HISTORY — LITERATURE — MATHEMATICS. 361 



Osgood, Herbert L., Columbia University, New York, N. Y. Completion 

 of an institutional history of the American colonies during the period of 

 the French wars. (For previous reports see Year Books Nos. 11, 12.) 



Dr. Osgood reports that his work on Institutional History of the 

 American Colonies has steadily progressed during the year. Near the 

 close of May he sailed for London, where he worked in the Public 

 Record Office, but this work was afterwards interrupted by the condi- 

 tions produced by the war. However, the most important part of the 

 material had already been obtained. Dr. N. D. Mereness collected 

 material at Baltimore and Washington until the close of March. 



LITERATURE. 



Bergen, Henry, Brooklyn, New York. Completion of preparation for publica- 

 tion of the text of Lydgate's Fall of Princes. (For previous reports see 

 Year Books Nos. 11, 12.) 



During the year 1914 progress has been made in the preparation for 

 the press of Lydgate's Fall of Princes, by collating it with the manu- 

 script in the John Rylands Library at Manchester, as well as by finish- 

 ing the work of copying the text and collating it with two British 

 Museum manuscripts. The time from July 20 until the winter of 

 1914 is being given to the completion of the glossary and revision of 

 the bibliographical introduction to his edition of Lydgate's Troy Book. 



MATHEMATICS. 



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

 tion of Cremona groups to the solution of algebraic equations. (For previous 

 reports see Year Books Nos. 9-12.) 



During the past year two papers on restricted systems of equations 

 were prepared by Professor A. B. Coble (American Journal of Mathe- 

 matics, April 1914 and October 1914). 



Ideas and material were developed for a series of papers on Cremona 

 groups associated with discrete sets of points and the relation of the 

 form problem connected with these groups to the solution of algebraic 

 equations. A general algebraic background is thus outlined for the 

 solution not only of the general equation of the ?ith degree, but also 

 for a number of special equations, such as that determining the lines 

 of a cubic surface. This investigation when completed will bring to 

 a logical conclusion the problem mentioned in the original application 

 for this grant. Important lines of further research suggest themselves. 

 One is a novel series of infinite discontinuous groups which appear both 

 in Cremona and in collineation form. A second is a very promising 

 relation between the n-point sets and theta-modular functions. 



