20 
PEOF. H. L. CALLENDAE ON THE VAEIATION OF THE SPECIFIC 
thermometers at different temperatures in rapid succession. It was important that 
the sensitiveness of the galvanometer should be the same for each, and it was 
desirable that the rise of temperature produced by the measuring current should be 
nearly the same for each thermometer. This last condition is approximately secured 
by keeping the current constant. ChapPuis and Harkee (‘ Phil. Trans.,’ A, 1900, 
p. 62 ; Callendar, loc. cit., p. 93) proposed to do this by keeping the watts 
constant, adjusting the current C to suit the value of R. But the emissivity of the 
wire increases somewhat more rapidly than R, so that the rise of temperature due to 
C at different points of the scale is nearly proportional to C^. The rise of temperature 
produced by a current of O'OOS ampere at 30° C. was measured and found to be 
0°‘0066 C. The rise at 100° C. was found to be 0°'0063 C. Assuming that the 
variation between these limits was regular, it was evident that it could not produce a 
systematic error of the temperature scale greater than 0°’0001 C. between the limits 
0° C. and 100° 0. In measuring the mean specific heat over a range of 30° C., a 
limit of accuracy of 0°'001 C. in the. thermometric readings appeared to be ample, 
because this would amount to only 1 in 30,000 of the heat measured, and it was 
hardly to be expected that the external heat-loss could be determined with a much 
higher order of accuracy than 1 in 10,000. 
Theory of the Continuous-Mixture Method. 
If X is the external heat-loss in calories per second, and Q the water current in 
grammes per second, the equation connecting the mean specific heats ^ 4,3 over the 
ranges h to t^ and ^4 to t^ for a single value of the flow Q is evidently 
^1,2 (b b) ~ '^4,3 (b b) +X/Q.(7) 
If the heat-loss X could be neglected by sufficiently increasing the flow, this equation 
would give the required ratio of the specific heats directly, being simply the inverse 
ratio of the temperature ranges. In any case, if X is small and Q large (say 10 to 
20 gr./sec.), this would give a good first approximation, better than 1 in 1,000 if X is 
less than 1 in 1,000 of the whole heat exchange. Assuming that the temperature 
distribution in the exchanger, and consequently the heat-loss X, does not vary 
appreciably when the flow is changed within reasonable limits, a second approximation 
could easily be secured by employing the first approximation to evaluate the heat-loss 
for a small flow, say 1 gr./sec., and employing the value so obtained for the large 
flow; or the heat-loss X might be directly eliminated by subtracting one equation 
from the other if the temperature ranges were so nearly the same that the values of 
the mean specific heats could be assumed to be the same for the small flow without 
sensible error. This method of reduction would undoubtedly give good results if the 
losses were small. In practice, however, it is impossible to secure exact similarity in 
the temperature distribution for flows varying in the ratio of 10 to 1 , and it is, 
