OF IRON, COPPER, AND GERMAN SILVER. 537 



found its asymptote. Thus the form of the empirical expression was suggested 

 at once. 



2. The allowance for the unequal heating of the stems of the thermometers 

 was obtained thus : — 



Let v be the observed temperature (not the temperature excess), w the true 

 temperature, and in accordance with § 10 of my paper e = 10/250 2 = - 00016. 

 From the result of Mr Mitchell's comparison of the two thermometers, one 

 partially, the other wholly, immersed in a paraffin bath, I have been confirmed 

 in my assumption of an error of 10° at 250° C. Then we have 



w = v + ev' 2 . 



Thus, for the true temperature-gradient in the statical experiment, 



dw . dv - 



dx dx 



Similarly, for the true rate of cooling, we have 



dw . .dv 



di = (1 + 2ev) dt- 



The quantities on the right-hand sides are given by the experiments, or 

 deduced directly by graphical methods or calculation. 



For the statical curve of cooling it is easy to see in this way that each instal- 

 ment of area must be multiplied by 



1 + 2, ^p, 



where v x and v 3 are the limiting temperatures of the instalment. 



It is clear that this correction increases the gradient at any point of the bar 

 in a greater ratio than that in which it increases the total area of the corre- 

 sponding part of the curve which expresses the flux of heat ; so that its effect 

 must be to diminish the estimates of conductivity at higher, more than at lower, 

 temperatures. 



3. I was much surprised at the first results obtained by Mr Mitchell for 

 the rates of cooling at high temperatures. At my instance he has repeated 

 this part of the experiment in a form similar to that which I had employed, 

 and certainly less likely to entail error, and the data thus obtained have been 

 incorporated in the paper, in so far as they relate to the specified tables. [The 

 remaining small difference between our results may be due to an over-estimate 

 in my 6 p.c. reduction for oxidation.] 



4. There still remains a possible source of error, due to the thermometers 

 themselves: — Kew Standards though they be. This arises from the way in 

 which the 200° C. and 300° C. points were determined at Kew. The 



