10 
PROF. H. L. CALLENDAR ON THE VARIATION OF THE SPECIFIC 
been fitted together. I have, therefore, devoted some attention to devising a single 
formula of a suitable type to cover the whole range. Of the many possible types of 
formula which might he devised for the purpose, the following has appeared to me, 
after exhaustive trials of many types from different points of view, to he the simplest 
and the most generally convenient ;—• 
.9 = 0-98536 + 0-504/(;^ + 20) + 0-b084(^/l00) + 0-009(//l00)". ... (6) 
This formula was obtained by combining a formula with Regnault’s coefficients to 
represent the variation from 100° C. to 200° C., with a formula containing a reciprocal 
term to represent the rapid fall in the neighhourhood of 0° C. The value of the 
constant term 0’98536 is adjusted to make = 1 when t = 20° C., which is the most 
convenient temperature in practice to use as a standard of reference. The other 
terms are all small and positive, and can be calculated with sufficient accuracy for all 
possible purposes by means of a 10-inch slide-rule, which is far from being the case if 
a formula of the Ludin type is employed. 
This formula is represented by the full line in fig. 3. The observations of Barnes, 
represented by the crosses, have heen reduced to a unit at 20° C., and corrected for 
the variation of the temperature-gradient in the flow-tube, as explained in my paper 
(/oc. cit., p. 129). The results are plotted in terms of the temperature scale defined 
l)y formida (l), and are not reduced to the hydrogen scale on account of the smallness 
and uncertainty of this correction, as previously stated. It may be observed that the 
agreement of the observations witli the curve would be slightly improved if the mean 
of the large group of observations near 30° C. had been taken as the basis of reduction 
in place of the few observations near 20° C. This would have the effect of depressing 
all the points by 0'00014, but would not alter the form of the curve. It happens that 
the absolute value of the specific heat can be most easily determined by the 
continuous-electric method in the neighbourhood of 30° C., which would naturally be 
selected as the standard temperature if this method were the only one to be 
considered. None of the observations deviate from the curve by more than 1 in 1,000, 
and only seven hy more than 1 in 2,000. The agreement is very good considering 
that the observations were taken with several different calorimeters and thermometers 
at dates extending over more than a year. Taking account of all the changes of 
condition which were made in testing the method, it seems hardly likely that the 
variation of the specific heat given by the formula (6) can be in error by so much as 
1 in 1,000 even at 80° C. 
0° C. -to 300° C. (Dieterici). 
The earlier experiments of Dieterici (‘ Wied. Ann.,’ 33, p. 417, 1888), in which ho 
determined the absolute value of the mean calorie (0° C. to 100° C.) by passing a 
current of 0'5 ampere to 07 ampere, measured with a silver voltameter, through a 
resistance of 171 ohms in a Bunsen ice-calorimeter, gave a result 4’2436 + 0'0017 
joules per gr. ° C., assuming the constant of the calorimeter as 15’44 mgr. of mercury 
