On the Measurement of the Viscosity of Gases. 1023 



mercury to be at and A. The difference of level is read 

 off the scales. The pinch-cock is then opened so as to let 

 the air or other gas escape, and the tube AB gradually 

 lowered so that the level of the mercury in the other tube 

 always remains at 0. After the lapse of a measured time 

 the pinch-cock is closed and. the difference of level of the 

 surfaces of the mercury again read off. These observations 

 are sufficient to determine the coefficient of viscosity pro- 

 vided the length and cross-section of the capillary tube are 

 known. 



Let V = volume of the bulb to the mark 0. Strictly V 

 should be the volume of the bulb together with that of the 

 capillary tube. This volume is kept constant in the experi- 

 ment. Then, if p is the pressure of the gas in the bulb at 

 any instant, 



__^jdp _ (p 2 — P 2 )7rr 4 

 Tt~ "Hrjl ' 

 where P is the atmospheric pressure, r the radius of the 

 capillary tube, I its length, and rj the coefficient of viscosity. 



Hence 



£> + P P 

 or log- — t=> = —kt + const., 



fe p-P 7) ' 



where k ( — -^^ j may be regarded as the constant of the 



apparatus. 



Thus if pi is the pressure at the beginning of the experi- 

 ment, p 2 the pressure at the end, and t the time, 



* (Pi + PXPa-P) V 

 from which tj may be easily calculated. 



The apparatus may be used in another way. Instead of 

 keeping the volume constant, the difference of level may be 

 kept constant during the time of outflow. In this case the 

 stem of the bulb must be graduated in parts of equal known 

 volume. The rise of mercury in the stem gives the volume v 

 of gas which has escaped, its pressure being supposed p, that 

 is the pressure due to the constant difference of level o)i the 

 mercury plus the atmospheric pressure P. We have, then, 



V= (p , -P')*r\ 



lfirjlp 



The apparatus resembles very much the ordinary form of 

 the air thermometer. It is just as easy to work with. 



