2 REPORT — 1841. 



fonnulse the values of the temperature corresponding with the conditions 

 existing in the experiment, and contrasting the results with the temperatures 

 actually observed. This critical discussion of the hypotheses will lead us in 

 the third place 



To point out, III. the utter inadequacy of the few experimental facts with 

 which we are furnished, to serve either as the basis of a true theory or as the 

 indication of a false one. We admit that, of a theory based on assump- 

 tions which have been for a century regarded as only approximative to trul h, 

 the experiments are sufficient to expose the incompetency, just as experi- 

 ments on bodies sliding under the retardation of friction will easily detect thje 

 inadequacy of formulae deduced from the hypothesis of absolute smooth- 

 ness. But we shall see that, as applicable to point out errors in the assumed 

 axioms on which reasonings are founded to constitute a physical theory, the 

 experiments we possess are defective both in their number and in their na^ 

 ture. We shall find three distinct theories equally verified or equally over- 

 turned by them, according as we choose to regard the conclusions as indi- 

 cating the one or the other ; and yet we are quite sure that only one of the 

 theories is the correct one, whilst on the other hand we can hardly entertain 

 a doubt that one of them is so. When we shall have made this appear, it 

 will only remain for us to point out, in conclusion, what are the most im- 

 portant results of theory which it is desirable that experiment should be 

 brought in to test, and to suggest a few of the most simple means of effecting 

 the object desired. 



I. The problem, in the solution of which consists the mathematical theory 

 of heat, is the following. Having given the state of heatijig, or the variation 

 of that state from time to time, at one or more points of a homogeneous body 

 of given form and dimensions, to find the permanent or variable temperature 

 at every other point. Thus a ring is kept at a certain temperature at one 

 point, and it is proposed to discover, 1. what is the variation from time to 

 time of the temperature at every other point, and 2. what is the ultimate 

 temperature to which that at any given point ai^proaches as the time during 

 which the constant heating of one point has been kept up is increased. 



From this statement it will appear that the experimental facts on which the 

 theory must rest are the answers to the following questions, a. According 

 to what law does a heated body lose its temperature to the air, or other me- 

 dium or space, by which it is surrounded ? h. According to what law is 

 temperature transmitted fi'om point to point of a body ? On the correctness 

 of the answers which may be assumed as given to these questions depends 

 the applicability of the results obtained to the state of things in nature. But 

 as in mechanics we may reason correctly on assumed laws which are not laws 

 of nature, and obtain conclusions of great importance as approximations to 

 facts, so in the theory of heat the results, although strictly commensurate only 

 with the laws on which they depend, are still highly important even in refer- 

 ence to the things actually existing, differing as they do in certain cases from 

 the expression of the laws. 



We proceed then to show what answers have been given to the above 

 questions by different theorists, and to explain the evidence on which their 

 truth is supposed to be established. 



a. Radiation, Sir Isaac Newton appears to have been the first who was 

 led to apply a law of radiation to experiment. The statement of the law is 

 given by him for the first time in a paper in the Philosophical Transactions 

 for 1701 *, and is reprinted in his Opusculaf. 



* Philosophical Transactions, 1701, vol. xxii. p. 827. 

 t Newton's Opuscula, vol. ii. p. 422, 



