CARBON DIOXIDE AT DIFFERENT TEMPERATURES. 209 



this quantity, and adding the result, reduced to centimetres of mercury, to the 

 atmospheric pressure. 



The density of the oil was not of primary importance for deducing the rate of flow 

 through the tubes, since the latter were calibrated with the pressure differences 

 measured in centimetres of oil, an approximate knowledge of the density was however 

 necessary in order to perform the reduction from oil pressure to mercury pressure 

 mentioned above. A determination of the density and coefficient of expansion of the 

 oil showed that if h is the head in centimetres of mercury at C. corresponding to 

 the head /* measured in centimetres of oil at C., the expression for h a is 



ho = h (0-0639) (1 -0-00076 [<-22]).* 



The rather large variation of the density of the oil with temperature made it 

 advisable to observe the temperature of the gauge after each set of readings, and it 

 was also necessary to ensure equality in the temperature of the two limbs, since 

 a difference in temperature of 0'5 C. between them might cause an error of 2 parts 

 in 1000 on a head of 10 cm. in a case where there were long lengths of column below 

 the menisci in the two limbs. Errors of this kind are not systematic however, and 

 the agreement of the final results is such as to show that they did not produce any 

 serious effect. A source of error might be expected to be introduced if the gauge 

 became tilted during the experiments ; the effect of a tilt is to produce on the pressure 

 readings a second order error varying as the cosine of the angle of tilt, and a first 

 order error due to the elevation of the graduations on one limb and the depression of 

 those on the other. The latter error becomes reduced to a second order one on the 

 specific heat, however, in virtue of the method of calculating this quantity from two 

 experiments with different flows of gas. It would be entirely eliminated if the flow 

 were accurately proportional to the pressure difference between the ends of the fine 

 tubes, for if x is the error in pressure due to tilt of the gauge, H the observed 

 pressure, and A the constant by which the pressure must be multiplied in order to 

 obtain the rate of flow, we have 



= A (R l + x) + fi, and (! 2 E 2 /S0 2 = A (K a + 



where CE and 80 have the meanings assigned to them on p. 200. On subtracting 

 the second equation from the first, it will be seen that x is eliminated just as h is 

 eliminated. The level readings of the oil in the gauge were taken several times 

 during the research, but the greatest variation amounted to only 0'06 mm., which is 

 much too small to produce any appreciable error ; even this variation may possibly 

 have arisen from inequalities in temperature between the limbs of the gauge. 



The oil was always drawn up so as to wet that portion of the gauge above the 

 point at which it finally settled ; it was rather sluggish in its movements, and readings 



* 22 C. is the temperature to which all the gauge readings were reduced. 

 VOL. OCX. A. 2 E 



