152 MEASUREMENT OF HIGH TEMPERATURES. Ibull.54. 
Having therefore obtained some general notions of the dependence 
of f(0) :/(0) on/(0), it is next in place to endeavor to inquire into the 
form of dependence of these two classes of experimental data on each 
other. With a view of arriving at as simple a relation as possible I 
have tested the hyperbolic equation — 
if(0)+l)(f(0):(f(0)+m)=:n (I) 
which contains three constants, and for the computation of which three 
pairs of values of/(0) and/'(0) :/(0) suffice. These may be taken from 
the figure, with some care as regards the judicious selection of points, as 
follows : 
/(0)=11.7 f (0) :/(0) 0.00300 
20.0 0.00164 
60.0 0.00050 
If we denote /(0) and /'(()) :/(0) for a moment by x and y, the values 
of I and m have the general forms 
1_(x—x")(xy—x'y') — (x—x')(xy—x"y") , 9 . 
~(y-y")(x-x')-(x-x")(y-y') * ' ' ' l | 
m = - (y— $")(*! !— x f y')—(y—y')(®y-x"y") (3 \ 
{y-y")(x-x')-{x-x")(y-y') ' \ 
which, together with equation (1) for the special values of x and y, lead 
to the constants 
l = -0.1360 m=0.0002548 ^=0.03764. 
Moreover, the curve 
(/(0)_0.1360)(/ / (0):/(0)+0.0002548)=0.03764 . . . (4) 
does not differ appreciably from the curved line which, in Fig. 26, has 
been accepted as the locus of the larger black dots. 
Equation (4), however, is exceedingly significant. Inasmuch as/(0) 
varies between 10 and 70, I is generally considerably less than 1 per 
cent. of/(0). Equation (4) therefore emphatically suggests that a sim- 
pler form of equation be assumed, in which 1=0. Equation (4), how- 
ever, contains still another striking suggestion. The positive character 
of the constant m indicates that a larger value than a m , or the mean 
temperature-coefficient between zero and 100°, will tend to further 
simplify equation (4). Now, since, generally, <V 00 ><*o 356 ? it follows that 
f(0):f(0) = a>a ™. 
Hence, with these modifications implied, 
/(0)(/(0):/(0) + w)=» (5) 
will in all probability hold good for the observations as a whole even 
more nearly than (4). 
(806) 
