THERMAL CONDUCTIVITY. 21 



that the flux of heat is directly proportional to 6 1 2 . 

 This law is not exactly correct, but tolerably near so, and 

 it will be sufficiently accurate if we still define conductivity 

 in the way I have done, and for that the conductivity is 

 not a constant quantity, but varies slightly with the tem- 

 perature. Nevertheless, these assumptions were sufficiently 

 near the truth to give very accurate results with proper 

 apparatus. Some experiments of the same kind had been 

 made previously by M. Biot. He had employed bars of 

 different metals about eight feet long, and the results 

 which he got were perfectly different from the results 

 which Despretz got, and in a most valuable examination of 

 oui- knowledge about conductivity, which was made by 

 Professor Kelland in 1840 in a report to the British Asso- 

 ciation, he was led to investigate the different causes which 

 might contribute to this difference between Despretz and 

 Biot, and he arrived at the conclusion that the only cause 

 could be that M. Despretz's bars were too short, and that 

 their extremities were not at the temperature of the 

 air, that is, that the bars were not sufficiently long to 

 answer the conditions of Fourier's problem. He said 

 Despretz does not mention what the length of these bars is 

 that he used, and I myself have not the means of examining 

 them. This has been the condition in which Englishmen, 

 remaining at home, have been ever since this report of 

 Professor Kelland in 1840 until the present summer, and 

 this is the first opportunity we have had here of deter- 

 mining whether Kelland's suggestion was true ; but I have 

 not the slightest hesitation in saying on seeing these bars 

 of M. Despretz, that they were very much too short to 

 have given that permanent state of temperature such as 

 was required by Fourier's theory. Consequently, this 

 extremely acute suggestion as to the difference in the 

 results of M. Biot and Despretz is, I think, wholly con- 

 firmed by the exhibition of this apparatus which we have 

 here. 



Fourier applied his theory to a variety of special cases. 

 He pointed out also that since the temperature of the 

 earth increases as we descend to greater depths under the 

 surface, it follows that heat must be continually being lost 

 from the body of the earth, because this difference of tem- 

 perature could not be maintained unless \iiere was a flux of 



