58 Temperature of the Teirestrial Globe, 



under another point of view, more in conformity with the natm-e 

 of the question ; and I have proposed to determine the tempera- 

 ture of the eai'th, at a given depth, and upon a given vertical 

 hue, from the quantity of solar heat which traverses the surface 

 at each instant. In any given place upon this surface, the quan- 

 tity of heat varies, during the day, and the year, with that of the 

 elevation of the sun above the horizon, and with the dechnation. 

 I have considered it as a function disconnected from time, nothing 

 while the sun is below the horizon, and expressed at all other 

 epochs, by means of the horary angle and the longitude of the 

 sun ; and by known formulas I have transformed this function 

 into a series of sines and cosines of the multiples of these two 

 angles ; and by means of the formulas of my preceding memoirs, 

 I have subsequently determined, for each term of this series, the 

 temperatm-e of any depth whatever — which is a complete solu- 

 tion of the problem. 



Of this temperature there are series of dim^nal inequalities, of 

 which the periods are of one entire day or a sub-multiple of a 

 day ; and annual inequalities of which the periodick times em- 

 brace a year or a sub-multiple of a year. Upon each vertical, the 

 maximum of each of these inequalities is propagated uniformly 

 downward, with a velocity dependent solely upon the nature of 

 the soil ; so that the interval comprised between the epochs of 

 this maximum', for two points separated by a given distance, is 

 the same, and proi^ortional to this distance, in all places of the 

 globe where the soil is of the same natm'e. At the surface, the 

 interval which separates the maximiim of one of these inequali- 

 ties from that of the correspondent inequality of the solar heat, is 

 invariable, with regard to geographical position ; but it depends, 

 at all times, upon the nature of the soil and the condition of the 

 surface. It is the same with regard to the relation between these 

 two maxima, of which the first is always less than the second ; 

 but the length of each vertical, the maximum of each inequality 

 of temperature decreases in geometrical progression v/hen the 

 depths increase by equal differences ; and the relation of this pro- 

 gression depends only upon the nature of the soil. If we exam- 

 ine, upon the same vertical, the inequalities of temperature, of 

 which the periods are different, their expression will show that 

 those which have the shortest periods are propagated with the 

 greatest rapidity, and that they decrease, also, the most rapidly. 



