Conduction of Heat by Rarefied Gases. 197 



gas pressures, as calculated from (2), may be called the relative 

 apparent conductivity. 



Now, if the increase of cooling time, at high exhaustions, 

 is caused by a decrease in the conductivity k, the value of 

 7 being put =0, the relative apparent conductivity must, 

 nevertheless, be the same at identical pressures in both vessels. 

 This will not be the case, on the contrary, if it is to be 

 explained by a finite discontinuity of temperature arising 

 at low pressures, according to formula (1), while k 

 remains constant ; but now the value of 7, which is given 

 by (3) and (4) as 



y = 



i r 



ft- 1 } • • • • w 



L a:L 



where ^=—=2 follows from (2), must be the same at equal 

 L /eh 



pressures in both vessels. 



To the above-calculated expressions (2) and (3) several 

 correction-terms must be added — first, on account of the 

 quantity of heat floAving to the ends of the thermometer- 

 bulb and through its glass stem ; secondly, on account of the 

 conductivity of the glass and mercury not being infinitely 

 great in comparison with that of the gas, as tacitly supposed 

 in the above calculations. They are taken into consideration 

 in the final results, though their omission would not pro- 

 duce any considerable difference. 



Results and Conclusions. 



6. The following table gives several examples of observa- 

 tions and the therefrom calculated quantities for air in vessels 

 I. and II. ; t means the observed time of cooling in seconds, 

 p the pressure in millimetres of mercury, K the apparent 

 relative conductivity, 7 the coefficient of discontinuity of 

 temperature, and y/X the ratio of it to the mean length of free 

 path of molecules. 



Air in Vessel I. 



t 184-0 184-05* 187-8 202*4 255-8 411-1 644-1 763-5 



P 710 41-0 4-74 0-90 0-213 0-0466 00086 00013 



K 1-00 0-973 0-876 0-621 0-267 0-0641 0-0095 



y 0-00271 0-0136 0-0587 0-264 1-41 10-1 



I , 1-69 1-61 1-64 1-61 (1-59) (1*72) 



