502 



of the relation between heat-condnction and frietion numerically 



correct results can only ba arrived at l\y taking for the mean free 



path in the case of conduction a somewhat higher value than that 



which follows from internal friction. In other words the velocity of 



the molecules at a collision is not that wiiich corresponds to the 



temperature at a distance ^, bul at a distance «A, where « is 2.5 



for monatomic gases and 1.7 for di-atomic gases. If we introduce 



this into the expression for M we obtain, as found by Knl'dsen, 



taking l\^=l, for di-atomic gases ^1=^ J.7 Xl for high values of 



2R 



— or k, = 2.3. For helium we shall have to take /■, = 2,5 .4= 3.33 : 



for this gas k\ thus changes between the limits Vs ci"'' «^-3. The 

 question, as to how k\ depends upon the mean free path will have 

 to be decided by experiment. This problem is analogous to that 

 concerning the relation between heat-conduction and friction, when 

 there is also slipping along tiie wall. Keeping that in view we have 

 ventured to make a simple assumption which does not clash with 

 the available experimental data and explains the nature of the 

 deviations between our thermometers with dilferent melting-point 

 pressures as well as possible. In how far this assumption maj^ be 

 correct, can only .1)6 settled l)y future experiments. In the mean 

 time it may perhaps be considered as a rough representation of 

 what will be found, when this problem, which is of great importance 

 for the insight into the mechanism of heat-conduclion and internal 

 friction, will be specially taken up. The assumption in question is, that 



2R 



1 + c,c, -^ 



^'=* 2-Ë ^'^ 



In this formula c^ and 6% are two coefficients, c, having a special 

 value for each gas and being 0.550 for helium and c, differing for 

 monatomic and diatomic gases. For the former c\ = 2.5 and for 

 the latter r, = 1.7. 



If we abandon the assumption, that L\ = i ■, 2.5 for large values 



2R 

 of — , there is an additional constant c, available to adapt the 



foi'mula to our observations. A very good agreement is in that case 

 obtained with ri=: 2.8(55 and c, = 0.3101 '). The corrections obtained 

 by this method are indicated in the tables of § 6 below by {). 



^1 It may be observed, that the ratio of this q to the more theoretical value 

 is the value of the power of 7' in the viscosity-law for helium. 



