CONTINUOUS ELECTRIC CALORIMETRY. 
123 
flow-tube is exactly compensated by the increase of resistance of the conductor with 
rise of temperature. I made use of this relation in some experiments on conduction 
of heat in metals by an electrical method with Mr. King in 1895, and also in some 
experiments on the conduction of heat in liquids, § 31, in which the elimination of the 
heat-loss was a matter of some importance as simplifying the differential equation. 
In the calorimetric experiment, the constancy of the gradient along the tube was 
not a matter of primary importance, provided that the temperature distribution was 
approximately the same for different flows. Moreover, the relation could not apply 
accurately to both the flows required in the experiment. Nevertheless, I thought it 
worth while, in designing- the dimensions of the calorimeter and the details of the 
experiment, to arrange that the compensation might hold for a value of the flow 
between ‘5 and l'O gramme per second in the water experiment, as nearly as it 
could be estimated beforehand. The gradient would then be nearly constant, and 
the mean temperature of the flow-tube nearly half the rise of temperature observed 
with the differential-thermometers. 
(35.) Application to the Mercury Experiments. 
Neglecting for the present that part of the heat-loss which occurs in the outflow- 
tube before the liquid reaches the middle of the thermometer bulb where its 
temperature is measured (which loss is a comparatively small fraction of the whole 
in the mercury experiment), the systematic error of the elementary theory given by 
Dr. Barnes, p. 152, consists in assuming that the mean temperature of the flow-tube 
is always the same for the same rise, or that the gradient is indejiendent of the 
How. This is equivalent to assuming the mean temperature of the flow-tube equal 
to 6i/2 instead of d m . The error of this assumption may be approximately estimated 
from equations (4) and (5) above, which give 
6 », ~ (1 + A.l/ 6 ) 0//2 .( 6 ). 
If we write (as in Barnes, p. 242) dd for the whole rise of temperature observed 
by the differential thermometers, and h dO for the heat-loss, we must then regard h 
as variable with the flow, since the heat-loss is really fpid,„. We thus arrive at the 
expression, 
Heat-loss = fpld m = fpl (1 fl- A// 6 ) di/ 2 = h 0 (1 fl- A// 6 ) dd . . . ( 7 ), 
in which dd is written for d ( , and h 0 is the value of the heat-loss per degree rise 
when the gradient is constant (A = 0), namely fpl /2. 1 We have also, to the same 
order of approximation, 
A l = 2/< 0 /J.5>Q — a dd 
R 2 
(8). 
