90 Prof. H. L. Callendar on the Thermodynamical 



With these values air would become pluperfect at about 

 90°C, and the value of b is not much smaller than the volume 

 of the liquid at low temperatures. The agreement with the 

 observations on the compressibility is very good over a wide 

 range of temperature. The agreement with the observations 

 of the cooling-effect is exact at 0° C, and the difference 

 at 100° C. does not exceed the possible error of the experi- 

 ments. If we abandon the hypothesis of integral degrees 

 of freedom for triatomic or tetratomic molecules, we might 

 of course calculate the value of the index n so as to obtain a 

 better average agreement with observation, but even from a 

 purely empirical point of view it is a matter of great con- 

 venience to have a simple value for the index n, provided 

 that it satisfies the observations within the limits of probable 

 error. Moreover the hypothesis of Maxwell, which is sup- 

 ported by the experiments on monatomic and diatomic gases, 

 is so simple and helpful that it is desirable to retain it as far 

 as possible. 



In applying the formula with the value n=l m 5 to deter- 

 mine the zero-correction and the scale-correction, the simplest 

 method of proceeding is to find q for each temperature, and 

 apply formulas (34) and (36). The results for the constant- 

 pressure thermometer do not differ materially from those 

 previously calculated. The zero-correction for the constant- 

 volume thermometer may be put in the form 



o -T o =3-73 (co-o^o/R- 



Taking <? =1'48 c. c, this gives C *72 for the correction at 

 76 cms., or o, 95 at 100 cms. Jf we assume the correction 

 for nitrogen to be the same as that for air, and employ 

 ChappmV pressure-coefficient, we find # = 273°'06. The 

 values of the scale-correction for the air-thermometer are as 

 follows at 50° C. and -150° C. :— 



Constant-Pressure, 76 cms. 



at 50° (J., dt = -'0185° ; at 450° C, dt= +-470°. 



Constant- Volume, p =76 cms. 



at 50° C, dt = --0044° ; at 450° C, dt = + -136°, 



Constant-Volume, ^j> = 100 cms. 



at 50 r 0.., dt= --0057° : at 450° C, dt= +'179°. 



The constant-pressure correction is nearly one-tenth larger, 

 the constant-volume correction is nearly one-third smaller 

 than in Table V., according to the previous method of calcu- 

 lation with oi = 2. The constant-volume correction is still 

 nearly twice as large as that given by the Rose-Innes formula 

 for nitrogen, and more than three times as large as that given 



