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XXXIY. 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. By Olivbe J. Lodge, JD.Sc., Lecturer 

 on Applied Mathematics and Mechanics at University College, 

 London*. 



[Plate X.] 



1. rf^HE approximate theory of the flow of heat down a 

 J- uniform rod heated at one end and exposed to cooling 

 influences everywhere else was, I believe, given by Biot before 

 the time of Fourier, and was also verified experimentally by 

 him. The " constants " occurring in Biot's equation to the 

 curve of temperature have long been known to be variable ; 

 and numerous experiments have been made to determine em- 

 pirically in what manner they depend upon the temperature, 

 Nevertheless Biot's method in its original form has been fre- 

 quently employed by subsequent observers in order to compare 

 the conductivities of different metals — by Ingenhousz for in- 

 stance, by Despretz, and even in the far more accurate expe- 

 riments of Professors Wiedemann and Franz. Principal 

 Forbes, on the other hand, devised and executed a method 

 which was quite independent of any equations to curves ex- 

 cept those deduced from experiment ; and by graphical and 

 other laborious methods he determined both the absolute con- 

 ductivity of wrought iron and its variation with temperature. 

 But, as far as I know, no recalculation of the curve of tempe- 

 rature with the improved data now accessible has been made. 

 It therefore seemed worth while to obtain as close an approxi- 

 mation to the equation of the true curve of temperature as is 

 practicable without cumbrous integration, and to see how far 

 the improvement affects the results of those experimenters 

 who, unlike Forbes, depended on the theoretical curve of tem- 

 perature. Moreover it seemed probable that the more accu- 

 rate equation to the curve would enable the variation in con- 

 ductivity of the rod with temperature to be calculated in some 

 moderately simple manner, and with far less labour than that 

 gone through by Forbes. Forbes's methods are perfect ; the 

 only objection to them is the excessive tediousness of the pro- 

 cess of discussing the experimental results. And as it is a most 

 important research at the present time to compare exactly the 

 law of variation of thermal and electrical conductivity in the 

 same piece of material, it seemed desirable to have some means 

 of calculating the law of thermal variation from some simple 



* Communicated "by the Physical Society, an abstract having been read 

 on the 8th of February, 1879. 



