42 IDEAL AND ACTUAL GASES 99 



on the other, to point out the means by which the defects 

 that have clung to it so far may be removed. The chief 

 ground of these defects we shall have to seek in our having 

 hitherto taken no account of the cohesion of gases. 



43. Rankine's and Recknagel's Modification 

 of Boyle's Law 



An attempt to carry the kinetic theory further in this 

 direction, and to find the correction of Boyle's law that 

 is necessitated by cohesion, has been already made by 

 Bankine 1 and by Be ckn a gel 2 with happy results. Beck- 

 nagel allowed for the influence of the cohesion of the gas, 

 in the calculation of the pressure exerted by it, by assuming 

 at every encounter between two molecules a temporary 

 retardation of their rectilinear motions what, in fact, might 

 be the simplest way of taking the influence of the curvature 

 of the paths into account. Joule's calculation of the 

 pressure given in 11 will hereby be so far altered that 

 the number of collisions of a particle in unit time against 

 the wall will be diminished by an amount which increases 

 with the number of collisions made by the particle with 

 other particles. We may, therefore, assume this diminution 

 to be directly proportional to the density of the gas, or in- 

 versely proportional to its volume, and thereby obtain for 

 the pressure, the value of which is proportional to this 

 number, not Boyle's law as before, but a more general 

 formula of the shape 



pv = A(l - Bv~ l ), 



where A and B are magnitudes depending on the tempera- 

 ture only ; and according to Bankine A is directly and B 

 inversely proportional to the absolute temperature. 



This formula agrees well with the experimental results 

 obtained in 1862 by Lord Kelvin and Joule 3 on the 

 cooling that accompanies the expansion of gases. Beck- 

 nag el also finds that the formula represents Begnault's 



1 Note in a Memoir by Thomson and Joule, Phil. Trans, cxliv. 1854, 

 p. 336. 



2 Pogg. Ann. Erg.-Bd. v. 1871, p. 563. 

 8 Phil. Trans, clii. 1862, p. 588. 



H 2 



