20 THEORY OF HEAT. [CHAP. I. 



description of different substances. It is a very imperfect know 

 ledge of bodies which ignores the relations which they have with 

 one of the chief agents of nature. In general, there is no mathe 

 matical theory which has a closer relation than this with public 

 economy, since it serves to give clearness and perfection to the 

 practice of the numerous arts which are founded on the employ 

 ment of heat. 



12. The problem of the terrestrial temperatures presents 

 one of the most beautiful applications of the theory of heat ; the 

 general idea to be formed of it is this. Different parts of the 

 surface of the globe are unequally exposed to the influence of the 

 solar rays; the intensity of their action depends on the latitude of 

 the place ; it changes also in the course of the day and in the 

 course of the year, and is subject to other less perceptible in 

 equalities. It is evident that, between the variable state of the 

 surface and that of the internal temperatures, a necessary relation 

 exists, which may be derived from theory. We know that, at a 

 certain depth below the surface of the earth, the temperature at a 

 given place experiences no annual variation: this permanent 

 underground temperature becomes less and less according as the 

 place is more and more distant from the equator. We may then 

 leave out of consideration the exterior envelope, the thickness of 

 which is incomparably small with respect to the earth s radius, 

 and regard our planet as a nearly spherical mass, whose surface 

 is subject to a temperature which remains constant at all points 

 on a given parallel, but is not the same on another parallel. It 

 follows from this that every internal molecule has also a fixed tem 

 perature determined by its position. The mathematical problem 

 consists in discovering the fixed temperature at any given point, 

 and the law which the solar heat follows whilst penetrating the 

 interior of the earth. 



This diversity of temperature interests us still more, if we 

 consider the changes which succeed each other in the envelope 

 itself on the surface of which we dwell. Those alternations of 

 heat and cold which are reproduced everyday and in the course of 

 every year, have been up to the present time the object of repeated 

 observations. These we can now submit to calculation, and from 

 a common theory derive all the particular facts which experience 



