376 CARNEGIE INSTITUTION OF WASHINGTON. 



MATHEMATICS. 



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

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

 reports see Year Books Nos. 9-13.) 



During the past year Professor A. B. Coble has continued his 

 researches on point sets and alHed Cremona Groups. The results are 

 embodied in a memoir in three parts. The first of these appeared in 

 the Transactions of the American Mathematical Society for April 

 1915. The other two should be completed for pubUcation this fall. 

 An abstract of parts II and III appeared in the Proceedings of the 

 National Academy of Sciences, May 1915. 



Professor Coble has also in hand a study of the relations between 

 point sets and theta functions. Professor Corner, a former associate 

 under the grant, has completed the work which as associate he under- 

 took in a memoir on "The Rational Space Sextic and the Cayley Sym- 

 metroid," which appeared in the American Journal of Mathematics, 

 April 1915. 



MATHEMATICAL PHYSICS. 



Moulton, F. R., University of Chicago, Chicago, Illinois. Investigations in 

 cosmogony and celestial mechanics. (For previous reports see Year Books 

 Nos. 4, 5, 8-13.) 



The unpubUshed investigations of the past year are as follows: 



(1) Computations on periodic orbits. — The discovery of critical peri- 

 odic orbits, closed orbits of ejection, and orbits of ejection and collision, 

 by computation for the purpose of estabUshing the relations among 

 the various famiUes of periodic orbits, has been continued and is now 

 complete. 



(2) Asymptotic orbits. — Certain classes of asymptotic orbits are 

 important in a general survey of the field of periodic orbits. A con- 

 siderable number of asymptotic orbits have been computed. 



(3) The solution of an infinite system of equations of the analytic 

 type. — This problem was originally suggested by certain processes 

 employed by Hill in his Lunar Theory, and whose vahdity he did not 

 prove. By a special application of the results reached, Hill's method 

 is justified in a suitably restricted domain. The work of Poincare 

 and von Koch on infinite determinants and infinite system of Hnear 

 equations had already completed the logic in Hill's work on the motion 

 of the moon's perigee. The present investigation fills the final gap in 

 his work on the Lunar Theory. But this is only a single apphcation; it 

 enables one to show, among other things, the possibiUty of the expan- 

 sion of the coefficients of the Fourier developments of certain elhptic 

 functions as power series in the parameters on which they depend. 



