252 OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 



let this value of the force of ascent, be substituted instead of it, in the 

 above value of s', and we shall obtain 



sw 



- w _j_W W" (198). 



302. The practical rule for reducing this equation, may be expressed 

 in words at length in the following manner. 



RULE. Multiply the absolute weight of the body, of which 

 the specific gravity is required, by the specific gravity of the 

 fluid; then, divide the product by the absolute weight of the 

 body, increased by its force of ascent, and the quotient will be 

 the specific gravity sought. 



303. EXAMPLE. A piece of wood which weighs in vacuo 22 ounces, 

 is attached to a piece of metal of such a magnitude as to weigh 12 

 ounces in water ; now, supposing that when the compound mass is 

 placed in water, it is found to weigh 20 ounces ; what is the specific 

 gravity of the wood, that of water being expressed by unity? 



Here, by proceeding according to the rule, we get 



and this, by referring to a table of specific gravity, is found to cor- 

 respond very nearly with the medium species of citron wood. 



PROBLEM XLV. 



304. Having given the weight of a vessel full of water, both 

 before and after a body of a given weight in air is immersed 

 in it, together with the specific gravity of the air at the time of 

 observation : 



It is required to determine the specific gravity of the 

 immersed solid, the weight of the air being taken into 

 consideration . 



This problem is perhaps more curious than useful ; but since it 

 tends to excite the reader's attention, and to render him familiar with 

 the resources of analysis, we have thought proper to introduce it in 

 this place ; and in order to its resolution, 



Put w i= the weight of the vessel when full of water, 



TV =n the weight of the solid body when weighed in air, 

 w":n the weight of the vessel with the solid in it, when filled 

 up with water, 



