OF FLUID PRESSURE ON CIRCULAR PLANES AND ON SPHERES. 91 



Put D zz AB, the diameter of the greater sphere ABD, 



d n= ab, the diameter of the lesser sphere abd, 

 '|D = AC, the radius of the greater sphere, or the perpendicular 



depth of its centre of gravity, 

 \d zz a c, the radius of the lesser sphere, or the perpendicular 



depth of its centre of gravity, 

 S zz the surface of the greater sphere ABD, 

 P z= the pressure perpendicular to its surface, 

 >S = the surface of the lesser sphere a b d, 

 p the pressure perpendicular to its surface, 



and TT nr 3.1416, the circumference of a circle whose diameter is 

 expressed by unity. 



Then, according to the principles of mensuration, the surface of a 

 sphere or globe 



Is equal to four times the area of one of its great circles, 

 or that whose plane passes through the centre of the sphere. 



Consequently, the convex surface of the greater sphere ABD, is 

 expressed as follows. 



and that of the lesser sphere abd, is 



S =: 3.1416 eP. 



But the pressure perpendicular to any surface, is equal to the area 

 of that surface multiplied by the perpendicular depth of the centre of 

 gravity, and again by the specific gravity of the fluid ; consequently, 

 when the specific gravity of the fluid is denoted by unity, we have for 

 the pressure on the surface of the greater sphere, 



P=r3.1416D a X iD=1.5708D 8 . (50). 



and for the pressure on the lesser sphere, it is 



hence, by comparison, we shall have 



P : p : : D 3 : d 3 . 



Consequently, if two spheres of different diameters be placed in a 

 fluid under similar circumstances, the pressures perpendicular to their 

 surfaces, are to one another as the cubes of their diameters. 



By the principles of mensuration, the solid content of a sphere or 

 globe, is equal to the cube of the diameter multiplied by the constant 

 number .5236 ; therefore, if c denote the solid content, we have 



cin.5236D 3 , 



