CONTINUOUS ELECTRIC CALORIMETRY, 
I 15 
The mean temperature 0. 2 of the outflow deduced from (8) is given by 
0 O ~ = Ar : 4 log, (rj/r 0 )/S — Ar^/2 - AS/4 .... (10), 
where S is the sectional area n (rq 2 — r 0 2 ) of the flow, and A = Q0' /27r/IS. Equation (10) 
gives the superheating of the conductor above the mean temperature of the outflow. 
The difference (9)-(l0) gives the error of the assumption that the glass is at the 
same temperature as the mean of the outflow at the outflow point. The limiting 
value of the latter error, if r 0 2 is negligible in comparison with rf 1 (the most 
unfavourable case), is 0. 2 — 0 X = AS/4 = Q0'/8Trlk. 
Although the above formulae cannot be directly applied to the experiments on the 
specific heat of water, it is interesting to make an estimate of the superheating of 
the conductor, and of the difference of temperature between the glass and the water 
under the assumed conditions of linear flow and concentric conductor. It is obvious 
from the formulae already given, that the differences of temperature in each case are 
directly proportional to the heat supplied by the electric current, and inversely 
proportional to the length of the tube and the conductivity of the liquid. To 
estimate the effects numerically, we may take the rate of heat supply as 
Qff = 5 calories per second, or 21 watts, for the larger flows. The conductivity k of 
water at 25° C. may be taken as ‘0016 C.G.S., but is much too uncertain to permit 
the estimate to be extended to other temperatures. Since l = 50 centims., we have 
inlk = l'OO very nearly. 
For the metallic flow-tube from equation (6) the superheating of the tube above 
the mean temperature of the flow in the limiting state would be about 5° C., and 
would be independent of the diameter. For the glass flow-tube, from equations (9) 
and (10), the temperature of the glass would be from 1 0, 5 to 2" - 0 below the mean of 
the outflow for tubes of the dimensions employed, increasing to 2°‘5 as a limit for a 
very large flow-tube with a very small conductor. In spite of its higher temperature 
the metallic flow-tube would have the advantage of a smaller heat-loss, owing to its 
smaller surface (l millim. diameter instead of 6 millims.), and far lower radiative 
power. It would also be possible to measure the actual temperature of the metallic 
flow-tube at any time from its resistance, without any knowledge of the conductivity 
of the liquid, and without assuming the flow to be linear. 
The superheating of the conductor in the glass flow-tube would naturally depend 
on the size of the conductor as well as that of the tube, as given by equation (10). 
With a wire '8 millim. in diameter, and the flow-tube 2 millims., the superheating 
of the wire would be about 4°‘5 for a heat supply of 21 watts. With a wire ‘4 millim. 
diameter, and a 3 millims. flow-tube, the superheating would be about 13 0, 2. 
This illustrates the importance of having a large surface for the wire and a small 
flow-tube. It is probable, however, that the superheating would not directly affect 
the radiation loss, as platinum is a bad radiator, and water is very opaque to heat- 
rays from heated water. 
