36 PROCEEDINGS OF THE AMERICAN ACADEMY 



affect the value of y to au equal extent, and the two must be deter- 

 mined with a precision ranging from 0.57 per cent at G0° to 0.22 per 

 cent at 225°, in order that each shall produce in y an error of less 

 than 0.1 per cent. It is well known that the value of a for all gases 

 changes with the pressure and temperature under which they expand. 

 In the case in hand, the gas expands under the constant pressure 

 7?2 from the temperature 0° of the first capillary, to that t of the 

 second. The experiments of Regnault furnish the best data for this 

 coefficient, and I have adopted his figures without reducing them for 

 the corrected value of the expansion of mercury, as the small change 

 which would be necessary would not sensibly affect my results. Reg- 

 nault gives as the coefficient of expansion of carbonic acid under 

 constant pressure 



At 760 mm. 100 a = 0.37099 



" 2520 " " = 0.38455 



Although the function connecting the pressure and coefficient of 

 expansion is unknown, yet simple extrapolation from these data gives 

 values of a of sufficient relative precision for the present results, as the 

 total variation of a within the range of />., used is only about 0.12 per 

 cent. The values actually used are given in the tables of experi- 

 mental data, so that the general effect of this correction can there be 

 noticed, and the data are sufficiently complete to allow a recalculation 

 with other values if desirable. It will be seen here also, as in the 

 value of A, the change in the coefficient is so small as to produce 

 effects of less than 0.1 per cent if neglected altogether, but the reten- 

 tion of both favors the elimination of accumulated systematic error in 

 y as a function of t. For this reason, a similar precaution has been 

 taken in the computations for air, although in that case it is even less 

 necessary. 



V. At. 



The precision necessary in the measurement of t, the tempera- 

 ture of the second capillary, is shown in the column headed A t in 

 Table VIII. 



1. As this investigation was aiming at the determination of the 

 change of rate of variation of the viscosity with the temperature, and 

 as this change was known to be small, it seemed of special importance 

 that all precautions should be taken to eliminate systematic errors. 

 And as thermometric measurements, even when conducted with more 

 than ordinary care, are particularly liable to such errors, especial atten- 



