66 



SPECIFIC GRAVITY. 



Hence, when T < A/fy> (1 p), the parallelepiped will 



float in an inclined position in indifferent equilibrium, the 

 inclination being given by (6). 



When j > v 6p (1 p\ the value of tan 6 is imaginary, 



i. e., if the ratio of the breadth to the height is greater than 

 V/6p (1 p), no value can be found for the inclination 

 which will cause the stability to vanish. (Compare with 

 last example.) 



3. If the breadth of the parallelepiped is equal to its 

 height, and if p = , find the inclination 6, that the paral- 

 lelepiped may float in indifferent equilibrium. 



Ans. e = 45 



29. Specific Gravity. Tlie specific gravity of a 

 body is the ratio of its weight to the weight of an equal 

 volume of some other body taken as the standard of 

 comparison. 



The density of a body has been defined (Anal. Mechs., 

 Art. 11), to be the ratio of the mass of the body to the mass 

 of an equal volume of some other body taken as the stand- 

 ard ; and since the weights of bodies are proportional to 

 their masses, it follows that the ratio of the weights of two 

 bodies is equal to the ratio of their masses. Hence, the 

 measure of the specific gravity of a body is the same as that 

 of its density, provided that both be referred to the same 

 standard substance. 



Thus, let S, W, V, and p be the specific gravity, weight, 

 volume, and density, respectively, of one body, and S lf W ly 

 F,, and p l the same of another body; then we have 



W gp_ V 



Pi v i 



(1) 



