12 
PEOF. IT. L. CALLENDAR ON THE VARIATION OF THE SPECIFIC 
l)eiiig obtained by differentiation, has an inferior degree of accuracy, which he sets at 
0’3 per cent, in the neighbourhood of 100° C. The curve marked Dieterici, in fig. 3, 
represents this forniida reduced to a unit at 20° C. by dividing lyy the factor 0'9974, 
representing his value at 20° C. Dieterici employs this formula for the actual 
specific heat, s^, in calculating the values given in his table down to a temperature of 
25° C., although it does not strictly apply below 35° C. Below 25° C. his values for 
the specific heat are calculated in a different way, but agree so closely with my 
formula that his curve could not be shown separately. This agreement is very 
satisfactory, but gives rise to a somewhat sharp change of curvature at 25° C., which 
is repeated at 35° C. in his formula for the mean specific heat, and introduces some 
uncertainty in the interpretation or application of the taludated results. Below 
35° C. his talde of mean specific heat appears to represent his experimental results 
between 35° C. and 20° C. (neglecting the discordant observation at 14°’6 C.) with an 
almost linear extrapolation which follows my curve very closely from 20° C. down to 
0° C. Values of the actual specific heat calculated from this table show a rapid fall 
from 1‘0075 at 0° C. to 0‘99I2 at 30° C., and a sudden jump from beloAv 0'9900 up to 
the value 0'9973 at 35° C. If, on the other hand, his table of actual specific heat is 
taken as the basis of calculation, the value of the meau specific heat from 0° C. to 
40° C. comes out 0'9992 in place of 0'9973, given in his other table. The observations 
themselves do not afford any valid evidence for the existence of these discontinuities, 
which might prove very troublesome in the practical application of his tables. A 
single continuous formula, such as (G), presents many advantages in tliis respect, 
especially for representing observatioiis on the mean specific heat, which ought not to 
show sudden changes of curvature. The deduction of the true specific heat at any 
temperature from the mean specific lieat is most uncertain in any case, and the 
observations cannot be said to support the minimum at 25° C., shown in Dieterici’s 
curve for the actual specific heat. The uncertainty in the reduction of the results 
from 0° C. to 35° C. must afiect the whole form of tlie curve, and even the apparent 
discrepancy of 0’4 per cent, at 100° C., shown in fig. 3, does not exceed the limits of 
possible error in the calculation. 
Apart from variations in the fundamental constant (depending possibly on the 
quality of the ice formed), and uncertainty of tlie correction for creep of zero, which 
might give rise to accidental errors, the main source of systematic error in Dieterici’s 
method would he in tlie correction for the water equivalent of the quartz-glass bulbs, 
and in loss or gain of heat during transference from the heater to the calorimeter. 
The water equivalent of each bulb was calculated from its mass by means of a formula 
for the variation of the specific heat of quartz, which is appropriate if there is no 
heat-loss in transference. It appears probable, however, that bulbs of different form 
and thickness would experience different losses in transference. In fact, a small 
systematic error of this kind is indicated bj^ the observations themselves, and might 
produce appreciable errors at the higher temperatures. 
