444 MISCELLANEOUS HYDROSTATIC QUESTIONS, WITH THEIR SOLUTIONS. 



-f- 3 :rz x, in the case of fresh water, 



1000 



O -V* 



and - + 3fH = * in the case of sea 



therefore, if one of these equations be subtracted from the other, we 

 shall have 



533520 



26xzz ' , or arm 40 inches, the side of the cube required ; 

 51 o 



hence, the altitude of the immersed part, as referred to fresh water, 

 is 40 3 = 37 inches ; and the altitude as referred to sea water, is 

 36 yVy inches ; and from either of these, the specific gravity of the wood 

 is found by the proposition referred to above ; for we have 



40 : 37 : : 1000 : siz:925; indicating the specific gravity 

 of oak, when that of fresh water is expressed by 1000. 



572. QUESTION 3. If a cube of wood floating in sea water be | below 

 the plane of floatation, and it sinks VV of an inch deeper in fresh 

 water ; what is its magnitude, and what is its specific gravity ? 



This question at first sight would appear to be the same as the last ; 

 it may indeed be resolved by the same principles ; but since the im- 

 mersed parts are given in this instance, instead of the extant parts, as 

 was the case in the preceding question, this circumstance suggests a 

 simpler and a better mode of solution ; for by the inference in art. 317, 

 page 261, it appears that the parts immersed below the surface of the 

 different fluids, are to each other inversely as the specific gravities of 

 the fluids ; hence, if x denote the side of the cube in inches, then by 



the question, is the altitude of the part immersed below the sur- 



3ar 3 3Qx -4- 12 

 face of sea water, and 4- TZ ~ IT; is the altitude of the 



4 ' 10 40 



part immersed below the surface of fresh water ; consequently, by the 

 inference above cited, we obtain 



1000 : 1026 : : : 30 * ."*" 12 ; 

 4 40 



and from this, by equating the products of the extreme and mean 

 terms, we get 



78x1= 1200, or arzr 15 T S T inches, the side of the cube required. 



Having thus determined the side of the cube, the specific gravity 

 of the material will be found as in the last question, for we have 



15 T T : IX 15 T T : : 1026 : 769, the specific gravity sought. 



