94 Mr. W. Duddell: Znstruments for the Measurement 
(3) Thermal Instruments.—Probably instruments depending 
on the heating produced by the current are as much used us 
any others for measuring alternating currents. If the re- 
sistance of that part of the instrument which is heated by the 
current is constant, then the mean rate of production of heat 
is accurately pr oportional to the mean square of the current. 
If this rate of production of heat can be accurately measured, 
then we obtain an ammeter whose accuracy is entirely inde- 
pendent of wave-form or frequency, and whose calibration is 
the same for both direct and alternating currents, with the 
further advantage that the instrument is unaffected by mag- 
netic fields, and can be constructed practically non-inductive. 
There would seem, at first sight, to be a very large number 
of ways of accurately determining the rate of production of 
heat ; but this is not the case if the watts lost in the instru- 
ment are kept small, as this corresponds to a small rate of 
preduction of heat which is difficult to measure. In practice 
the methods of measuring the rate of production of heat have 
been reduced to four, viz.:—The linear expansion of the 
heated wire. The expansion of a gas or liquid near or sur- 
rounding the wire. The measur rement of its change in 
resistance. The measurement of the temperature by means of 
a thermocouple. 
It must be noted that in all these methods what is actually 
measured is a rise in temperature and not the rate of pro- 
duction of heat, which is really required, the assumption being 
that when the steady state is attained and the heat losses froin 
the wire or other heated part equal the rate of production of 
heat, then the heated part will be at a definite temperature 
above some other part of the instrument. This fact that what 
is really measured is a difference of temperature, and not the 
rate of production of heat, is the cause of most of the defects 
of thermal instruments. The main defects are the following:— 
Slowness of action caused by having to wait till the steady 
state is attained. 
Creep of zero caused by change of temperature of sur- 
rounding bodies. 
Comparatively large power required to work the instrument 
due to the creat inefficiency of converting electrical 
energy into ‘heat and then reconverting the heat into 
mechanical energy to move the pointer. 
Temperature errors caused either by the resistance of the 
heated part varying with temperature, or by the means 
of measuring the rate of production of heat not being 
independent of temperature. 
Easily destroyed by an abnormal current owing to the small 
mass and normally high temperature of the heated part. 
