68 MEASUREMENT OF HIGH TEMPERATURES. 
Hence in a couple in which the junctions are at temperatures T and 
t, we find by difference 
e=e T -e t =a (T—ty+b (T 2 -* 2 )-f-c (T 3 -f )+ ... (2) 
an equation which in most cases applies so fully that the terms of the 
right-hand member, whose powers of T and t are greater than the third, 
may be neglected. 
From equation (2) follows at once that 
— dT 
dT 
dT= a~+WT+tcT2+ . . (3) 
Inasmuch as the constants a, &, c, . . decrease so rapidly in mag- 
nitude that a mean or approximate value of T may be introduced into 
equation (3), it appears that in proportion as the increment of tem- 
perature becomes smaller it may be measured with the same accuracy 
with which the constants a, b, . . have been found. Methods of 
measuring e and of calibrating the thermo-element will be indicated in 
the next chapter. 
List of thermo-couples. — It is expedient to insert for future reference 
a list of the thermo-couples used for measurement here, In the first 
part of this table the wires are given in the order in which their thermo- 
electric powers, were originally determined. The other part contains 
the thermoelements used for temperature measurement. The table 
also contains values for the constants a and b in equation (1). In the 
case of Nos. to 15 the calibration interval is not larger than 0° to 
200° ; in the others as large as 0° to 400°, or 0° to 450°. The data are 
referred to a zinc sulphate Dauiell standard, the electro motive force of 
which is assumed to be one volt. Lord Kayleigh's recent value for 
this standard is 1.072 volt. Hence to reduce the data to absolute units, 
a and b must be increased 7.2 per cent. We have refrained from intro- 
ducing this correction in the first two chapters because the relative 
values of the data there given are alone of interest, and because of the 
confusion and labor which a reconstruction of the whole series of data 
and of graphic representations would involve. 
(722) 
