SECT. I.] INTRODUCTION. 23 



makes a smaller angle with the element of surface, and that it is 

 proportional to the sine of that angle \ This general law of 

 emission of heat which different observations had already indi 

 cated, is a necessary consequence of the principle of the equilibrium 

 of temperature and of the laws of propagation of heat in solid 

 bodies. 



Such are the chief problems which have been discussed in 

 this work; they are all directed to one object only, that is to 

 establish clearly the mathematical principles of the theory of heat, 

 and to keep up in this way with the progress of the useful arts, 

 and of the study of nature. 



17. From what precedes it is evident that a very extensive 

 class of phenomena exists, not produced by mechanical forces, but 

 resulting simply from the presence and accumulation of heat. 

 This part of natural philosophy cannot be connected with dy 

 namical theories, it has principles peculiar to itself, and is founded 

 on a method similar to that of other exact sciences. The solar 

 heat, for example, which penetrates the interior of the globe, dis 

 tributes itself therein according to a regular law which does not 

 depend on the laws of motion, and cannot be determined by the 

 principles of mechanics. The dilatations which the repulsive 

 force of heat produces, observation of which serves to measure 

 temperatures, are in truth dynamical effects; but it is not these 

 dilatations which we calculate, when we investigate the laws of 

 the propagation of heat. 



18. There are other more complex natural effects, which 

 depend at the same time on the influence of heat, and of attrac 

 tive forces: thus, the variations of temperatures which the move 

 ments of the sun occasion in the atmosphere and in the ocean, 

 change continually the density of the different parts of the air 

 and the waters. The effect of the forces which these masses obey 

 is modified at every instant by a new distribution of heat, and 

 it cannot be doubted that this cause produces the regular winds, 

 and the chief currents of the sea; the solar and lunar attractions 

 occasioning in the atmosphere effects but slightly sensible, and 

 not general displacements. It was therefore necessary, in order to 



1 Mem. Acad. d. Sc. Tome V. Paris, 1826, pp. 179213. [A. F.] 



