OF SPECIFIC GRAVITY AND THE WEIGHING OF SOLID BODIES. 241 



specific gravity is nine times greater, are in equilibrio with one another 

 in a fluid whose specific gravity is unity ; required the weight of the 

 copper ? 



Here we have given m s' = 20 ounces ; / = 8 ; s" 9, and s \ ; 

 consequently, by substitution, the above analogy becomes 



20 : m's" : : 8(91) : 9(81); 

 and by equating the products of the extremes and means, we get 



64mVzzl260, 

 and dividing by 64, we have 



m 1 s" in =19-f^- ounces. 



It therefore appears, that 20 ounces of brass and 19|^ ounces of 

 copper, are in equilibrio with each other, when immersed in a fluid 

 whose specific gravity is unity ; but if put into a fluid of greater 

 density, the copper will prevail. 



PROBLEM XXXIX, 



288. Suppose a cylinder and cone, of the same altitude, base, 

 and specific gravity, to balance each other at the extremities of 

 a straight lever, when immersed in a fluid of given density ; the 

 cone being suspended at the vertex, and the cylinder at the 

 extremity of the axis. Now, suppose a cone equal to the one 

 proposed, to be abstracted from the cylinder, and its place sup- 

 plied by another of the same magnitude and half the specific 

 gravity ; it is manifest that in this state, the cone will prepon- 

 derate : 



It is therefore required to determine, how much must be 



taken from the cone, in order that the equilibrium may be 



again restored. 



Let AB be a straight inflexible lever, supported upon and easily 

 moveable about the fulcrum F, and 

 let the cone CDE and the cylinder 

 GHIK, (equal in altitude, base, and 

 specific gravity,) be suspended from 

 the extremities at A and B. 



Then it is manifest, that in conse- 

 quence of the equality of the bases ,y. 

 and altitudes, the magnitude of the cylinder is equal to three times 

 the magnitude of the cone ; and since the specific gravities of the 



VOL. i. B 



