64 Prof. H. L. Callendar on the Tliermodynamical 



the basis of equation (38), assuming only the data already 

 given for the cooling-effect according to Joule and Thomson. 



In the simple case here considered it is unnecessary to 

 calculate the values of q for each temperature separately, 

 and then apply formula (36) to find the correction dt. The 

 expression for dt may with advantage be greatly simplified, 

 before beginning the calculation, by putting in the numerical 

 values of O and X , namely, 273 and 373, and substituting t 

 for — 0^. We thus obtain the following simple formulas. 



For the Constant-Volume Thermometer : — 



Absolute Zero-Correction, O — T = 646C, . (40) 

 Scale-Correction, dt = Ct(t-lOQ) l 6. . (41) 



in which C is used as an abbreviation for the constant factor 

 c 2? /373R, which has the values given in Table II. above 

 for an initial pressure p Q = 760 mm. 



For the Constant-Pressure Thermometer : — 



Absolute Zero-Correction, 6> -T = 846C~^ /E, . (42) 

 Scale-Correction, dt = Ct {t- 100) (1' 7 32 + 273/<9)/6>. (43) 



The covolume b occurs only in the zero-correction of the 

 constant-pressure thermometer. The values of the constant 

 C are the same as for the constant- volume thermometer. 

 The corrections for the constant-pressure thermometer are 

 deduced from those for the constant-volume thermometer by 

 multiplying by the factor (1*732 + 273/0), which has values 

 between 2 and 3 at ordinary temperatures. When the 

 corrections for any one gas have been calculated, those for 

 any other follow by simple proportion. The corrections 

 given in the table are all calculated for an initial pressure 

 p = 7Q0 mm. The corrections for any other initial pressure 

 are simply proportional to the pressure. 



If we apply the above formulas to calculate the value of 

 the absolute zero from PegnauhVs pressure-coefficients, we 

 find considerable discrepancies in the results, as illustrated 

 by the following table. 



Table III. — Absolute Zero from Regnault's 

 Pressure-Coefficients. 



Gas employed 



Pressure-Coefficient (£>:=76 cms.), a ... 

 Fundamental Zero of Gas. T = l, a ... 

 Correction to Absolute Zero, O -T O ... 

 Absolute Zero deduced, 9 



Air. 



Hydrogen. 



CO,. 



•0036650 



•0036678 



•0030880 



272°-85 



272°-64 



271 ° - 2 



+ -56° 



+ -09° 



+4°-2 



273° -41 



272°-73 



275°-4 



