254 OUTLINES OF NATURAL PHILOSOPHY. 



sphere. The height of this homogeneous atmo- 

 sphere, in fathoms, is therefore 



4342.944(1 + .0040- 



345. Let a balloon, of a given cubical content, 

 c*, in feet, be filled with hydrogen gas, 13 

 times as elastic, and therefore 13 times as rare as 

 common atmospheric air, under the same com- 

 pression ; and let it also be loaded with a given 

 weight W ; required to what height it will as- 

 cend. 



If y be the specific gravity of any stratum of air, in 

 which the balloon is placed, that of water being 

 unity, since a cubic foot of water weighs 62.48 Ib. 

 avoirdupois, c 5 x (62.48) y is the weight of the 

 air displaced, or the whole force tending to support 

 the balloon. But the whole weight of the balloon is 







W + (62.48) c 3 x ^ , and therefore when the bal- 

 io 



loon is just supported, and has no tendency to as- 

 cend, 62.48 x <?y - W + 6 ^' 48 c 5 y, or 



,fv/ 



13 W 

 ~ 749.76 e' 



1 When 



