iunus.j CALIBRATION OF ELECTRICAL PYROMETERS. 103 
cause of this variation may be sought for iu the composition of the mixt- 
ures. I have, moreover, kept the paste wet with a layer of zinc sul- 
phate, in this way decreasing the internal resistance. In the case of 
zero work, standards with enormous internal resistances are undesirable, 
because all necessary resistance is introduced by the rheostats. I made 
a number of experiments to study the dangers due to polarization in the 
batteries, and it is the outcome of this work that the large resistances 
in the connections have been retained. The data themselves are su- 
perfluous here. 
METHOD OF COMPUTATION. 
Many experiments go to show that the quadratic relation 
e=a(T-t)+b(T 2 -l 2 ), 
where e is the electro-motive force for the temperatures T and t of the 
junctions of the thermo-element and a and b are constants, is a very com- 
plete interpolative equation, so long as the temperature Tis not too far 
above red heat. In general, however, it is desirable to express e graphic- 
ally for each element. The method of measuring e has just been indi- 
cated. T is the temperature given either by some known high boiling 
point or by direct evaluation with the air-thermometer, while t is di- 
rectly read off by a mercury thermometer. If the graphic chart thus 
obtainable is subsequently to be used for temperature measurement, it 
is desirable to refer all values of e to e 20 , i- e., to the electromotive force 
which obtains when the hot junction is at T°, the cold junction at 20°. 
This correction follows easily from equation (1), for if 
e =a(T-t) +&(T 2 -f), and 
e 20 =:a(T-20)+b(T 2 -2tf 
% 
e w -e=a (t-20) +6 (£ 2 -4Q0). 
The constant a and b may be determined from the steam and mercury 
vapor calibration. A table is then to be constructed for the correction 
e 2(i —e as varying with t. By adding this to any given value of e the 
temperature results are at once comparable with the values of the chart, 
in which e is represented as a (unction of T. t should of course be kept 
as near 20° as possible. 
In the measurement of e, a small table in which the log r is once for 
all inserted for each r, and another in which the log E is inserted for 
each i£, greatly expedite the computations. 
My original plan of calculating the constants of e as a function of T 
and t by the method of least squares was soon abandoned. These con- 
stants do not represent the function truly, and since many calibrations 
are to be made the computation becomes excessively laborious. Finally, 
Tcan be taken from the interpolation chart quite as accurately as it 
(757) 
