466 MATHEMATICAL APPENDICES 57* 



where c denotes the specific heat at constant volume. Hence the 

 conductivity expressed in thermal units is 



f = r-lfefe f fe uB- l (mu>* - 2-2107 Ar 1 )^*"-' 

 **l(m* - 2-2107 AT >-*"-', 



where I is the mean free path of the particles which move with 

 speed o>. 



We find upper and lower limits of the value of this integral by 

 the approximate methods employed in former paragraphs, in which 

 we put for B or I their mean values. In this calculation I have 

 not taken the exact value of h, but its approximate value f , and 

 therefore 2- 25 instead of 2-2107 ; and I have obtained 



f |7 



or 



0-333 mNQLc < I < 0-818 mNQLc. 



If we compare this determination with the theoretical value of 

 the coefficient of viscosity, which with sufficient approximation is 

 given by 



we have 



or 



1-047 rjc < I < 2-570 rjc, 



so that the upper limit coincides nearly exactly with that calcu- 

 lated by Boltzmann. 



Since these limiting values are rather far apart, an exact 

 evaluation of the integral by mechanical quadrature, as in the 

 case of viscosity, is necessary. This has been very kindly done 

 at my request by P. Neugebauer, by means of the tables 

 left behind by Conrau; and my best thanks are due to him for 

 his kindness. The calculation has given that, if h is taken equal 

 to |, 



I = 1-53716 TIC, 



as was assumed in the first edition of this book ; but with the 

 more correct value 0-71066 for h calculated by Conrau we have 



f = 1-6027 r ic . 



This value lies between those calculated by Clausius and 

 Maxwell, viz. j^c and |j?c respectively. A comparison of thes e 

 theoretical formulae with experiment is given in 108. 



