402 SMITHSONIAN MISCELLANEOUS COLLECTIONS VOL. 51 



But since at the time of the summer solstice we must have 



qp-q p >0 (22) 



therefore we must also have 



u p > % - % 



Hence the excess of insolation, large as it is in the polar region at 

 this season, still does not suffice to supply the demand for heat to 

 increase the energy, i. e., that needed for melting the ice and 

 evaporating the water. 



It is not difficult to deduce other theorems from these and thus 

 increase their number. 



But these will suffice, since we have only intended to attain a 

 general point of view in connection with which various individual 

 investigations are to be conducted, and since the preceding theorems 

 suffice we will proceed to their application. 



The general views thus set forth show that there are essentially 

 three points to which attention must be given in investigations 

 concerning the economy of heat: 



(1) Insolation and radiation, including reflection. 



(2) Increase and diminution of energy over individual portions 

 of the surface of the earth and in the atmosphere. 



(3) Convection, or the transportation of heat by air and water. 

 The first of these subjects has already been studied by many and 



will therefore not here be made the subject of new investigations. 

 On the other hand, attention will be given to the two other 

 headings which it seems to me offer less difficulty than the first, 

 although as yet less attention has been given to them. 



(ill.) THE THERMAL EXCHANGE IN THE GROUND 



During the warmer portions of the day and the year the ground 

 absorbs heat which it again gives up during the colder portions. 

 It therefore plays the part of an accumulator or reservoir which 

 during special times stores up the energy that must be consumed 

 again at other times. 



In this case the energy occurs in its simplest form and therefore 

 this investigation offers by far the least difficulties of all that refer 

 to heat exchange. 



If the ground contains no water (which, however, can only be the 

 case approximately in rocks and in the desert) or if the water 

 content remains unchanged, while at the same time its temperature 



