OF FLOATATION AND THE SPECIFIC GRAVITY OF BODIES. 219 



and again, if all the terms be divided by p the parameter of the 

 parabola, and the square root be extracted from both sides of the 

 equation, we shall have 



But because the parameter of a parabola is a third proportional to 

 any abscissa and its ordinate ; it follows, that if b denote the base A B 

 of the paraboloid, of which the axis is d, we shall have 



let this value of the parameter be substituted instead of it in the above 

 equation, and we shall obtain 



(180). 



240. The following practical rule supplied by this equation, will 

 serve to direct the reader to the method of its reduction. 



RULE. Multiply thirty -two times the axis of the paraboloid, 

 by the cube or third power of the radius of the sphere drawn 

 into its specific gravity ; then, divide the product by three 

 times the square of the base of the vessel multiplied by the 

 specific gravity of the Jluid, and to the quotient, add the 

 square of the axis or depth of the vessel, divided by the 

 number, which expresses what part of it is occupied by the 

 Jluid ; then, the square root of the sum, will give the height 

 to which the Jluid rises after the immersion of the spheric 

 segment. 



241. EXAMPLE. The axis of a vessel in the form of a paraboloid is 

 27 inches, and the diameter of its mouth is 18 inches ; now, supposing 

 that the vessel is one fifth full of water, into which is dropped a sphere 

 of hazel whose diameter is 8 inches ; to what point of the axis will 

 the fluid ascend, the specific gravity of hazel being 0.6, when that of 

 water is expressed by unity ? 



By proceeding according to the rule, we get 



32X27X4X4X4X.6 = 33177.6, the dividend, 



and in like manner, for the divisor, we have 



3X18X18X1 = 972, the divisor ; 

 consequently, by division, we obtain 



