12 THEORY OF HEAT. 



to the analytical subject which, we have considered. This question 

 connected with the theory of radiant heat has just heen discussed 

 by the illustrious author of the Me canique celeste, to whom all 

 the chief branches of mathematical analysis owe important 

 discoveries. (Connaissance des Temps, years 1824-5.) 



The new theories explained in our work are united for ever 

 to the mathematical sciences, and rest like them on invariable 

 foundations ; all the elements which they at present possess they 

 will preserve, and will continually acquire greater extent. Instru 

 ments will be perfected and experiments multiplied. The analysis 

 which we have formed will be deduced from more general, that 

 is to say, more simple and more fertile methods common to many 

 classes of phenomena. For all substances, solid or liquid, for 

 vapours and permanent gases, determinations will be made of all 

 the specific qualities relating to heat, and of the variations of the 

 coefficients which express them 1 . At different stations on the 

 earth observations will be made, of the temperatures of the 

 ground at different depths, of the intensity of the solar heat and 

 its effects, constant or variable, in the atmosphere, in the ocean 

 and in lakes ; and the constant temperature of the heavens proper 

 to the planetary regions will become known 2 . The theory itself 



1 Hemoires de VAcademie des Sciences, Tome VIII., Paris 1829, contain on 

 pp. 581 622, Memoire sur la Theorie Analytique de la Chaleur, par M. Fourier. 

 This was published whilst the author was Perpetual Secretary to the Academy. 

 The first only of four parts of the memoir is printed. The contents of all are 

 stated. I. Determines the temperature at any point of a prism whose terminal 

 temperatures are functions of the time, the initial temperature at any point being 

 a function of its distance from one end. II. Examines the chief consequences of 

 the general solution, and applies it to two distinct cases, according as the tempe 

 ratures of the ends of the heated prism are periodic or not. III. Is historical, 

 enumerates the earlier experimental and analytical researches of other writers 

 relative to the theory of heat ; considers the nature of the transcendental equations 

 appearing in the theory ; remarks on the employment of arbitrary functions ; 

 replies to the objections of M. Poisson ; adds some remarks on a problem of the 

 motion of waves. IV. Extends the application of the theory of heat by taking 

 account, in the analysis, of variations in the specific coefficients which measure 

 the capacity of substances for heat, the permeability of solids, and the penetra 

 bility of their surfaces. [A. F.] 



2 Memoircs de VAcademie des Sciences, Tome VII. , Paris, 1827, contain on 

 pp. 569 604, Memoire sur les temperatures du globe terrestre et des espaces plane- 

 taires, par M. Fourier. The memoir is entirely descriptive ; it was read before the 

 Academy, 20 and 29 Sep. 1824 (Annales de Chimie et de Physique, 1824, xxvu. 

 p. 136). [A. F.] 



