AEROSTATICS. 253 



h = (4342.944) (1 + .004 t) hyp. log -^ . 



b b 



But r^r = l + ~ nearl y ; 



b b b 



hyp. log (1 + - ^ = - , therefore 



h = (4342.944) (1 + -004 *) . 



is here given in fathoms, but in inches h = 

 (4242.944) (72) (1 + .0040 *. 



Hence = 4342.944 x 72 (1 + .004 . 

 b & 



But h: b: : specific gravity of mercury, to specific 

 gravity of air ; because the column of air, of the 



height h, and of mercury, of the height 6, have the 

 same weight. This gives the proposition above 

 enunciated. 



The quantity - x b is the height of an atmosphere 

 b 



which, having throughout the same density and 

 the same temperature as the air at the surface, 

 would have the same weight with the real atmo- 



sphere. 



