216 OF FLOATATION AND THE SPECIFIC GRAVITY OF BODIES. 



235. Either of these equations will resolve the problem, but the 

 latter form is the most convenient for a verbal enunciation, and the 

 practical rule which it supplies is as follows. 



RULE. Multiply sixteen times the specific gravity of the 

 sphere, by the cube or third power of its radius ; then, divide 

 the product by three times the specific gravity of the fluid, 

 drawn into the square of the cylinder's diameter, and the 

 quotient will give the increase of height, in consequence of the 

 immersion of the spheric segment. 



236. EXAMPLE. A cylindrical vessel whose diameter is 8 inches, is 

 filled with water to the height of 10 inches; how much higher will 

 the water rise, and what will be its whole weight, when a globe of 

 alder of 6 inches diameter is dropped into the vessel ; the specific 

 gravity of alder being equal to .8, when that of water is expressed by 

 unity ? 



Here, by operating according to the above rule, we get 



16rV=16x3x3x3x. 8 z= 345.6, 



and in like manner we have 



33^ = 3x8x8x1 192; 



consequently, by division, we obtain 



ar'zr - z= z= 1.8 inches, and the whole height is 11.8 inches. 



v oo s ly.2 



237. If the specific gravity of the globe, and that of the fluid in which 

 it is placed, are equal to one another, then equation (178) becomes 



, 33* ' (179). 



In this case it is manifest, that the sphere is wholly immersed in 

 the fluid ; consequently, the increase of height wilt be equal to the 

 altitude of a cylinder, whose diameter is 3, and whose capacity is 

 equal to that of the immersed body ; hence, the method of computa- 

 tion is obvious ; but the practical rule deduced from the equation for 

 this purpose, may be expressed in the following manner. 



RULE. Divide sixteen times the cube or third power of the 

 radius of the sphere, by three times the square of the cylin- 

 der s diameter, and the quotient will give the increased height 

 of the fluid. 



238. EXAMPLE. A cylindrical vessel whose diameter is 12 inches, 

 is filled with fluid to the height of 6 inches; to what height will 



