PROCEEDINGS OF THE ACADEMY AND AFFILIATED 



SOCIETIES 



PHILOvSOPHICAL SOCIETY 



84 1st meeting 



The S41st meeting was held at the Cosmos Club, November 20, 1920, with 

 President Sosman in the chair and 50 persons present. The program was as 

 follows : 



C. F. Marvin: The law of the geoidal slope and fallacies in dynamic meteor- 

 ology. 



This paper presented matters of unusual interest and importance relating 

 to what are beheved to be important fundamental errors in mathematical 

 meteorolog}^ which have almost completely eluded detection throughout the 

 past sixty years. Within that time the faults in question have been subscribed 

 to by many of the highest authorities on the dynamics of atmospheric motions 

 among both popular and mathematical writers. 



The question deals with a correct representation of the possible motion of 

 the atmosphere or of any bodies on a rotating globe when the motions occur 

 entirely without friction of any kind. This question has occupied the at- 

 tention of scientists for nearly 200 years. A correct statement of the under- 

 lying dynamic principles was first arrived at about 1858 by one of our own 

 countrymen, William FerrEL, a member of the Philosophical Society after 

 1872. FerrEL was many years the senior and the leader of all 'other writers 

 on the mathematical analysis of atmospheric motions, and it is difficult to 

 adequately commend the originality and completeness of his studies. Not- 

 withstanding this there appear to be certain errors in his application of the 

 principles of his own discovery. These have since been perpetuated in many 

 standard text-books on meteorology which call attention to the super-hurricane 

 wind velocities required by the operation of the law of equal areas and claim 

 that these inconceivable velocities are prevented by atmospheric friction, 

 convection, turbulence, etc. 



These conclusions are inconsistent with Ferrel's very lucid demonstration 

 that the action of gravity upon bodies moving freely over a rotating globe is 

 expressed in two wholly independent inertia reactions. One of these has 

 long been known and dignified by a specific title, the law of the conservation 

 of angular momentum. The other reaction has also long been known, but 

 strangely enough has never been christened. The important part it pla3^s in 

 controlling the motions of the air has been overlooked, or ascribed to friction 

 and turbulence. Beheving these errors to have arisen and spread, at least 

 partly, because of the lack of an appropriate name, it is proposed that the 

 neglected principle be designated by the name of the law of the geoidal slope. 

 For a globe rotating from the west to the east the law may be stated to be : 

 A geoidal surface is a neutral or horizontal surface only for bodies at rest upon it. 

 That is, gravity is powerless to set up any lateral motions among such bodies. 

 The surface slopes towards the equator for every body having a relative motion 

 eastward and towards the pole for every body with a motion westward. A com- 

 ponent of the force of gravity pulls the moving bodies down the slopes. 



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