4 
PROF. H. L. CALLENDAR ON THE VARIATION OF THE SPECIFIC 
difference between the mercury and gas scales of temperature over the range 0° C. to 
100° C., both of wliich facts would appreciably affect the reduction of the readings of 
the thermometers employed for observing the rise of temperature in the calorimeter. 
The correction for these two sources of error combined might reduce Regnault’s 
values by 5 or 6 parts in 1,000 if the thermometers he employed were of French 
“ cristed ” glass. In any case the reduction could hardly be less than 2 or 3 parts in 
1,000. This would bring the observations into fairly good agreement with my 
extrapolated formula, indicated by the lower curve in fig. 1, but the corrections 
involved are so hypothetical that no great stress can be laid on them. The only 
satisfactory solution is to repeat the observations, for which I have affeady made 
such preparations as my scant intervals of leisure will permit. In the meantime we 
may regard Regnault’s observations as giving, with some degree of probability, the 
rate of increase of the mean specific heat between 100° C. and 200° C., although the 
absolute values given by his formula probably require reduction by about 0'4 per cent. 
It should be observed that, even if all the corrections could be applied with certainty, 
the order of accuracy of his final results could not be expected to exceed 1 or 2 parts 
in 1,000, because the calorimetric thermometers were read to 0°'01 C. only on a rise 
of temperature of 8° C. to 15° C., and the individual observations in each group show 
corresponding discrepancies from the means. Regnault himself did not claim any 
higher order of accuracy, and endeavoured to indicate this by the values of the 
coefficients given in his formula. 
Range 0° C. to 100° 0. (Ludin). 
Many of the investigations by able experimentalists extending over the range 0° C. 
to 100° C. have given rates of variation exceeding 10 per cent, per 100° C., which 
were doubtless due to defective experimental methods and insufficient appreciation of 
the real difficulties of the problem. Such results are of no value except as an 
indication that the problem is not quite so simple as it appears at first sight. The 
first investigation in which sufficient attention was given to the well-known difficulties 
of mercurial thermometry, was that of E. Ludin (‘ Die Abhangigkeit der specifischen 
Warme des Wassers von der Temperatur,’ Inaug. Diss. Zurich, 1895), carried out by 
the method of mixtures under the direction of Prof. Pernet. His observations gave 
directly the mean specific heat over eight different ranges of temperature above 
18° C., and two different ranges below 11° C., in terms of the mean specific heat over 
the range 11° C. to 18° C. The variation of the actual specific heat was deduced by 
assuming a formula of the type 
s = 1at-\-hd + cd, .(3) 
and calculating the values of the coefficients by the method of least squares to agree 
with the observed ratios of the mean specific heats over the various ranges. This 
method is somewhat indirect, and makes the result depend to some extent on the 
