CONTINUOUS ELECTRIC CALORIMETRY. 
93 
In differential work it is seldom necessary to take any account of current heating 
of the thermometers, unless the difference of temperature is considerable, or the 
thermometers are very differently situated. With a single thermometer, it is 
desirable to measure the heating effect occasionally, especially if a galvanometer of 
suitable sensibility is not available, or an excessive current is employed for any other 
reason. The simplest method of determining the rise of temperature due to the 
current in any case is to use two similar cells of low resistance, preferably storage 
cells, which can be connected in series or parallel by changing a switch. The normal 
measurements are effected with the cells in parallel. On putting the cells in series, 
the current through the thermometer is very nearly doubled, and the heating effect 
is nearly quadrupled, provided that it is small. The correction for current heating is 
obtained by subtracting from the first reading one-third of the difference between the 
two readings. I have used this method in all accurate work for the last ten years, 
and it appears to be worth recording, as there is some conflict of opinion with regard 
to the proper method of procedure. Harker and Chappuis measured the heating 
effect of the current on one of their thermometers at 0° C., and, assuming that the 
effect would vary as the watts expended on the coil, they adjusted the external 
resistance in the battery circuit so as to give always the same ivatts in the coil at 
different temperatures. This is not quite correct, since the cooling effect of 
conduction and convection-currents of air in the tube increases nearly in proportion 
to the absolute temperature. The effect of radiation also becomes important at high 
temperatures, and the cooling is then more rapid. If, therefore, the watts are kept 
constant, the heating effect will diminish as the temperature rises, and a small 
systematic error will be produced. Assuming that the rate of cooling increases as 
t 
the absolute temperature 9, and that the watts are kept constant, the heating effect 
at any temperature 9 is 273 h/9, where h is the heating effect in degrees of 
temperature at 0° C. It is easy to see that the corresponding systematic error in the 
temperature t on the centigrade scale, would be approximately ht(t — 100)/373(U-|-273). 
In the case described by Harker and Chappuis (‘ Phil. Trans.,’ A, 1900, p. 62), the 
heating at 0° C. was , 014° C. The systematic error at 50° C. would be only ‘0003°, 
and at 445° C. only '008°. 
A better rule is to keep the current through the thermometer constant. In this 
case the heating effect is nearly constant, since the resistance of the thermometer 
increases very nearly as fast as the rate of cooling, i.e., a little faster than the 
absolute temperature. In this case it is evident that the error would be negligible, 
even if the heating effect at 0° C. were as large as a hundredth of a degree. In any 
case, provided that a galvanometer of suitable sensibility is used, the error due to the 
heating effect will be practically negligible, even if no account is taken of it, i.e., if 
the resistance in the external battery circuit is kept constant. It is assumed, of 
course, that the current is kept flowing through the thermometer continuously, so 
that the heating effect is steady. Some -writers have advised keeping the circuit 
