142 
PROFESSOR HUGH L. CALLENDAR ON 
experiments, it is evidently desirable from a practical point of view to employ the 
simplest possible formulae for its representation. The variation from unity over this 
range cannot be determined more closely than 2 or 3 parts in 10,000 (i.e., 10 per 
cent, of the variation itself), so that it would appear ridiculous to employ coefficients 
with five significant figures in the formulae. 
For the above reasons, in the ‘British Association Report,’ 1899, the following 
simple formula was given as representing the results between 10° and 60° within the 
limits of accuracy of the observations, in terms of a unit at 20° C.— 
s = -9982 -f -000,0045 (t — 40) 2 .(5). 
It was stated that the variation of the specific heat near the freezing-point was 
apparently more rapid than the formula indicated, and could he approximately 
represented by the addition of the constant quantity '020 calorie to the total heat. 
This correction to the formula has since been further verified, and may be represented 
by the addition of a small cubic term below 20°. 
Below 20° C. add to (5) -f- -000,000,5 (20 — ?) 3 .... (6). 
At that time the observations had not been extended above 60°, and the formula 
of Regnatjlt, emended as already described, was therefore adopted for the higher 
temperatures, namely, 
Above 60° to 200° C. 5 = '9944 + -000,04£ + -000,000,9£ 2 . . . (7). 
Shortly afterwards, Dr. Barnes succeeded in obtaining six observations at higher 
temperatures. One of these was vitiated by dissolved air, and another was incomplete. 
There remain four good observations, which could be represented within 1 part in 
10,000 by the linear formula, 
From 68° to 92°. s = 1 + '000,14 (t - 60) . . . . (8). 
This formula gives a value nearly 1 part in 1000 lower than (7) at 90°, and it 
cannot be satisfactorily fitted on to Regnault’s observations at higher temperatures. 
1 think on the whole it would be better to retain Regnault’s formula as previously 
emended, until further observations are available. Although the agreement of the 
four observations is so perfect among themselves, it is possible that they may be 
affected by a constant error of this order of magnitude, if all the difficulties of the 
work are rightly considered. Besides, the linear formula cannot represent the 
probable increase in the rate of variation of the specific heat at higher temperatures, 
which is theoretically required to account for the vanishing of the latent heat at 
360° C., the critical temperature. 
It would of course be easy to represent the observations a little more accurately in 
any particular part of the curve by using more complicated formulae, but it is 
