220 OF FLOATATION AND THE SPECIFIC GRAVITY OF BODIES. 



This is the value of the first term under the radical sign, in the 

 expression for x equation (180), and the value of the second term, is 



27 8 



- = 145.8 ; 



therefore, by addition and evolution, we obtain 



a;=^/179.93 = 13.414 inches nearly. 



242. If the specific gravity of the ball, and that of the fluid in 

 which it is placed, be equal to one another, then equation (180) 

 becomes 



_ /32^ ^ 

 'V -W~ + n' 



and by reducing the fractions under the radical sign or vinculum to a 

 common denominator, we obtain 



a? = 



243. The practical method of reducing the above equation, is 

 expressed in words at full length in the following rule. 



RULE. Multiply the cube or third power of the- radius of 

 the sphere, by thirty two times the number which indicates 

 what part of the vessel is occupied by the fluid, and to the 

 product add three times the axis of the vessel drawn into the 

 square of its diameter ; then, divide the sum by three times 

 the square of the vessel's diameter, drawn into the number 

 which denotes what part of it the fluid occupies ; multiply 

 the quotient by the axis of the vessel, and extract the square 

 root of the product , for the height to which the fluid rises. 



244. EXAMPLE. Let the dimensions of the vessel and the immersed 

 body, remain as in the preceding example, the vessel containing also 

 the same quantity of fluid ; to what height on the axis will the fluid 

 ascend, supposing its specific gravity to be the same as that of the 

 immersed body ? 



Here, by operating as directed by the rule, we get 

 32wr 3 = 32X5X4X4X4 = 320X32 = 10240, and 



3b*d= 3X 18 X 18 X27 = 972 X27 = 26244 ; 

 consequently, the sum of the parenthetical terms is 



32r 3 4- 3b*d = 10240 + 26244 = 36484, 



and for the denominator of the fraction, we have 



36 7 w = 3X18X18X5 = 324X15 = 4860; 



