INTERCHANGE OF HEAT VON BEZOLD 393 



of energy within the volume under consideration; a negative sign 

 indicates a diminution. 



This increase may consist in an increase of temperature, an 

 increase of the quantity of vapor, a conversion of ice into water, 

 a development or an increase of pressure differences (potential 

 energy) or of motions (kinetic energy). 



Frequently such an increase of energy is also called incidentally 

 a storage of heat. 



On the other hand, if q aT is negative this teaches that the total 

 energy has diminished during the interval of time under considera- 

 tion, which must indicate either a fall of temperature, or conden- 

 sation or freezing of the water, a diminution of pressure gradient 

 or the diminution of the existing motions. If we have to do with 

 changes in bodies that are stationary or scarcely movable, like 

 water frozen into ice, or like the solid earth, then we could include 

 also the storage of heat or cold. 



For t 2 — t t = T we have q oT , = o or u a<2 = u ali , since in accord- 

 ance with the assumption that lies at the base of this whole investi- 

 gation the thermal and kinetic condition of the earth at the close 

 of a year always returns to its same initial condition no matter 

 what moment of time t t we choose as our starting point. 



Since therefore the total increase of heat within a year is zero, 

 whilst it has finite values during the separate seasons, therefore for 

 each point of the earth the whole year is divided into periods of 

 excess of insolation and excess of radiation or, briefly, seasons of 

 warming and cooling. 



In the passage from one such period of one kind over to one of the 



dq 

 opposite kind the differential quotient — changes its sign, and q 



itself at this moment of time therefore attains a maximum or 

 minimum value. 



Such extreme values occur within every day, but the absolute 

 maxima and the minima in general only once during each year 

 except twice at the equator. 



If we ignore the daily extremes, and at least for regions outside 

 the tropics, we can by appropriate choice of dates for the beginning 

 of the year, divide the year into two halves such that for one 

 we have an increase of heat and for the other a decrease. 



These halves will in general be unequal, since the inflow and the 

 outflow of heat follow very different laws. 



If therefore t x = o be so chosen that u is the absolute minimum 

 and if we remove the secondary maxima and minima by some 



