105 CONDUCTION OF HEAT 283- 



used the formula for the coefficient of viscosity as given by 

 Stefan, 1 viz. : 



7) = 



which, if we are contented with a somewhat less accuracy, 

 seems quite justified, and is therefore mentioned fre- 

 quently in memoirs. The reason that we have arrived at 

 different values of the numerical coefficients in our formulae 

 for D and 77, viz. JTT = O39270 and 0-30967, is that in the 

 calculation of rj a higher degree of approximation has been 

 aimed at and attained. 



We have already met with a similar uncertainty of the 

 numerical factors that come into formulae ; it is in all cases 

 caused by the different way in which the mean is taken of 

 the varying properties and circumstances of the molecules. 

 In an elementary theory it is not, indeed, possible to keep 

 up the consideration of all conceivable particular cases right 

 on to the end through the whole calculation, and then at 

 the conclusion and not till then if we are to be accurate 

 to form the sum and take the mean. We are obliged, on 

 the contrary, for greater simplicity and clearness of pro- 

 cedure, not only to deduce the mean result for each part of 

 the calculation by itself, but also to employ from the first 

 average values of the magnitudes that come into the 

 calculation instead of the real ones. Since the concluding 

 result of such a calculation can be only approximate, we 

 must not be surprised that the theories given by different 

 investigators have led to different values of the numerical 

 coefficients. All, however, agree in concluding that the 

 conductivity I and coefficient of viscosity 77 are connected by 

 the relation 



I = /eye, 



where c is the specific heat of the gas at constant volume, 

 and K a numerical coefficient which has the same value for 

 all gases. This value lies between 0'5 and 2'5. 



In 57* of the Mathematical Appendices to this work 

 I have given a calculation in which I have striven to find 



1 Wien. Sitzungsber. 1872, Ixv. Abth. 2, p. 363. Compare 48* in the 

 Mathematical Appendices. 



