56 Prof. H. L. Oallendar on the Tliermodynamical 



the fundamental coefficient of expansion, which may be called 

 the "fundamental zero"), we obtain for the absolute zero 

 correction the simple result, 



^,-T =S A Q/R (16) 



This expression was applied to calculate the coefficients of 

 expansion at various constant pressures, and to determine 

 the value of the absolute zero from Regnault's coefficients of 

 expansion of air, hydrogen, and C0 2 at^j> =:7() cms. 



The following table contains the results given in the article 

 in question : — 



Table I. — Absolute Zero from Reonault's 



Expansion-Coefficients. 



Gas employed Air. H 2 . CO,,. 



Coefficient of Expansion, a -0036706 '003(5613 -0037100 



Fundamental Zero of Gas, T =l/a ... 272°-44 273°-13 269°-50 



Correction to Absolute Zero, O -T O ... +"70 -\L3 +4/4 



Absolute Zero deduced, O 273* 14 273-00 27 3"90 



Thomson remarks as the result of these figures that the 

 correct value is probably within a tenth of a degree of 273 o, 0, 

 and that it is satisfactory to find that a gas so imperfect as 

 G0 2 , with so large a value of the correction, should differ so 

 little when corrected from air and hydrogen. As a matter 

 of fact, the discrepancy, small as it is, appears to be due lo 

 an error in Regnault's coefficient of expansion, for if we 

 adopt instead ChappmV value of the expansion-coefficient for 

 C0 2 at 100 cms. pressure, namely "003742; which gives 

 T =267°-24, we find (increasing the correction in the ratio 

 100/76) the value of the absolute zero O =267'24 4-5°'8 = 

 273°*04, which agrees with hydrogen. 



A similar method has been applied by other writers to 

 estimate the zero correction for the constant-volume ther- 

 mometer. If we neglect the term d(pv) in equation (5) 

 (which is not justifiable), and write — (d6/dv)-p = Q,plv (which 

 is a good approximation considering that this term is small), 

 we obtain 



l + SQ/v= {dp/d6) v 0/p (17) 



Integrating this at constant volume, assuming SQ constant , 

 we have the solution 



log^0/0o)=log e (pM,)/(l + S©>), . . (18) 



