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LX. On the Determination of the Variation of the Thermal 

 Conductivity of Metals with Temperature, by means of the 

 ■permanent Curve of Temperature along a uniform thin Rod 

 heated at one end. {Second Paper*.) 



To the Editors of the Philosophical Magazine and Journal. 



GrENTLEMEJS, 



I WROTE to you last May stating that I had made an 

 oversight in the beginning of the paper on Thermal Con- 

 ductivity which you published in the March and April Num- 

 bers of the Philosophical Magazine, and promising to go 

 through the calculation again and make the necessary correc- 

 tion as soon as I conveniently could. 



The slip consisted in setting out with the ordinary equation 

 to the curve of permanent temperature down a rod 



d?0 = lKp 



da? ~ kq 

 which is true when k is constant, and working with it as if it 

 were equally valid when k is assumed to be variable. The 

 oversight was inexcusable, because in § 2 of the paper referred 

 to I indicated, for the sake of completeness, the ordinary way 

 in which this fundamental equation is obtained, and I thought- 

 lessly wrote the gain of heat per second by an element of the 

 rod at a distance x from the origin as 



as usual, instead of what it obviously becomes when k is not 

 considered constant, 



77 de 



dkq T*'> 



and this slip it is which necessitates my troubling you with the 



following further communication on the subject, and requires 



an apology from me both to you and to your readers. 



dk 

 The term containing — ^ which I omitted is but a small one, 



however, and does not make very much difference to the 

 result : hence the sections 16-20, though superseded by the 

 present communication, are not exactly incorrect, but are first 

 approximations ; and the curve A spoken of in § 21, and 

 drawn in Plate X., does represent the character of the curve 

 of temperature down a long iron rod in vacuo, with one end 



* Communicated by the Physical Society, as a correction of the first 

 paper. 



