VHlVERSiTY 



MISCELLANEOUS HYDROSTATIC QUESTIONS, WITH THEIR SOLUTIONS. 445 



Mr. Dalby makes the side of the cube equal to 13| inches, and the 

 specific gravity 772 ; but this only shows that he has employed a 

 higher number for the specific gravity of sea water; 1030 brings out 

 his results. 



573. QUESTION 4. How deep will a globe of oak sink in fresh 

 water, the diameter being 12 inches and the specific gravity 925, that 

 of water being 1000? 



By the rules for the mensuration of solids, the solidity of the globe 

 is expressed by the cube of its diameter multiplied by the decimal 

 .5236 ; consequently, we have 1728 X .5236 = 904.7808 cubic inches 

 for the solidity of the globe; therefore, according to art. 311, page 

 257, we get 



1000 : 925 : : 904.7808 : 836.923 cubic inches, the solidity of the 

 immersed segment. Now, according to the principles of mensuration, 

 as applied to the segment of a sphere, if x be put to denote the height 

 of the segment, then its solidity is expressed by .5236 (36ar 2z s ), 

 and this must be equal to the solidity of the segment found by the 

 above analogy ; hence we get 



1 So; 2 x 3 = 799.2. 



In order to reduce this equation, let the signs of all the terms be 

 changed, and put a;zr z -f- 6 ; then, by substitution, we have 



x a = z s -f 18z 2 + 108z + 216, 

 and 18**=:* 18s 2 216z 648; 

 hence, by summation, we obtain 



3 8 108zr= 367.2, 



and from this equation, the value of z is found to be 3.9867 very 

 nearly ; but by the supposition, x z -f- 6, and consequently, it is 



x =. 3.9867 4- 6 = 9.9867 inches very nearly, for 

 the height of the segment, or the depth to which a globe of oak 

 descends in fresh water, the diameter being 12 inches, and the specific 

 gravity 925. This result agrees with that obtained by Dr. Hutton, in 

 the second volume of his Course of Mathematics. 



574. QUESTION 5. If a sphere of wood 9 inches in diameter, sinks 

 by means of its own gravity, to the depth of 6 inches in fresh water ; 

 what is its weight, and also its specific gravity ? 



By the corollary to the third proposition, art. 233, page 212 214, 

 it is manifest, that the weight of the body is the same as the weight 

 of the fluid displaced by its immersion ; that is, the weight of the 

 entire sphere, is equal to the weight of as much fluid as is represented 

 by the solidity of the immersed segment ; but by the principles of 



