546 MR A. CRICHTON MITCHELL ON THE THERMAL CONDUCTIVITY 



It may be remarked that once the standard experiment, along with, say, two 

 other decidedly trustworthy experiments, is chosen, and the three represented 

 by a curve in the manner already described, we have therein furnished a. test of 

 the correctness of the others ; indicated by the extent to which they agree with 

 the first, By this means, the calculator is enabled to set aside as less trust- 

 worthy, certain of the experiments. The only discrepance, which falls to be 

 reported in this connection, between the several experiments on the same bar, 

 lies in the uncertainty connected with the representation by the curve of the 

 temperature excess at the cool end of the bar. Here it was somewhat difficult 

 to trace the curve accurately, and to determine the point on the bar where, for 

 all practical purposes, at least, the temperature excess disappears. An error 

 of a tenth of a degree is quite sufficient to cause this doubt. This circumstance 

 argues strongly in favour of the adoption of that modified form, already 

 detailed, of the long bar experiment, viz., where the bar is cooled midway by 

 the application of a cold water bath ; for in this case there is no dubiety what- 

 ever as to the point where the horizontal axis is crossed by the curve of 

 temperature-excess. 



Regarding the equation representing the curve, two formulae were 

 employed : — 



logtf = logA- I: ^ (A) 



}ogv = logA+-^-ea; (B) 



where v = temperature excess, 



x = distance along bar, reckoned from any 

 arbitrary origin ; and where 



A, b, c, and e are constants. 



The formula (A), involving three constants, originally employed by Regnault 

 (Mem. Ac. Sci., vol. xxi.) to represent the relation between the temperature 

 and pressure of saturated water- vapour, was that used by Forbes and also 

 by Prof. Tait, to represent the curve of temperature-excess in iron. But the 

 differences between the calculated and observed values of v, both as shown by 

 the tables in Forbes' last paper, and also when used by myself, were such as to 

 lead to the construction, for use in this work, of the empirical formula (B). It 

 was constructed by Prof. Tait to suit as closely as possible, by four disposable 

 constants, the curve plotted from the logarithms of* the temperature excesses 

 obtained in one of my earlier experiments on Forbes' iron bar. For the iron 

 curve, it has been found to work very well, and certainly much better than its 

 predecessor. But in the case of both copper bars and German silver, as well 

 as the iron bar cooled midway, the equation (A) has been found to be more 

 applicable, and has accordingly been used. In some cases it was found better 



