CARBON DIOXIDE AT DIFFERENT TEMPERATURES. 219 



oil gauge was measured, since this pressure difference varied slightly according as the 

 bell was rising or falling, owing to the viscosity of the oil. In some cases the mean of 

 the readings with the bell very slowly rising and very slowly falling was taken. 

 After H had been measured, the taps associated with the oil gauge were turned so as 

 to cause it to record the excess pressure at the high pressure ends of the tubes over 

 that of the atmosphere, in the manner described on p. 208. 



It may be thought that since it was impossible to keep the bell quite still during 

 the passage of the gas from the reservoir to the bell an error might arise, owing to 

 the motion of the bell affecting the pressure, and consequently the flow, in virtue of 

 the viscosity of the oil in the pressure regulator. The fact that the bell was in the 

 same position when both times were recorded, however, insured, as will be seen from 

 the following consideration, that no error arose from this cause, even though the 

 motion of the bell might be quite irregular. For let f be the deviation of the rate of 

 flow of the gas from its normal value* owing to the fluctuations in pressure, p the 

 deviation of the pressure of the gas in the bell from its normal value, owing to the 

 motion of the bell. Over the small range of pressure considered we may assume / 

 proportional to p, say f= cp. If we assume that the frictional force on the bell was 

 proportional to the velocity for the small velocities under consideration, we have 

 px dyfdt, where y is the displacement of the bell from the position in which S touched 

 the lever. Hence f Cidy/dt, c being a constant. If t^ and t a refer to the two 

 times at which the contact was broken, we have for the total error in the flow during 

 the experiment, 



since initial and final positions of the bell were the same. Hence the compensation 

 is exact. 



The volume of the reservoir was determined by filling it with successive weighed 

 quantities of water. The weights were corrected to vacua, and corrections were made 

 for the temperature of the water. The effect of pressure in altering the volume of the 

 reservoir was investigated by filling it and its connections with water, forcing more 

 water in until the pressure rose by about 80 cm. of mercury, and then noting the 

 pressures as successive quantities of water were allowed to escape through a side tube. 

 The corrections, as determined in this way, contain the corrections for the alteration 

 in volume due to the mercury in the gauge tube altering its position as the pressure 

 changes. The observations, full details of which are preserved in the archives, lead to 

 the expression V = 51094 + 5'355P + & for the volume of the reservoir as a function of 

 the internal excess pressure P. The expression (5'355P + &) represents the alteration 

 in volume due to internal pressure. The smoothed values of k for different values 



* By the normal value is meant the value when the bell is still. 



2 F 2 



