
728 PROFESSOR TAIT ON THERMAL AND ELECTRIC CONDUCTIVITY. 
temperatures) by a rough graphic method from my own numbers. The rates 
are in degrees C. per minute :— 
Rates of cooling of Iron Bar. 
Ratio. 
20° 0-275 0°29 1:06 | 
50° 0°80 0°85 1:06 
100° 1:84 1:95 1:06 
160° 318 3°45 1:09 
200° 3°78 4-60 1:22 
260° 4:52 6°50 1-44 
I have every reason to believe that Forses’ results, in this matter, for 
temperatures under 150° C. are more exact than mine, especially as his bar was 
not exposed to air during the heating. Thus it would appear that my numbers 
are, throughout, about 5 or 6 per cent. too high. The really vital difference 
between our results appears in the three last numbers in the column of ratios. 
[§ 11.* Added, January 1879. |—I was so well satisfied with the explanation 
given above, as in character thoroughly consistent with the observations, that 
I did not work out its numerical consequences. While the paper was passing 
through the press, however, I tried to estimate the time required for the dis- 
appearance of the abnormal state, and arrived at conclusions which are not quite 
consistent with this mode of accounting for the difference between ForBss’ 
results and my own. To make this statement intelligible, a short account of 
Fourier’s treatment of the problem is necessary. 
The equation for the cooling of an infinitely long cylinder, in which the 
temperature depends only upon the distance from the axis, is (assuming con- 
ductivity constant) 
Pun Lde\ de 
tGatia) =a 
This linear equation FouRIER integrates by assuming as a particular integral 
o Scere 
where w is a function of 7 only. We thus have 
du ldu .m 
ea Tee” 

The surface condition (assuming rate of surface-loss to be proportional to 
excess of temperature over air) is 
k (=),+ hii 10% 
From the first of these equations we have uw in terms of mand 7. The 
