100 
PROFESSOR HUGH L. CALLENDAR OX 
others on the compressibility of gases over considerable ranges of temperature and 
pressure, indicate a real difference between the scales, similar to that calculated from 
the observations of Joule and Thomson by the modified equation (3). 
The differences between the nitrogen and hydrogen scales at a constant pressure of 
1 atmosphere calculated from the observations of Joule and Thomson by the same 
equation are given in the same table. In each case the difference between the 
hydrogen scale, tj t , and the absolute scale, 6, is added. In the case of the constant- 
pressure thermometer the correction is larger than at constant-volume, but there is 
less uncertainty in its value, as the results calculated by different formulae ( e.g ., Van 
der Waals and Clausius) are very nearly the same. 
Table IV.—Difference between Scales of Nitrogen and Hydrogen Gas- 
Thermometers. 
Temperature, 
Centigrade. 
Chappuis, 
formula (2). 
Chappuis, 
corrected. 
Joule-Thomson, 
constant-volume, 100 centims. 
Joule-Thomson, 
constant-pressure, 7 6 centims. 
in ~~ ih- 
in ih• 
ih - 0* 
tn-ih. 
ih - 
o 
10 
+ -0057 
+ -0053 
+-0030 
+•0005 
+ -0062 
+ -oon 
20 
+ -0095 
+ -0087 
+'0050 
+ -0009 
+-0103 
+-0019 
30 
+ -0113 
+ -0105 
+ -0065 
+ -0012 
+-0131 
+-0024 
40 
+ -0110 
+ -0110 
+ -0073 
+-0013 
+ -0143 
+-0026 
50 
+ -0086 
+-0103 
+ -0073 
+-0013 
+ -0144 
+-0026 
60 
+-0049 
+ -0090 
+ -0066 
+ -0013 
+ -0130 
+ •0025 
70 
+-0010 
+ -0069 
+-0055 
+ -0011 
+ -0112 
+ -0020 
80 
- -0023 
+ -0045 
+-0044 
+ -0008 
+ -0083 
+ -0015 
90 
- -0032 
+ -0022 
+ -0025 
+-0004 
+-0044 
+ -0008 
In order to reduce the value of the specific heat of water expressed in terms of any 
scale of temperature t! to the corresponding value expressed in terms of any other 
scale of temperature t", it is only necessary to multiply by the factor dt'jdt". This 
factor is readily obtained if the formula giving the relation between t' and t" is 
known. For instance, in order to reduce from the platinum scale by means of the 
difference-formula, we obtain at once by differentiation of the formula the factor 
dpt/dt = 1 + (100 - 2t) cZ/10,000 .(4). 
Since the specific heat of water varies so little from unity, the correction to be 
added at any point may be taken as being practically equal to the excess of the 
correction factor above unity. The corrections from the nitrogen to the hydrogen 
scale, obtained by differentiation from the table of differences above, are very uncer- 
