138 M. 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 increasing 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 in a 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 the sun, to which I have applied the formulae 

 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 Avhich arise from its double motion. These 

 formulae show, that at the equator the annual inequalities are much less 

 than elsewhere ; a circumstance which furnishes the explanation of a 

 fact obsei-ved 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- 

 mulae agree also, in a remarkable manner, with the temperatures which 

 M. Arago has observed at Paris during many yeai-s, and at depths vary- 

 ing from two to eight metres (from 6*56 to 26*24' English feet). 



