58 Temperature of the Terrestrial Globe, 
under another point of view, more in conformity with the nature 
of the question; and I have proposed to determine the tempera- 
ture of the earth, at a given depth, and upon a given vertical 
line, 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 declination. 
Ihave 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 
temperature of any depth whatever—which is a complete solu- 
tion of the problem. 
Of this temperature there are series of diurnal 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 Bis ea for two points separated by a given distance, is 
the same, and proportional to this distance, in all places of the 
globe where the soil is of the same nature. At the surface, the 
interval which separates the maximum 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 when 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 liflirons, their expression will show that 
hose which have the shortest periods are propagated with the 
greatest rapidity, and eh teay doceoate; sis the most rapidly. 
