in relation to Pressure, Volume, and Temperature. 401 



may assume that from it also a deviation takes place which 

 becomes the greater the smaller the volume becomes. 



Now I have tried to construct for p a formula which retains 

 what appears to me to be correct in previous formulas, but at 

 the same time makes allowance for the above-mentioned mo- 

 difying circumstances, and, while as simple as possible, is in 

 satisfactory accordance with both the older and the newer ob- 

 servations of Andrews, as well as with the other extant obser- 

 vations. This, on account of a peculiar circumstance, is beset 

 with great difficulties. The formula to be formed for p has, 

 as may be seen even from the equations (2), (3), (4), and (5) 

 when solved with respect to p, the peculiarity that it is the 

 difference of two quantities which may both have much higher 

 values than p. The effect of this is, that inaccuracies which 

 in proportion to the two single quantities are but little may 

 yet in p produce deviations from experiment considerable in 

 comparison with its value, and therefore each single quantity 

 must be so much the more precisely determined. 



The formula which I have constructed has the following 

 form : — 



^= E ^-T(^8/> • • • • (7) 



wherein R, c, a, and /3 are constants. 



For carbonic acid these constants, if (as before) the chosen 

 unit of pressure be one atmosphere, and the unit volume that 

 which is occupied by the carbonic acid under the pressure of 

 one atmosphere and at the temperature of the freezing-point, 

 are to have the following values : — 



R= lj00682 =0-003688, 



c=2-0935, 

 a=0-000843, 

 ^8=0-000977. 



(8) 



If, on the other hand, as pressure-unit the pressure of a kilo- 

 gram upon a square metre, and as volume-unit a cubic metre 

 be chosen, it being presupposed that the quantity of carbonic 

 acid is a kilogram, we have to attribute to the constants the 

 following values : — 



R=19-273, 1 



c=5533, I , g x 



«= 0-000426, | W 



/3= 0-000494. j 



