INTERCHANGE OF HEAT VON BEZOI.D 397 



in fact at regions whose surfaces have entirely different properties, 

 therefore there is really no reason -whatever for such equality. 



Hence there probably are, even for the whole earth, some portions 

 of the year during which the increase of heat is in excess and other 

 portions in which the loss of heat is in excess; in other words, "The 

 total energy of the whole earth is probably subject to periodic 

 variations within the year." 



The fact that the average temperature of the lowest stratum of 

 air over the whole earth is higher during the summer half-year of 

 the northern hemisphere than during the winter half-year seems to 

 agree with this idea. 



But of course we must not forget that this temperature is by no 

 means a measure of the total energy. On the contrary it is very 

 probable that the changes of total energy of the whole surface of 

 the earth including the atmosphere are not so large, by far, as 

 one would expect from the change of the mean temperature of the 

 lowest stratum of air. 



For since the masses of water that in the course of a year are 

 frozen to ice and afterward again melted are apparently much 

 larger in the southern hemisphere than in the northern, and since 

 the same is certainly true of the quantities of water that are evap- 

 orated and condensed — therefore a larger portion of the added 

 energy is applied to the work of melting and evaporating during 

 the summer of the southern hemisphere than during the summer 

 of the northern hemisphere. Therefore even in the case of equal 

 values of the total energy [of the two halves of the year] the mean 

 temperature of the whole earth must be lower in the half-year con- 

 taining the northern winter than in that containing the northern 

 summer, since in the winter half-year of the northern hemisphere 

 the larger portion of the added heat falls in [southern] regions in 

 which the consumption of energy in [producing] changes of condi- 

 tion [snow and ice to water and vapor] is far greater than it ever 

 can be in the northern hemisphere. 



But only detail investigation can decide to what extent the com- 

 pensation just indicated takes place or, in other words, whether 

 and to what extent the total energy of the whole earth has an 

 annual period. 



Of course in this matter, as indeed throughout the whole of this 

 class of investigations, one must be content with estimates, but 

 certainly the problem itself is a striking example of the special 

 question to which we are led by these general considerations. 



In order to put this theorem into algebraic form it suffices to take 



