in the Kinetic Theory of Gases. 93 



which values are possibly more exact than those given by 

 Prof. Tait. The total number of impacts which all the mole- 

 cules contained in the unit volume make in a second is 

 %nn v N v = '2,nn v v : p v . Only the third of these integrals, as 

 already remarked in § 1, was published in the second part of 

 my " Theory of Gaseous Friction," in formula 9, p. 45. One 

 other circumstance deserves mention. We have spoken all the 

 time as if during the entire second the same n . n v molecules 

 would move with a velocity lying between v and v+dv. In 

 fact, the velocities of the molecules are constantly changing ; 

 but since, on the whole, for a molecule which loses the velocity 

 v, another gains the same velocity, the above expression does 

 not lead to a false result. 



§ 4. On the Heat-equilibrium of Gases upon which External 

 Forces act. 



Prof. Tait, in his first paper in the Edinburgh Transactions, 

 page 91, also raises objections to my calculation of the heat- 

 equilibrium of a gas on which external forces act, and treats 

 this case differently, starting from an assumption, which he 

 gives in italics on page 92 of the paper referred to at the 

 conclusion of § 31. 



We have to distinguish between a defining-assumption, the 

 object of which is to define the problem which is to be mathe- 

 matically handled, and an unproved assertion that, from the 

 defining-assumptions made, certain consequences would follow. 

 If, for example, we assume that the molecules are elastic 

 spheres, that glass walls are rigid elastic planes, &c, these are 

 defining-assumptions. In nature these assumptions are cer- 

 tainly not exactly fulfilled, but the logical consequence of the 

 conclusions drawn from them is not thereby affected. But 

 Prof. Tait's above-cited assertion is of the latter kind, since 

 he gives no proof that it is a mathematical consequence of the 

 defining-assumptions made. Also I am sure that my defining- 

 assumptions in many respects correspond extremely imper- 

 fectly with the properties of the actual gas. On the other 

 hand, both my proof of Avogadro's law, and my calculation 

 of the heat- equilibrium of a heavy gas, are free from preju- 

 dicial and unproved assumptions. In order to show this I 

 will give what seems to me a greatly simplified treatment of 

 this problem, using the results of others which have appeared 

 in the last twelve years upon this subject. And in this I will 

 make use altogether of the method which H. A. Lorentz, in 



