118 



DISPLACEMENT INTERFEROMETRY APPLIED TO 



Thus, after integration of the equated values of dW, 



Rr p' 



A0 = rr- log 

 JK p 



The constant factor is about 83 X2.3, since Naperian logarithms are needed. 

 In this way the values above given were obtained. They represent the total 

 accumulation of heat in over half an hour ; but it is at once radiated by the 

 gas and finds lodgment on the walls of the apparatus. Even if these radiated 

 nothing, their temperature increment would be infinitesimal in the ratio 

 principally of their mass to the mass of the air-content (probably for the 

 plenum 0.3 gram to several kilograms), which is then further diminished by 

 radiation. The available heat does not differ as much at all the pressures as 

 does the temperature. I question whether such small thermal effects, if they 

 are such and so circumstanced, could be detected in any other way. 



93. Experiments with the exhausted case. The case, figure 139, having 

 been carefully sealed, measurements were made in partial vacua, as shown in 

 figure 150, for an exhaustion between 20 and 30 cm. and figure 151, for an 



II;\K: 



0.85 

 0.86 



exhaustion between 37 to 45 cm. In the former an error was made in the 

 second triplet, which is therefore discarded. It is seen at once that, as the ex- 

 haustion increases, the drift grows less and the triplets are nearly repetitions 

 of each other. The double amplitude changes but little; thus, for 



Plenum, = 76 cm. 

 Vacuum, 51 cm. 

 Vacuum, 35 cm. 



a result to be anticipated, if the viscosity of air is independent of pressure, and 

 in view of the very slow motion of the needle, the resistance is not due to tur- 

 bulent motion of the air. The case leaked slightly, but this does not seem to 

 be of moment here. 



An important consequence follows : Since the frictional resistance is inde- 

 pendent of pressure, it may be computed as a case of viscosity, the problem 

 being that of a cylindrical shaft rotating on a normal axis, at its middle point, 

 in a viscous medium. This is further borne out by the fact that in the above 

 three-minute triplet curves, the branches, after being released from the 

 turning-points, are very nearly straight lines. Moreover, midway between 

 the turning-points the elastic force of the fiber is necessarily zero. In the pre- 

 ceding report, many instances were given in which, even for larger periods, 

 the curve soon consisted practically of zigzagged straight lines. 



