300 CARNEGIE INSTITUTION OF WASHINGTON. 



groups has been established in the article Theta Modular Groups 

 Determined by Point Sets (Amer. Jour. Math., vol. xl, Oct. 1918). 

 The abstract verification of the connection mentioned unfortunately 

 affords no clue to the algebraic nature of the connections. To clear 

 this up the geometric properties of the P*io are under investigation, 

 in the hope that with the P^e disposed of, and the P^g in manageable 

 form, the geometry will throw light on the required relations. It may 

 well be that when these three cases are completely developed, the 

 general nature of the relations will be apparent. 



METEOROLOGY. 



Bjerknes, V., Bergen, Norway. Preparation of a work on the application of the 

 methods of hydrodynamics and thermodynamics in practical meteorology and 

 hydrography. (For previous reports see Year Books Nos. 5-16.) 



Dr. H. U. Sverdrup, who during a period of more than eight years 

 has served successfully as scientific assistant of the Carnegie Institu- 

 tion of Washington, retired at the beginning of this year in order to 

 devote himself entirely to the scientific equipment of Amundsen's 

 North Pole expedition, and has departed as scientific leader of that 

 expedition. In the service of the Institution he has been succeeded 

 by Mr. J. Bjerknes. 



It was pointed out in the previous report that a principal reason 

 why every calculation of future wind has been a failure is the com- 

 plicated nature of atmospheric friction in the neighborhood of the 

 ground. The investigation of this friction has therefore been continued. 

 Choosing suitable data of observations, we have succeeded in finding 

 further characteristic features of it. The investigations have been 

 conducted to a point where new experimental or observational data 

 are desirable. Such observations have been planned, but no oppor- 

 tunity for practical use has been presented. 



The law for the propagation of lines of convergence and divergence 

 announced in the previous report* has been the subject of further 

 research. The testing of these laws made it necessary to draw very 

 detailed synoptic maps. These detailed maps have made evident 

 that every cyclone which is not perfectly stationary has two charac- 

 teristic lines of convergence, which are intimately related to its propa- 

 gation. Reckoned relatively to the tangent of the track, both lines 

 come in from the right side (on the southern hemisphere from the 

 left side), but under different angles. One forms approximately a 

 right angle with the track. The other clings more closely to the track 

 and seems to touch it at the cyclonic center. Drawing the tangent 

 to this line of convergence at the center of the cyclone, we therefore 



*See the more complete account of J. Bjerknes listed in the Bibliography, p. 31. 



