CONTINUOUS ELECTRIC CALORIMETRY 
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(34.) Correction for Variation of the Temperature-Gradient in the Floiv-Tuhe. 
The elementary theory of the elimination of the heat-loss in the steady-flow method 
of calorimetry assumes that, if the electric current and the flow of liquid be simul¬ 
taneously varied in such a manner as to keep the rise of temperature the same, the 
heat-loss by radiation, &c., will remain constant. Dr. Barnes (p. 225) has quoted 
experiments to show that this condition is very closely satisfied in the present method, 
and has calculated all the results of the investigation on this assumption. It will be 
noticed, however, that there are small systematic divergences in the experimental 
verification for the small flows, which, though amounting only to a few parts in 10,000, 
require careful examination as possible indications of constant errors. 
So long as the distribution of temperature throughout the apparatus is accurately 
the same for the same rise of temperature, whatever the flow, the heat-loss must also 
be identical. But if there is any systematic change in the temperature distribution 
with change of flow, then there must be a corresponding systematic difference in the 
heat-loss, which will lead to constant errors in the calculation if no account is taken 
of it. A possible source of error of this type is loss of heat by conduction along the 
outflow-tube. When the flow is large, the heated liquid passing along the tube will 
keep it nearly at a uniform temperature, so that the gradient in the outflow-tube will 
be small, and the conduction loss correspondingly minute. As the flow is diminished, 
supposing the temperature of the outflow to remain the same, the gradient in the 
outflow-tube must increase in proportion to the reciprocal of the flow, since the 
radiation-loss remains nearly the same. The conduction-loss will vary directly as the 
gradient, ,or inversely as the flow, for a given rise of temperature. 
A small error of this kind, due to conduction, was detected at an early stage in the 
mercury-calorimeter, owing to the large mass of mercury in the flow-tube, the small 
rate of flow, and the relatively high thermal conductivity of the liquid. It was 
practically eliminated by filling the greater part of the outflow-tube from the end of 
the vacuum-jacket with paraffin wax, leaving only a small passage for the outflow of 
mercury. This made the conduction-loss very small, and nearly independent of the 
flow. In the water experiment it is easy to see that the conduction loss must be 
practically negligible in any case, but special pains were taken to make it as small as 
possible, and to verify its non-existence. 
A more important correction of this type is that due to variation of temperature 
gradient in the fine flow-tube, which can be estimated with considerable precision. 
As the liquid flows along the tube it is receiving heat at a nearly uniform rate from 
the electric current, but it is also losing heat more and more rapidly by radiation as 
its temperature rises. As a result, the mean temperature of the fine flow-tube, upon 
which the radiation-loss chiefly depends, usually exceeds the mean between the initial 
and final temperature by an amount which varies, to a first approximation, inversely 
as the flow. 
VOL. CXCIX.-A. 
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