214 THE MECHANICS OF THE EARTH's ATMOSPHERE. 



JMobu* fiud the reason therefor iu the work tbat is done in raising- tbe 

 air, and that is bahmced by an equivalent quantity of heat taken from 

 tbe air. Since by both methods of consideration the same vabie is 

 found for the diminution of temperature with the height, therefore in 

 the well-known excellent treatise of Sprung t both methods of consid- 

 eration are i)resented beside each other as equally proper. But in fact 

 only the first of these two is allowable, while that of Guldberg and 

 Mohn contains in itself an error as to which one can only wonder that 

 it could have escaped two such thoughtful investigators, and evidently 

 also has hitherto not been remarked by others. 



In order to obtain i)erfect clearness on this point one must first recall 

 Low it is that the ascending and descending currents in the atmosphere 

 come to exist at all. This is, however, always brought about by differ- 

 ences iu specific gravity that cause an ascent at certain jilaces, while a 

 corresponding mass descends at other i)laces. The work that is re- 

 quire<l to raise the air at the one place is therefore always obtained by 

 the falling of an equally great mass at another place. If no friction 

 occurs the corresponding rising and falling movements once started 

 would continue without any further addition of energy to infinity, and 

 such an external addition of energy is only needed in order to overcome 

 these frictions. These latter, however, are left out of consideration in 

 all the discussions that are here considered, and this will also be done 

 in the present memoir. We can consequently then comjjare the process 

 with which we have to do, with movements iu closed systems of tubes, 

 such as a closed series of hot water pipes, or the movements of a con- 

 tinuous chain that hangs freely upon a roller. But it would never 

 occur to any one to consider that the ascending water in the warmer 

 half of a conduit, or the ascending i)ortion of an endless chain must cool 

 because of the work done in raising it. Similarly in the case of the 

 ascending or descending currents in lakes or in the ocean, we must ex- 

 pect cooling or warming in consequence of these motions, if the ascent 

 is accomplished at the expense of the heat latent in the i3uid. The tern- 

 l^erature changes occurring in the vertical motions of the air are there- 

 fore exclusively to be attributed to the work of expansion and com- 

 pression, which is to be done or acquired respectively, and they would 

 occur to precisely the same extent if the corresponding changes in pres- 

 sure and volume occurred within a horizontal cylinder where rising 

 and sinking was entirely out of the question. 



On the other hand if we have air compressed within a vertical cylin- 

 der whose base is fixed, but which is closed above by a movable piston, 

 and if we should now by a proper change in the load cause an expauv 

 sion of the air then, besides the work of expansion, it would be neces- 

 sary also to consider the work necessary in order to raise ihe center of 

 gravity of the inclosed mass of air, and thus the cooling would be more 



* Zeit. OestP.rr. Ges. Met,, 1878, xiii, p. 113. 



t Lehrbuch d. Meteorologie, Hamburg, 1865, p. 162. 



