G04 
DE. J. T, BOTTOMLEY ON THERMAL 
is to solve the equation above as though e were constant—which is, of course, 
approximately true if the ditference of temperatures is small—and then to determine, 
numerically, the value of e at different places in the temperature scale, taking an 
exact account of the circumstances. When a sufficiently large number of such values 
have been obtained a basis for a proper theory will have been laid in a logical way. 
This is practically what I am endeavouring to do. 
Taking, then, the equation 
- = eS (^ - v^), 
and its solution 
V — V, 
where v is the temperature of the cooling globe when t = 0, we have for the 
numeiical calculation of e 
e = [Ic'ge (y - 'f’u) - log. 
or, using common logarithms, 
e = [log (ff - - log {v -'Vq)]. 
Here t = 300, the intervals of time used in my experiments being 5 minutes; 
c = 28'31 and S = 50'26, with an addition which, for the present, I roughly estimate 
at about 0'6 per cent.—the correction applied for the carrying away of heat by the 
conducting wires. This I calculate, assuming that the emissivity of the surface of the 
conducting wires is much the same as that of a tolerahly clean silvered surface. 
The following tables and curves (Plate 18) show most of the numerical results 
obtained. The tables are made self-explanatory, as far as possible, by means of suitable 
headings ; and the curves which I have drawn corresponding to most of the series are 
dated, and the multiplier is given for reducing the ordinates to C.G.S, measure. 
The curves were drawn chiefly for my own satisfaction ; but there are one or two 
matters to which I may be permitted to call attention. 
In the first place, it will be seen from the curves that in each series the results are 
in very exact accordance. Certainly they are more so than I ventured to hope when 
I commenced putting them down. The difficulties surrounding experiments of this 
kind are really very great, if anything more than rough approximation is aimed at; 
and, unfortunately, uncertainties connected with the temperature measurement easily 
creep in, and are difficult to detect till it is too late to remedy them, or even to 
determine the limits of possible error. 
The different series of determinations represented by the several curves are also in 
agreement, and some of them, as, for instance, those of March 7 and 10 (silvered 
globe in air), and those of October 29, 1889, and April 2 and 8 (sooted globe in 
vacuum), are quite unexpectedly close to each other. There are differences between 
