PAPER BY PROF. OBERBECK. 177 



will here be cousidered as "steady niotioii." On the other baud I 

 have labored so to arrange the calculation that it can be applied to 

 anj^ condition of the atmosphere and to the general currents between 

 the poles and the equator, or the atmospheric circulation, as well as 

 also to individual cyclones or anticyclones. 



In order to test the applicability of the formula thus obtained, the 

 first of the problems just mentioned is completely solved. 



1 begin with an enumeration of the factors upon which the movement 

 of the atmosphere depends, and with a description of the manner in 

 which I have introduced these into the calculation. 



II 



(1) Since the ultimate cause of the motion of the air is to be sought 

 in the eifect of gravity and in the differences of temperature in the 

 atmosphere, therefore the attraction of the earth must enter into the 

 equations of motion as the moving force. But it is entirely sufiScient 

 here to consider the earth as a homogeneous sphere. 



(2) The temperature of the atmosphere is to be considered as a 

 function of the locality, but entirely independent of the time. The last 

 condition is necessary if one confines himself to steady motions. For 

 the temperature T, the analytical condition 



,-)2T fT ?"T 



must be satisfied. 



This equation, as is well known, follows from the assumption that 

 the heat is distributed through the medium in question according to 

 the laws of the conduction of heat. Although I am by no means of the 

 opinion that the conduction of heat principally determines the flow of 

 heat from the earth's surface through the atmosphere into the 

 planetary space, still it is very probable that the totality of all the 

 phenomena here coming into consideration (conduction, radiation from 

 the earth's surface with partial absorption in the atmosphere, vertical 

 oonvection currents, etc.) will bring about a distribution of tempera- 

 ture analogous to that due to the conduction of heat. 



(3) According to the rules of mechanics, the influence of the rota- 

 tion of the earth can be expressed by a deflecting force, so that after 

 its introduction the earth can be considered as at rest. 



(4) Friction is furthermore to be considered, since without it the 

 atmospheric currents under the continuous influence of accelerating 

 forces would attain to indefinitely great velocities. In my opinion, the 

 attempts made hitherto to give a correct theory of the motions of the 

 air, especially one that can be developed analytically, have failed 

 because of the insufficient or incorrect introduction of friction. I have 

 adhered to the si modest assumption, namely, that the same law of 

 friction holds good for atmospheric currents that has also been shown 



80 A 12 



