ON THE CONDUCTION OF HEAT. 8 



We should not have thought it necessary to mention this subject were we 

 not desirous of seeing the attention of philosophers directed to this branch 

 of physics. It is extraordinary, that a theory, professing to be a physical 

 theory based on experiment, should have been suffered to lie for twelve years 

 hardly known in fact, but occasionally alluded to as complete and satisfac- 

 toi'y. In the kindred science of optics half the time would have sufficed to 

 attract the attention of the whole scientific world ; and experiment and analy- 

 tical investigation would have been lavished on the subject. We hope M. 

 Libri will be induced to pursue his investigations^ further, and to reduce the 

 results to a tangible form. 



The next theory to be mentioned is that of Poisson. In his ' Theorie Ma- 

 thematique de la Chaleur' (1835), he adopts the law established by Dulong 

 and Petit for extra-radiation, and conceives that a similar law may apply to 

 the interior transmission of heat. The hypothesis on which he proceeds re- 

 lative to the changes of heat between all parts, the complication of his re- 

 sults, and a degree of uncertainty which hangs over the law of change, 

 render his work rather a display of analytical artifice than an attempt to 

 build up a theory by applying to it the test of an examination by contrast 

 with the facts it is designed to account for. It is to be regretted that M. 

 Poisson, in turning his attention to the fundamental difficulties in the theory, 

 did not adopt the plan of endeavouring, in the first place, to remove them, 

 and afterwards to advance to the application of the same principles to the 

 more difficult and complex questions which might present themselves. As 

 it is, we can find in his work only one conclusion to which we can turn, in 

 the present state of our knowledge, with the view of applying to it the test 

 of experimental examination : this result we shall exhibit in its proper 

 place. We have only to add, that M. Poisson's equation has been deduced 

 by Mr. Rankine in the ' Edinburgh Academic Annual,' and applied to the de- 

 termination of the temperature of a heated globe. 



Lastly, the author of the present report has suggested that it is proper to 

 try a fourth theory, the last which the combinations of the laws of radiation 

 and conduction admit of. It does not appear improbable, that although the 

 flow of temperature does not depend on the dift'erence of temperature, the 

 flow of heat should depend on the difference of heat, provided we regard 

 heat as a certain state of the body different from temperature. This theory 

 then rests on the hypotheses, 1 . That the variation of v due to cooling in 

 vacuo depends directly on v, 2. That the flow of v across a given plane 

 varies as the difference of the values of v on the two sides of that plane. 



Thus this theory coincides altogether with Fourier's, except that v is no 

 longer the temperature, but a certain function of the temperature. The 



function appears to be z; = A (1 —a ~ ) + B*, where 6 is the temperature 

 and a is Dulong and Petit's constant. 



These are the four theories which at present exist, each based on the com- 

 bination of one of the two axioms of radiation with one of the three axioms 

 of conduction. We propose now to write down some of the most import- 

 ant and simple of the conclusions to which they respectively lead. 



I. Fourier's hypotliesis. That the flow of temperature depends directly on 

 the difference of temperature, both within and at the surface of a body. 

 As we have already stated that one of the formulae had been given by Biot 

 prior to the appearance of Fourier's memoir, it will save confusion, if, not- 

 withstanding, we make our references to Fourier's work alone. 



Formula 1. — The permanent temperature of an infinite homogeneous 



* Athenffium for October 24, 1840, and Report of British Association for 1840. 



