INTERCHANGE OF HEAT VON BEZOLD 385 



Oa, Q"l> &a, £ia the quantities of heat respectively entering and 

 leaving an area a of the surface of the earth or of the boun- 

 dary of the atmosphere within a whole year, 

 u the total energy contained in an enclosed portion of the surface 



of the earth or the atmosphere at the time /. 

 u x the corresponding quantity for the time t v 

 r the radius of a sphere centered at the earth's center and enclosing 

 the whole atmosphere, or a quantity exceeding the greatest 

 radius of the globe by ioo kilometers. 

 da an element of a surface. 

 /? the geographic latitude. 

 X the geographic longitude. 



5 the solar constant or kilogram calories of heat received by 

 the earth from the sun at the earth's mean distance, per 

 minute per square meter. 

 If we consider this system of notation we shall perceive that the 

 following points of view have been kept in mind: 



The quantities relating to the unit of surface have been designated 

 by Roman letters, those relating to larger areas and the boundaries 

 of the whole atmosphere by German letters. 



The quantities relating to the unit of time are indicated by small 

 letters; those relating to other intervals except the whole year are 

 indicated by the same letters but with special index. For all 

 quantities that relate to a whole year the capital letters are used. 

 The quantities of heat are considered as absolute quantities and 

 letters indicating added heat have one accent while those indicating 

 subtracted or lost heat have two accents. These accents are placed 

 above and to the right when the heat passes through surfaces that 

 are within the boundary surface of the atmosphere, but are horizontal 

 lines placed above the letters when the heat passes through this 

 boundary itself. 



We now proceed to establish the following theorems: 



I. "The quantities of heat received by insolation and lost by 

 radiation by the whole earth in the course of a whole year are on 

 the average equal to each other." 



For if these quantities were not equal there would occur either a 

 progressive warming or progressive cooling, which has not been the 

 case during the time accessible to more accurate investigation. 



Translated into algebra this theorem assumes the simple form 



n = S (i) 



