144 PROCEEDINGS OP THE AMERICAN ACADEMY 



difference of their temperatures, but also upon the absolute tempera- 

 tures of each. Poisson published, in 1835, his ''Theorie de la Chaleur," 

 in which he assumed that the expression which Dulong and Petit had 

 given for the loss of heat from radiation also represents the passage 

 of the heat from molecule to molecule in the interior of the body. 

 Libri, shortly before Poisson's book was pu!)li>hed, presented to the 

 Academy of Sciences a paper in which he assumed that Fourier and 

 Biot were correct in their hypothesis that the internal flux of heat 

 could be written 



, dn 



dx 



but that the law of extra radiation was that stated by Dulong and 

 Petit. In 1837, Kelland published his "Theory of Heat." He 

 applied Libri's hypotheses to the problem of determining the final 

 distribution of heat in a ring, and showed that the solution thus 

 arrived at was not very different from that wliich Fourier had de- 

 termined. In other* respects, Kelland simply gave Fourier's work 

 with corrections, as his object was to furnish a book for students. 

 In 1841, Professor Kelland made a report to the British Association 

 for the Advancement of Science " On the Present State of our 

 Theoretical and Experimental Knowledge of the Laws of Conduction 

 of Heat." 



In this report, Kelland says that, although olyections might be made 

 to the particular assumptions of Fourier, Libri, and Poisson, it is very 

 probable that the flux of heat in the interior of a body may be written 



where c is a constant depending upon the bofly and /{i") is some un- 

 determined function of the temperature. Kelland assumed a particular 

 value for f{v), and compared the temperatures calculated from the 

 different hypotheses of Fourier, Libri, Poisson, and himself, with the 

 corresponding temperatures observed by Biot in his experiments upon 

 long bars. This comparison does not give the jDreference to any one 

 of the different assumptions. Since 1841, nothing of any importance 

 has been done, so far as I know, in the general theory of heat con- 

 duction. Lame, whose "Theorie de la Chaleur" was published in 

 18G2, follows Fourier in his hypotheses, and those writers who, like 

 Sir William Thomson, have had occasion to discuss practical questions 

 about the cooling of bodies, have also made the same assumptions, 



