PRELIMINARY DISCOURSE. 9 



its gradual progress. When this knowledge has been acquired 

 and the principles thoroughly fixed, it is preferable to employ at 

 once the most extended analytical methods, as we have done in 

 the later investigations. This is also the course which we shall 

 hereafter follow in the memoirs which will be added to this work, 

 and which will form in some manner its complement *; and by this 

 means we shall have reconciled, so far as it can depend on our 

 selves, the necessary development of principles with the precision 

 which becomes the applications of analysis. 



The subjects of these memoirs will be, the theory of radiant 

 heat, the problem of the terrestrial temperatures, that of the 

 temperature of dwellings, the comparison of theoretic results with 

 those which we have observed in different experiments, lastly the 

 demonstrations of the differential equations of the movement of 

 heat in fluids. 



The work which we now publish has been written a long time 

 since ; different circumstances have delayed and often interrupted 

 the printing of it. In this interval, science has been enriched by 

 important observations ; the principles of our analysis, which had 

 not at first been grasped, have become better known ; the results 

 which we had deduced from them have been discussed and con 

 firmed. We ourselves have applied these principles to new 

 problems, and have changed the form of some of the proofs. 

 The delays of publication will have contributed to make the work 

 clearer and more complete. 



The subject of our first analytical investigations on the transfer 

 of heat was its distribution amongst separated masses ; these have 

 been preserved in Chapter III., Section II. The problems relative 

 to continuous bodies, which form the theory rightly so called, were 

 solved many years afterwards ; this theory was explained for the 

 first time in a manuscript work forwarded to the Institute of 

 France at the end of the year 1807, an extract from which was 

 published in the Bulletin des Sciences (Societe Philomatique, year 

 1808, page 112). We added to this memoir, and successively for 

 warded very extensive notes, concerning the convergence of series, 

 the diffusion of heat in an infinite prism, its emission in spaces 



1 These memoirs were never collectively published as a sequel or complement 

 to the Theorie Analytiquc de la Chaleur. But, as will be seen presently, the author 

 had written most of them before the publication of that work in 1822. [A. F.] 



