REPORTS 



ON 



THE STATE OF SCIENCE. 



On the Present State of our Theoretical and Experimental Knowledge 

 of the Laws of Conduction of Heat. By the Rev. Piiii^ip Kell and, 

 M.A., F.R.SS. Lond. and Edin., Prof of Math, in the University 

 of Edinburgh, late Fellow of Queen's College, Cambridge. 



1 HE object of the following report is simply to lay before the Association an 

 outline of the present state of our theoretical knowledge of the law of trans- 

 mission of heat by conduction, and to examine how far conclusions deduced 

 from theory have been tested by experiment. Reports on the general pro- 

 blem of Radiant Heat have already appeared by Professor Powell * ; and on 

 the theoretical laws of conduction and radiation, a portion of the subject- 

 matter of our present question, Mr. Whewell has briefly touched in his report 

 < On Magnetism, Electricity, Heat, &c.t' We shall, in consequence, confine 

 ourselves strictly to our immediate limits, noticing only such other branches 

 of the general theory as bear directly or necessarily on the question. We 

 shall avoid all mention of theoretical investigations, however important in 

 themselves, which are not capable of being examined rigidly by direct expe- 

 riment ; nor shall we scruple to pass over the names of a host of illustrious 

 experimenters on conduction and radiation, when we find that their experi- 

 ments are not calculated to serve as the immediate test of theory. This pro- 

 ceeding will materially shorten our labour, and will have the effect of con- 

 densing into a narrow compass all the remarks we have to make. 



To render wiiat has to be said as clear as possible, the subject-matter has 

 been arranged under three heads. Two of these are distinctly marked out 

 by the statement of the object proposed to be effected, and the third is sug- 

 gested by a consideration of the former two. 



We shall examine, then, I. What is the present state of our theoretical 

 knowledge of the phsenomena of conduction. W^e are here to seek for the 

 principles on which the reasoning is based, to inquire what are the axioms of 

 radiation and conduction, or of the flow of heat, which, from observation, 

 experiment or analogy, have been assumed to hold true, and to point out the 

 conclusions to which these axioms have led. We have to distinguish between 

 differing theories, and to contrast with each other some of the most simple of 

 the results to which they respectively lead. This portion of our subject must, 

 to a certain extent, be treated historically. 



We shall inquire, H. into the state of experimental investigation, so far as 

 it has been undertaken with a view to test or to illustrate the conclusions 

 arrived at by theory. We shall examine how the different consequences of 

 certain hypotheses bear the test thus applied to them, by computing from the 



* Report on Radiant Heat in Reports of British Association, vols. i. and ix. 

 t Reports of the British Association, vol. iv. 

 1841. B 



