RESEARCHES IN THERMOMETRY. 571 
From the means of all the results we obtain the equation : 
a ='00014148 + -000000037880N . 
In other terms, for equal increments of exposure, z receives equal increments 
in value. The comparison is— 
N. az Found. x Cale. Diff. 
105°19 00014498 00014546 + 00000048 
202:28 | 15014 14917 — 97 
300°81 15239 15284 + 45 
The probable error of a single determination of the middle tabular co- 
efficient ‘00015014 is (0000063155, or 4:21 per cent. ; of the mean of the sixteen 
determinations, ‘0000015790, or 1:05 per cent. 
Similar experiments, of about the same value, have been made with other 
similar thermometers. The resulting equations are : 
Therm. Equation. 
2) «='00013197 +-000000057030N , 
+ #='00012513 +-000000058727N , 
6 x="'00013427 +:000000058547N . 
The values of y agree first when N has the following values :— 
Therm. N. 
Z 0-0, 
3 166°0 , 
4 2786), 
6 123°2 . 
Thus each thermometer is proved to have its own independent equation for 
exposure correction ; and the general equation to y, the correction is— 
y=(a+BN\(T—A)N. 
For all ordinary purposes, and certainly for short exposures, we may take 
the mean of the above four equations ; and thence, in terms of the centigrade 
scale, 
y = (00013321 + :000000013261N)(T—aN . 
Thus, if we suppose (T—Z) to remain constant, the correction is proportional 
to the square of the length of scale exposed; and the relation between them 
is graphically represented by a parabolic curve. 
