224 OF FLOATATION AND THE SPECIFIC GRAVITY OF BODIES. 



w zz the weight of an equal quantity of the fluid, 

 s zz: its specific gravity, and 



/ zz the force with which the body ascends or descends in 

 the fluid. 



Then, because as we have elsewhere demonstrated, the absolute 

 weights of bodies, are as their magnitudes and specific gravities ; it 

 follows, that 



w zz: ms, and w' zz ms' ; 



but according to the third inference preceding, the difference between 

 the pressures downwards and upwards : 



Is equal to the difference between the weight of the solid 

 body, and that of an equal bulk of the fluid. 



But the difference between the upward and downward pressures, is 

 equivalent to the force of ascent and descent ; consequently, we have 



/zz: w^w'-mms^ms', 

 and this, by collecting the terms, becomes 



/z=m(sv-s'). (182). 



If, therefore, the specific gravity of the solid be less than that of 

 the fluid, the force of ascent will be 



/z=m(s-/); 



but when the specific gravity of the solid exceeds that of the fluid, the 

 force of descent becomes 



/zz:m<X-s), 



and when the specific gravities are equal to one another, the force of 

 ascent and descent vanishes, in which case, the body will remain at 

 rest, in whatsoever position it may be placed ; this agrees with what 

 we have already stated in the first inference to Problem 32. 



From the above proposition and its subordinate formulae, the fol- 

 lowing inferences may be deduced. 



252. INF. 1. When a solid body is immersed, or suspended in a 

 fluid of equal or of different specific gravity : 



It loses the weight of an equal magnitude of the fluid in 

 which it is placed. 



This is obvious, for when the specific gravities are equal, the body 

 loses the whole of its weight ; and therefore, it neither endeavours to 

 ascend nor descend ; but when the specific gravities are unequal, the 

 body only endeavours to ascend or descend, by the difference between 



