48* VISCOSITY OF GASES 451 



which may be drawn somewhat closer. For, from the remark that 

 the least value of B is T/N/2, it follows, for instance, that 



ir<0'37. 



Accurate knowledge of this coefficient can only be obtained 

 from a numerical evaluation of the integral by which the viscosity- 

 coefficient is expressed. I have, therefore, already calculated the 

 value of the integral for the first edition of this book, and I then 

 obtained the value K = O318. But, since in this calculation I used 

 o'nly ten of the values of the free path given in 37*, and also 

 employed only the simplest process of mechanical quadrature, the 

 value obtained could only be approximately accurate. 



A more exact calculation was made in 1892 at the instance of 

 E. Dorn, of Halle, by one of his pupils, Wilhelm Conrau, 

 of Magdeburg, now deceased, with the help of tables which were 

 even more complete than those published by Tait 1 , and by the use 

 of Cotes' s formulae. This calculation has given the somewhat 

 smaller value 



K = 0-30967, 



which is said to be correct to all five places of decimals. I have 

 tested this calculation in different ways, firstly by repeating my 

 former calculation with a greater number of calculated values of I, 

 by which I found the value K = 0'311, and, secondly, by a different 

 process of calculation, viz. by breaking up the integral, which 

 stretches from to oo, into a number of parts, and putting I in 

 each part equal to a linear function of w, whereby the integrations 

 can be performed ; this process, which by reason of the curvature 

 of the curve that represents I as a function of w can only give too 

 small values, gave K = - 308. The number found by Conrau 

 lies half-way batween these two approximate values, and may, 

 therefore, be assumed to be accurately calculated. Besides, P. 

 Neugebauer, who has had the goodness to carry out similar 

 calculations for the theory of the conduction of heat in gases 

 which is given in 57*, has tested Conrau' s numbers, so far as 

 was necessary for his purpose, by forming the first, second, third, 

 and fourth differences, and has thereby found only unimportant 

 errors which can be of no influence on the figures given. 

 I therefore consider 



rj = 0-30967 mNClL 



1 Trans. R.S.E. 1887, xxxiii. p. 277. 



G tt 2 



