291 Mr. C. K. Akin on the Compressibility of Gases* 



that (since — = 2) the following equations, referring to the p 's in 



equations (A), will not hold good, viz. 



Pl=**P» K'=V', iV"=W", and^=2;V v ; 

 consequently the following will be equally false, 



Po"=Wi iV" = W, and p*=2p<!"; 



and putting now for /> ' its value P , these last will be false 

 a fortiori : 



Hence it would be erroneous to use in the above calculations, as 

 M. Regnault has done, values of m having respectively for 

 abscissae. 



l w , 2 m , 4 W , and 8 m ; 



but such values ought to be chosen as the equations (B) neces- 

 sitate. 



The values of the proper m's, and consequently their numerical 

 variation from those actually employed, maybe readily computed 

 in the following manner. The value of m', as to which there is 

 no difference, being known in numbers, as well as that of p ' = l } 

 Pq=Pi may be calculated. Corresponding to p n , considered as 

 an abscissa, the curves will furnish a new ordinate, which is the 

 true m" ; this, in its turn, will give p " ! =Pi" : hence m" ! ; and 

 so on. By this means it is easy to ascertain that in the case of 

 CO 2 gas, for instance, m ix as assumed and its accurate value 

 differ by more than 0*006 ; and since in the values n, which are 

 formed by multiplication of the several m's, the errors of the 

 latter become successively summed (or nearly so), it is evident 

 that n lv , for example, which is one of the numbers actually em- 

 ployed in computing the constants so often already mentioned, 

 will be considerably more erroneous than even wi iv . It is evident 

 that in the case of CO 2 gas, which is more compressible than 

 according to the Boylean law should happen, the compressibility 

 has been actually exaggerated in consequence of the above mis- 

 understanding. But it is fair to add that the example quoted 

 shows this exaggeration far greater than would the other three 

 gases ; in regard of one of which, viz. H, the error committed 

 amounts even to a diminution of apparent compressibleness, 

 though still an augmentation o.f deviation from law. 



3. In the Appendix will be found briefly indicated a simple but 

 rigorous mode of evaluating the constants of any preferred em- 

 pirical formula, by which to render more accurate, or rather to 

 supersede provisionally, the Boylean law, with the sole aid of 

 the experimental data respecting this matter furnished by M. 



