138 MM. POISSON ON THE MATHEMATICAL THEORY OF HEAT. 
but it does not appear that these variations can ever produce any consi- 
derable effect on the heat of the globe. The quantities of solar heat 
which fall in equal times upon the two hemispheres are nearly equal ; 
but on account of the different states of their surfaces, those quantities 
are absorbed in different proportions; and the power of absorbing the 
rays of the sun inereasing in a greater ratio than. the radiating power, 
which is greater for dry land than for the sea, we conclude that the 
mean temperature of our hemisphere, where dry land is ina greater pro- 
portion, must be greater than that of the southern hemisphere; which 
agrees with observation. 
The solar heat, which reaches each point of the globe, varies at dif- 
ferent hours of the day ; it is null when the sun is beneath the horizon ; 
during the year it varies also with its declination; and the expression 
changes its form as the latitude of the point under consideration is 
greater or less than the complement of the obliquity of the ecliptic. I 
have therefore considered the part of the exterior temperature which 
arises from this source of heat as a discontinuous function of the horary 
angle, and of the longitude of thesun, to which I have applied the formule 
of the preceding Chapters, in order to convert it into series of sines and 
cosines of the multiples of these two angles. By this means I have ob- 
tained the complete expressions of the diurnal and annual inequalities of 
the temperature of the earth which arise from its double motion. These 
formule show, that at the equator the annual inequalities are much less 
than elsewhere; a circumstance which furnishes the explanation of a 
fact observed by M. Boussingault in his journey to the Cordilleras, and 
upon which he had relied in order to determine with great facility the 
climateric temperatures of the places which he visited. The same for-. 
mul agree also, in a remarkable manner, with the temperatures which 
M. Arago has observed at Paris during many years, and at depths vary- 
ing from two to eight metres (from 6°56 to 26°24 English feet). 
