388 CAKNEGIE INSTITUTION OF WASHINGTON, 



MATHEMATICS. 



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

 tion of Cremona Groups to the solution of algebraic equations. (For pre- 

 vious reports see Year Books Nos. 9-16.) 



Professor Coble has published his memoir on the Ten Nodes of the 

 Rational Sextic and the Cay ley Symmetroid (Amer. Jour. Math., 

 vol. 41, No. 4, pp. 243-265, October 1919). He has completed a 

 memoir on Double Binary Forms and the Closure Property, which 

 develops some new points of view and many new instances. 



Two other researches of Professor Coble which are in progress may 

 be mentioned: In the first the modular functions of genus 3 are used 

 to obtain a system of irrational invariants of the ternary quartic which 

 can be identified with a similar system arising from the set of seven 

 points in a plane. This connects the rational invariants of the quartic 

 with the invariants of a finite colhneation group in 15 variables and 

 would indicate that the complete system of the quartic consists of 

 not more than 17 members. 



The second research connects his discovery that the sjnnametroid 

 can be transformed by Cremona transformations into only a finite 

 number of distinct types with the fact discovered by Schottky that the 

 symmetroid arises from the modular functions of genus 4. Cremona 

 transformations of the symmetroid are induced by the integer linear 

 transformations of the modular functions, when reduced modulo 2. 



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. 5-18.) 



In the previous report the following general result was stated : 



"The atmosphere is crossed and recrossed by surfaces of discontinuity 

 separating from each other masses of air having more or less different velocity 

 and different physical properties, showing themselves by differences of temper- 

 ature and humidity, and (as pointed out by Mr. Bergeron) also by marked 

 differences of transparency. Almost every change of weather is due to the 

 passage of a surface of this kind." 



On the weather-chart a surface of this kind manifests itself by the 

 line of discontinuity, along which it cuts the ground. Using the de- 

 tailed weather charts produced for the new Norwegian Weather Service 

 (of the two previous reports), J. Bjerknes, H. Solberg, and T. Bergeron 

 have continued the investigation of these lines. They are seen, from 

 day to day, to sweep over the chart as curves of a more or less wavy 

 form, the waves entering generally at the western and disappearing 

 at the eastern border. Originally the subsequent wave-lines were 

 believed to be independent of each other, but it has become evident 

 that they are connected, forming parts of a single continuous line of 



