296 Mr. C. K. Akin on the Compressibility of Gases. 

 according to Boyle's law, 



P== P \ Pn ~~ 9 { pdx }' 

 J* 



R being the density corresponding to the normal pressure P; p a 

 the pressure at the bottom of the column to which the layer of the 

 density p belongs j finally, ^ = the acceleration of gravity. Dif- 

 ferentiating this last expression, and integrating the result between 

 the limits a and #, we shall find 





p _^l (*-«). 



Pa 



or observing that 



T> 



P=#QH, and making g =D : 



where Q denotes the density of the matter, and H the height of 

 the column, in which the normal pressure of the gas is to be eva- 

 luated, whilst D is introduced only for brevity : it will result that 



Employing this last expression in the integral (1), we get 

 M=±p a {l-e-H°}=f{l-e-B°h 



■ H P Pa 



since ^p a =- Pa= I-. 



Let a assume now in two special cases the values a and «,, 

 and the corresponding pressures be simply designated 3isp ,p l ; 

 we shall then have, since the mass is supposed the same, the 

 equation 



-%=;'o{l-e"»° }=^,{l-e-S"'}> 

 from which at once follows the relation 



D , , . . . . 



* I-.-H' 



(I) 



identical with that first quoted in art. 1. 



5. In establishing the above formula, it was necessary to em- 

 ploy the law of Boyle. As the latter, however, is not quite accu- 

 rate, it shall now be shown how a formula similar to (I.), but 

 not implying the truthfulness of the Boylean law, may be de- 

 duced, and ultimately serve to accomplish the purpose adverted 

 to in the beginning of art. 3. To arrive at this new formula, we 



