430 CARNEGIE INSTITUTION OF WASHINGTON. 



MATHEMATICS. 



Morley, Frank, Johns Hopkins University, Baltimore, Maryland. Appli- 

 cation of Cremona Groups to the solution of algebraic equations. (For 

 previous reports see Year Books Nos. 9-16, 19.) 



Professor A. B. Coble has published his memoir on "Multiple binary 

 forms with the closure property." (Amer. Jour. Math., vol. 43, pp. 

 1-19, Jan. 1921.) 



He has begun, in the Proceedings of the National Academy of 

 Sciences, the publication of a series of abstracts which presents results 

 as to the nodes of the rational sextic, the symmetroid, and the modular 

 functions of genus 4. With these there occur a variety of geometric 

 configurations whose interrelations are of exceptional interest. Many 

 of these are defined by multiple forms with variables drawn from dif- 

 ferent domains. The invariant theory of such forms, hitherto little 

 used, has been a valuable auxiliary. 



Some of the principal problems that hold over are the determination 

 of the sextic or sextics of genus 4 whose modular functions define 

 Cayley's symmetroid; of the connection between the 120 planes on 

 three nodes of the symmetroid with the 120 tritangent planes of such a 

 sextic ; and of the automorphic Cremona group of the rational sextic and 

 more particularly the binary group thereby induced on the parameter 

 of the sextic. 



Much of the work already accomplished is necessarily preliminary 

 to an attack on these problems. 



METEOROLOGY. 



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

 the methods of hydrodyiiamics and thermodynamics in practical meteorology 

 and hydrography. (For previous reports see Year Books Nos. 5-19.) 



The main work of the current year has been to start a systematic 

 publication of the results reached in the last three years by the Nor- 

 wegian Weather Service (c/. the two last reports). Two papers are 

 now being printed, as No. 3 and No. 4 of Vol. II of "Geofysiske Publi- 

 kationer" (Cammermeyers Boghandel, Kristiania). These papers are: 



J. Bjerknes and H. Sclberg: Meteorological conditions for the formation of rain. 

 V. Bjerknes: On the dynamics of the circular vortex, with applications to the atmosphere 

 and atmospheric vortex and wave motion. 



The investigations of the first of these papers concludes with the 

 following scheme for the classification of rain: 



(1) Cyclonic rain: (o) Warm front rain, formed in warm air pushing upwards a retreating 



wedge of cold air; (6) Cold front rain, formed in warm air displaced by an advancing 

 wedge of cold air. 



(2) Instahility showers- (a) Instability produced by heating from warm sea surfaces; (6) In- 



stability produced by insolation over land (local showers). 



