X. 



THE MOVEMENTS OF THE ATMOSPHERE ON THE EARTH'S SURFACE.* 



Bv A. Oberbeck 



I. INTRODUCTION. 



The iDvestigatioiis of Guldberg aud Molint ou the motions of the 

 atmosphere certainly occupy a prominent place in the development of 

 theoretical meteorology. If not the first they are at least the most ex- 

 tensive and successful attempt to explain the most important phenomena 

 of the motion of the air by the principles and fundamental equations 

 of hydrodynamics. I would especially indicate as the special service 

 of the authors that they have brought the problem of the motions of 

 the air into a form amenable to mathematical treatment by simple but 

 as I believe thoroughly appropriate assumptions. They themselves 

 have already computed a series of interesting atmospheric movements 

 that frequently occur in nature, especially the cases where the isobaric 

 systems consist of parallel straight lines or concentric circles. 



I have attempted in the present work to go further on in the patii 

 laid out by Guldberg and Mohn, especially in that I have endeavored 

 to apply to the atmosphere the methods developed in hydrodynamics 

 for other problems. 



In the present memoir the steady movements of the atmosphere, or, 

 as Guldberg and Mohn call them, " invariable systems of winds," are 

 principally treated. It is natural to refer the movements of the atmos- 

 phere back to the general modes of motion of fluids, that is to say, to 

 motions that are characterized by a velocity jjotential aud to vortex 

 motions. In this way it is possible to attain solutions of great gener- 

 ality that can be api)lied to any system of isobars whatever. By this 

 method of treatment it is further possible to overcome a difficulty that 

 occurs in the theory of cyclones of Guldberg and Mohn, without as it 

 would appear haviug been hitherto observed. These investigators dis- 

 tinguish correctly an inner and an outer region for each cyclone, in 



* Translated from Wiedemann's Annalen der Physik und Chemie, 1882, vol. xvii., 

 pp. 12S-148. 

 t " Studies on the Motions of the Atmosphere.'" Christiauia, Part i., 1876, Part ii, 



18d0. 



151 



