
is $21". Q EL. 
Prositem UI. Lect AOB and aob, 
(plate 4, fig. 5.) be two levers, revolving 
with the angular velocities C and ¢ about the 
‘points O and o; and let two material points, 
whose masses are B and b revolve with the 
levers; these things being supposed, let two 
forces F’and f act for an instant at the points A 
