536 MR A. CRICHTON MITCHELL ON THE THERMAL CONDUCTIVITY 



probably of no great importance) is concerned. It is clear that its effect will 

 be to make the rate of cooling a little too small at the lower, as compared with 

 the higher, temperatures. 



Another defect, which indeed Forbes pointed out, is due to the very small 

 temperature-gradients towards the colder end of the long bar. Mr Mitchell 

 has carried out my suggestion of an artificial cooling of the middle of the bar, 

 and it is highly interesting to compare together the results he has obtained 

 with and without this cooling. 



Angstrom expressly stated (Pogg. Ann., cxviii. 1863) that no account 

 need be taken of the change of specific heat with temperature. In my paper 

 above referred to, I said that it appears that, in iron especially, this change 

 produces a very considerable effect on the estimated values of the conductivity. 

 In default of better data, Mr Mitchell has used those given (after Nicol and 

 others) in a short paper in Proc. R. S. E., p. 126, 1880-81, and in my Heat, § 246. 

 The importance of this correction is shown by the comparison of the results 

 obtained from it with those obtained when it is not applied. Mr Mitchell's 

 experimental results are given in such a form that any subsequent improve- 

 ment in these data can be taken advantage of without further experiment, and 

 with very little trouble in the matter of calculation. The fact that the various 

 short bars were exactly similar in surface in his experiments has enabled him 

 to make a rough test of the accuracy of these data. 



In the short paper above referred to, I showed, that the consideration of 

 the rise of specific heat with temperature would destroy if not overcome the 

 apparent fall of conductivity of iron at higher temperatures. But I had not 

 then the means of properly applying the correction without repeating about 

 one-half of the laborious calculations incident to Forbes' method. Mr Mitchell 

 has in his calculations taken account of this consideration : and it must be 

 regarded as one of the chief features of his paper that he has thus shown that 

 iron does not form an exception to the law that ordinary metals improve in 

 thermal conductivity as their temperature is raised. 



As I am responsible for the methods employed by Mr Mitchell in the 

 experiments and calculations, though not for the calculations themselves, I 

 must state here the directions given and the grounds for them, at least in so 

 far as they introduce processes differing (to any considerable extent) from those 

 used by Forbes or by myself. 



1. As to the empirical formula (B) for the statical curve, in the special 

 case of the iron bar when there was no artificial cooling. 



This I obtained by plotting the logarithms of the temperature excesses as 

 ordinates, the abscissa? being distances along the bar. The curve so obtained 

 was nearly straight at the lower temperatures, and became rapidly more curved 

 at higher temperatures. I therefore treated it as a branch of a hyperbola, and 



