256 MR. CLEEK MAXWELL ON THE VISCOSITY 



Hence 



If we make -=/3, and -,=/3', then 



or the friction is equal to what it woul J have been if there had been no slipping, and if 

 the interval between the planes had been increased by /3+/3'. By changing the interval 

 between the planes, a may be made to vary while /3-{-/3' remains constant, and thus the 

 value of j3 4-/3' may be determined. In the case of air, the amount of slipping is so small 

 that it produces no appreciable effect on the results of experiments. In the case of 

 glass surfaces rubbing on air, the probable value of /3, deduced from the experiments, 

 was /3=*0027 inch. The distance between the moving surfiices cannot be measured so 

 accurately as to give this value of /3 the character of an ascertained quantity. The 

 probability is rather in favour of the theory that there is no slipping between air and 

 glass, and that the value of |3 given above results from accidental discrepancy in the 

 observations. I have therefore preferred to calculate the value of [l on the supposition 

 that there is no slipping between the air and the glass in contact with it. 



The value of jm. depends on the nature of the gas and on its physical condition. By 

 making experiments in gas of different densities, it is shown that /u- remains constant, 

 so that its value is the same for air at 0-5 inch and at 30 inches pressure, provided 

 the temperature remains the same. This will be seen by examining Table IV., where 

 the value of L, the logarithm of the decrement of arc in ten single vibrations, is the 

 same for the same temperature, though the density is sixty times greater in some cases 

 than in others. In fact the numbers in the column headed L' were calculated on the 

 hypothesis that the viscosity is independent of the density, and they agree very well 

 with the observed values. 



It will be seen, however, that the value of L rises and falls with the temperature, as 

 given in the second column of Table IV. These temperatures range from 51° to 74° 

 Fahr., and were the natural temperatures of the room on different days in May 1865. 

 The results agree with the hypothesis that the viscosity is proportional to (461°+^), 

 the temperature measured from absolute zero of the air-thermometer. In order to test 

 this proportionality, the temperature was raised to 185° Fahr. by a current of steam 

 sent round the space between the glass receiver and the tin vessel. The temperature 

 was kept up for several hours, till the thermometer in the receiver became stationary, 

 before the disks were set in motion. The ratio of the upper temperature (185° F.) to 

 the lower (51°), measured from — 461° F., was 



1-2605. 

 The ratio of the viscosity at the upper temperature to that at the lower was 



1-2624, 



