OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 235 



Put W zz the real weight of the globular body, 

 S zz its specific gravity, 

 w zz the weight which the body indicates when weighed in 



water, 



s zz the specific gravity of water, 



vf zz the weight which the body indicates when weighed in air, 

 s' zz the specific gravity of air, and 

 d zz the required diameter of the solid body. 



Then, according to the principles of mensuration, the solidity of a 

 globe is expressed by the cube or third power of its diameter, multi- 

 plied by the constant decimal .5236 ; therefore, we have 

 dx dxd* .5236 zz .5236d 8 ; 



but it has been stated in a former part of this work, that the absolute 

 weight of any body, is expressed by its magnitude drawn into the 

 specific gravity ; hence we have 



Wz=.5236Sd 3 ; 

 consequently, by division, we obtain 



and from this, by extracting the cube root, we get 



.52365* (187). 



274. The equation in its present form, expresses the diameter of 

 the body in terms of its absolute weight and specific gravity ; this is 

 certainly the simplest and only mode of determining the magnitude 

 of any body or quantity of matter, when the weight and specific 

 gravity are known a priori ; but when this is not the case, we must 

 have recourse to other methods ; and a very elegant and simple one, 

 consists in weighing the body in water and in air, as implied in the 

 problem, and then proceeding as follows. 



By equation (185), Problem XXXIV., it appears, that the real or 

 absolute weight of the solid, expressed in terms of its relative weights, 

 and the specific gravities of the fluids in which it is weighed, viz. water 

 and air, is 



!j /-V^ 

 s s 1 ' 



and by equation (186), Problem XXXV., the specific gravity of the 

 solid expressed in terms of the same quantities, is 



