in the Kinetic Theory of Gases. 85 



but fundamentally equally sound, and obtained (on page 320) 

 a different numerical result. 



If we wish to neglect as few terms as possible of the order 

 of magnitude of the coefficient of friction, we must improve 

 the method adopted by Tait and myself, which in fact leads 

 to Meyer's numerical result. We must in fact observe that 

 each molecule in its path passes through layers in which a 

 progressively different motion of masses prevails, and that 

 consequently the probability of collision has a different value 

 in each layer. If we adopt Prof. Tait's notation exactly, then, 

 taking this circumstance into account, his conclusion must be 

 modified somewhat as follows. As on page 259 of his second 

 paper, let the layer of gas parallel to the ys-plane which has 

 the abscissa x move with the mean velocity Bx parallel to the 

 Y-axis. If in the unit volume there are, on the whole, n 

 molecules, then, according to Prof. Tait, there are 



n . v . e . v . dx 

 molecules emitted in unit time by the unit surface of the layer 

 lying between x and x + dx whose velocities lie between v and 

 v + dv. We will denote the product ev by f(v) . If, further, we 

 put 



1/= ^^Le-W+ 3 2+r2) dp dq drj 



we obtain 



N = n dp dq dr dx ^/^ e -^ 2 +^+^f(^ p2 + 2 * + r 2) 



for the number of molecules emitted by the layer whose 

 velocity relative to the resultant motion of the layer has com- 

 ponents along the three axes of coordinates which respectively 

 lie between the limits p and p + dp, q and q + dq, r and r + dr. 

 But since the layer itself has the velocity Bx in the direction 

 of the Y-axis, the components of the absolute velocity of these 

 emitted molecules lie between the limits p and p + dp, q + Bx 

 and q + Bx + dq, and r and r + dr. Of these N molecules 

 let N, without further coming into collision, reach the plane of 

 abscissa ff. Let us further imagine the layer which lies between 

 £ and f + ^l constructed, and ask how many of our N mole- 

 cules will come into collision in this layer. As Prof. Tait 

 finds in his first paper (p. 73), in a layer whose mean velocity 

 is zero, during the time dt out of N molecules, which all move 

 with the same velocity v, N . e. v. dt=~Ndt ./(¥) molecules 

 come into collision. 



In the above case the N molecules have velocity-components 

 p, q + Bx, r in the directions of the axes of coordinates, but 

 the layer itself has the mean velocity Bf in the direction of 

 the Y-axis ; the relative motion is therefore exactly as if the 



