ON THE CONDUCTION OF HEAT. 7 



Vestigations the latter factor had been regarded as a function of the positions 

 of the particles only* ; although he Avas led by analogy to the adoption of the 

 above law, as he himself informs us f , yet he does not appear to have adopted 

 the law of Dulong and Petit itself as the law of conduction. He leaves it 

 indeterminate, having found, as we shall show in another part of our report, 

 difficulties in admitting such to be the case. 



Lastly, the author of the present report, in a short memoir which he read 

 to the Royal Society of Edinburgh %, suggested the possibility of the ex- 

 istence of a third law of conduction, differing considerably from either of the 

 former as they are actually adopted, but which might be made to differ 

 little from Poisson's by the change of a few of the quantities to which that 

 author has assigned values. The law may be stated briefly as follows : — 

 " The flow of a function of thermometric temperature across a given plane 

 varies as the difference of the values of this function on the two sides of the 

 plane." It will be seen at once that this law restores us all Fourier's con- 

 clusions, provided we regard his phrase " heat " or " temperature," Avhich 

 he uses indifferently, as signifying a given function of thermometric tempera- 

 ture. These are the only laws of conduction which have been suggested : 

 they are mere hypotheses. In seeking for a law of radiation we may have 

 recourse to direct experiment, but here no such means are in our power. 

 All that we can do is to experiment on the combined effects of radiation and 

 conduction ; and then, supposing ourselves in possession of the effects due 

 to the former, to eliminate them, and infer the law of conduction from the 

 remainder. But this cannot be done without computation, and computation 

 cannot be effected without formulae, which latter must be based on the hypo- 

 thesis of conduction itself. Thus we are reduced to the indirect method of 

 assuming the law, and testing by experiment the conclusions which spring 

 from the assumption. We must prepare, therefore, to examine the results 

 of analytical investigation applied to certain laws of radiation and conduc- 

 tion which are at first conceived to be true, but only to be finally esta- 

 blished by the conclusions themselves. Before we proceed, it will, perhaps, 

 be as well to repeat that we have found two laws of radiation and three of 

 conduction to exist as the assumed laws of nature. By the combinations of 

 these laws we could conceive six different theories of heat to arise. Of these 

 two would be obviously at variance with our present notions of fact ; the 

 other four have to be examined. 



All the earlier theorists assumed, as we have already stated, the most 

 simple axioms of radiation and conduction, viz. that the flow of temperature 

 is proportional to the excess of temperature. Such being the case, we may 

 venture to pass over the labours of Biot, Laplace, and others, not because 

 they are unimportant, but because the same results are to be found in the 

 more extensive and systematic writings of Fourier. In 1807 this philosopher 

 read before the Institute a memoir, in which the subject was treated in a 

 masterly manner, and the difficulties which had previously encompassed it 

 were removed §. The Academy of Sciences, with the laudable design of 

 inducing the author to prosecute his researches, proposed as the subject of 

 the Prize Essay to be awarded in 1812, " To give the Mathematical Laws 

 of Radiation and Conduction, and to establish them by experiment." Ac- 

 cordingly, on Sept. 28, 1811, M. Fourier's second memoir was deposited^in the 

 archives of the Institute. The prize was decided to have been gained by it, 



* Journal ile I'Ecole Polytechnique, torn. xii. p. 87. 



t Thuorie de la Chaleur, Preface, p. 6. 



X Proceedings of the Royal Society of Edinbiu'gh, Dec. 16, 1839, p. 2?9. 



§ Bulletia des Sciences, 1808, torn. i. p. 112. 



