INTERCHANGE OF HEAT VON BEZOLD 395 



If therefore again q T indicates the heat added during the interval 

 from any moment of one secondary minimum of total energy to 

 the same moment of the next following secondary maximum, and 

 q r the heat lost from the latter maximum to the moment of the next 

 following secdndary minimum, then we have 



q Tl ^ - <Ir 2 



where, however, the difference between the two quantities q Tj and 



q T is always small. 



Consequently the amount of the daily exchange is 



. £ (q Tl + <Jr 2 ) 



These considerations lead naturally to the determination of the 

 total energy contained in any portion of the atmosphere or the 

 earth. 



For the present purpose it is important to choose such portion 

 of the atmosphere appropriately and to bring it in connection with 

 a corresponding limited part of the earth's surface. 



By the term "total energy of any portion of the earth's surface" 

 I will therefore understand the total energy in that portion of the 

 earth's crust and the atmosphere resting on it, cut out by a straight 

 line that, starting from the center of the earth, passes around that 

 part of the earth's surface while its upper end is at the limit of the 

 atmosphere, but its lower end is limited by a surface parallel to the 

 earth's surface but so chosen that no annual period of temperature 

 is observable therein. 



On the other hand by the expression "total energy of a definite 

 place on the earth's surface" I understand the energy within a 

 truncated cone whose apex is at the center of the earth while its 

 conical surface cuts a unit of area from the surface of the earth, 

 and whose upper and lower surfaces are defined respectively by the 

 upper boundary of the atmosphere and by a surface lying deep 

 enough below and parallel to the earth's surface. 



The determination of the total energy for the different points of 

 the earth's surface, both as to its average value and also as to its 

 variation with time constitutes an important problem in the theory 

 of the thermal economy of the earth. 



The amplitude of the variation of the total energy, that is to 

 say, the difference of its extreme values, affords a measure of the 

 thermal exchange both for the annual period and also, with a 

 small modification, for the diurnal period. 



