6 
PROF. H. L. CALLENDAR ON THE VARIATION OF THE SPECIFIC 
97° C., could not give very certain information with regard to the actual specific heat 
between 89° C. and 97° C. The observations themselves, giving the ratios of the 
mean specific heats over different ranges, cannot be represented graphically in relation 
to the curve of actual specific heat represented by formula (4), which is shown by the 
dotted line in fig. 3. It is easy, however, to deduce the corresponding formula for 
SPECIFIC HEAT OF WATER AT t 
OBSeRV/TTIONS BY CflLLENDflB BND B/3BNES METHOD + 
. "^lUd 
IN’S FORMU 
OlETERICi- 
-A 
. 
=4^ ' 
\ \ 
' 
+ ^ 
- — "x 
''CALI 
.ENDAR’S FC 
>RMULA 
rf***--,-1- 
0° 10° 20° 30° 40° , 50° 60° 70° 80° S0° 100" 
Fig. 3. 
the mean specific heat from 0° C. to t° 0., shown in fig. 2, in relation to which the 
observations may be represented by a slight reduction (as in the case of Regnault’s 
observations) which does not materially affect their relative errors. The individual 
observations at each point are shown by the small crosses. The large crosses 
surrounded by circles represent the means of each group. The full curve, marked 
Lupin’s formula, represents the equation 
.V = l‘0084-0-00038656^ + 0-000006588^"-0-00000002929^® . . . (5) 
which gives the mean specific heat from 0° C. to t° C. by Ludin’s formula in terms of 
the specific heat at 20° C. taken as unity. The group means are seen to differ by less 
than 1 in 1,000 from Ludin’s curve. It must be remembered, however, that the 
observations in each group were all taken consecutively under the same conditions 
with the same calorimeter and thermometers, and would give no indication of possible 
constant errors. Thus in Ludin’s method of operation it was necessary to vary the 
quantity of hot water introduced into the calorimeter from 460 gr. at 30° C. to 
102 gr. at 90° C., with a corresponding variation in the initial water content of the 
calorimeter, and in the temperature of the walls above the water level. In spite of 
the great care taken in reading the thermometers and applying all corrections to 
0°’001 C., the results of consecutive observations under the same conditions often 
differ by 2 or 3 parts in 1,000, especially near the ends of the range. This is probably 
due to the uncertainty of heat loss or gain during the transference of the hot water 
to the calorimeter, of which no account could be taken. Such gain or loss would 
