CHAPTER XVI. 



MISCELLANEOUS HYDROSTATIC QUESTIONS, WITH THEIR 

 SOLUTIONS. 



570. QUESTION 1. How deep will a cube of oak sink in fresh water, 

 each side of the cube being 15 inches, and its specific gravity 0.925, 

 that of the water in which it is immersed being expressed by unity ? 



The solution of this question is extremely simple, for by art. 311, 

 page 257, it is announced as an established hydrostatical principle, 

 that the magnitude of the whole body is to the magnitude of the 

 immersed part, as the specific gravity of the fluid is to the specific 

 gravity of the solid. But since the base of the whole solid and that 

 of the immersed portion are the same, it follows from the principles of 

 mensuration, that the magnitudes are as the altitudes, and conse- 

 quently, the altitudes are as the specific gravities ; hence we have 



1 : 0.925 : : 15 : 13.875 inches, the depth required. 



571. QUESTION 2. If a cube of wood floating in fresh water, have 

 three inches of it dry, or standing above the surface of the fluid, and 

 3J-I-3 inches dry when in sea water; it is required to determine the 

 magnitude of the cube, and what sort of wood it is made of? 



This question may be resolved on the same principles as the last ; 

 for if we put a; ~ the side of the cube in inches, and s the specific 

 gravity of the wood ; then, by art. 311, page 257, we have 



1000 : s : : x : TT the part immersed in fresh water, 



and 1026 : s : : x : SX the part immersed in sea water; 



but the part immersed and the part extant, together make up the 

 whole altitude or side of the cube ; hence we have 



