pfBus.] DEGREE OF CONSTANT TEMPERATURE. 81 
very closely to the mathematical examination of a function for conti- 
nuity. 
If any equation between electromotive force and temperature, such 
a one, for instance, as e=a(T—t) + b(T 2 — tf 2 ), were rigidly true for all 
ranges of temperature, T, then our methods would enable us to calculate 
the constants a and b from measurements of e, T, t, made at tem- 
peratures not exceeding the boiling point of mercury, with a degree of 
accuracy which would introduce a perceptible error only at very much 
higher temperatures. If the thermo-electric equation hold, in other 
words, the calibration of a thermocouple throughout an interval of tem- 
perature within which a glass-bulb air thermometer is quite available, 
would enable us satisfactorily to measure temperatures lying in the 
regions of white heat. But such extrapolation is unwarranted because 
we possess no known criterion for the temperature above which the 
assumed equation appreciably fails. 
In our original endeavor to surmount this difficulty we ventured to 
reason as follows : Suppose there be given a series of thermo-couples of 
the kind specified, in all of which platinum is the electro-positive metal 
and the platinum alloy the negative metal. In such a series the con- 
stants a and b both vanish with the amount of foreign metal alloyed to 
platinum. Hence the relation between electro-motive force and temper- 
ature is ultimately linear, and, a fortiori, within the limits prescribed by 
the foregoing paragraph, the assumed equation will apply more accu- 
rately as the couple approaches the final couple platinum-platinum, 
from which the foreign metal has been wholly eliminated. If the quad- 
ratic equation (1) is more than an empirical relation, it would be practi- 
cally sufficient at an earlier stage of progress ; i. e., it would be practi- 
cally sufficient for couples lying between platinum-platinum and a 
couple the electro-negative part of which contains a certain determinate 
addition of the foreign metal of the series under consideration. To 
illustrate the manner of using such a principle, let a series of couples 
whose constants are known from a calibration between 0° and 350° be 
in hand; and then let a given fixed temperature (the boiling point of 
zinc for instance) be determined by each of them. There will be as 
many values for boiling point as elements. If we regard these as func- 
tions of the respective quantities of foreign metal in the negative parts 
of the couples, and if we represent the calculated boiling points as ordi- 
nates, and the percentage compositions of the alloys as abscissa*, we 
obtain a locus the nature of which may be sufficiently obvious to enable 
us to prolong it as far as the axis Y. The point of intersection, there- 
fore, approaches very closely to the datum of the hypothetical element 
platinum-platinum. 
If the effect of alloying metals were merely that of joining them in 
multiple arc, the interest which belongs to the problem in hand would 
at once vanish. 
For if ei and e 2 be the electromotive forces of two wires thermo elec- 
Bull. 54 6 (735) 
