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. 9-17, 19-21.) 



The investigation of the equation of the eighth degree — the problem pro- 

 posed for the current year to the Carnegie Institution — has reached a satis- 

 factory stage of completeness. The detailed treatment of this case, with 

 constant thought in regard to the possibilities of extension to equations of any 

 even degree, has required the development of some new modes of approach 

 and has led to some rather unexpected results. Thus, it appears that the 

 generalized Weddle surface is a more convenient field for the allied hyper- 

 elliptic functions than the generalized Kummer surface, which is not true of 

 the sextic equation. One unlooked-for result is the occurrence of linear 

 relations among the hyperelliptic theta functions of order two and genus 

 p2 > 4 which do not exist in general. 



A sketch of these researches will be made in an address before the joint 

 meeting at Cincinnati of the American Mathematical Society, the American 

 Mathematical Association, and Section A of the American Association for the 

 Advancement of Science. This sketch will appear in the Bulletin of the Mathe- 

 matical Society. A fuller account will be prepared for publication elsewhere. 



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. 5-21.) 



The last four reports have been devoted entirely to phenomena connected 

 with atmospheric discontinuities, which give the key to theoretical under- 

 standing and practically forecast phenomena of the weather. During the 

 current year the investigation of these discontinuities and their disturbances 

 has been continued along both empirical and theoretical lines. 



Mr. J. Bjerknes has been working in Switzerland this year, where he has 

 had access to the important observations from the high stations in the Alps. 

 He has taken up a detailed examination of different typical outbreaks of polar 

 air, which inundated the greater part of Europe, including even the highest 

 summits of the Alps, and studied the weather phenomena connected with the 

 progressive advance of the cold front. This investigation has confirmed and 

 completed the general conclusions which had been drawn in a more summary 

 way from the study of the Norwegian daily weather maps. This work has 

 not yet been accomplished, but when published will bring the final demonstra- 

 tion of many results which we have hitherto been able only to enunciate 

 without demonstration. 



A general view of the central theoretical problems of dynamic meteorology 

 after the latest empirical discoveries has been given by V. Bjerknes in his 

 paper "Dynamics of the circular vortex, with application to atmospheric 

 vortex and wave-motion" (see Year Book No. 20). The problems may be 

 stated thus: (1) To determine the condition of equilibrium of the atmospheric 



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