386 CARNEGIE INSTITUTION OF WASHINGTON. 



orators in various parts of the country. Begun in April 1919, they are 

 now all in the hands of the editor, and have been twice verified and 

 otherwise edited by a staff of assistants. Slips for variant readings 

 are being prepared by volunteers and by the editor; also slips for 

 selected examples of words not to be printed in full. Alphabeting is 

 now proceeding rapidly and it is hoped will be completed by the end of 

 the summer of 1920. The chief remaining task will then be adjusting 

 and standardizing the arrangement. 



MATHEMATICAL PHYSICS. 



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

 mathematics, cosmogony, and celestial mechanics. (For previous reports 

 see Year Books Nos. 5, 6, 8-18.) 



During the past year the volume on Periodic Orbits, Publication No. 

 161, has appeared. A large amount of work was done on the last chap- 

 ter, pp. 485-524. Three papers on optical subjects have been pub- 

 lished in Visual Education (Chicago), as follows: 



1. Human eyes, January, pp. 25-34. 



2. Telescopes, April, pp. 17-23. 



3. Spectroscopes, May, pp. 11-17. 



At the American Mathematical Society Colloquium, which was held 

 in Chicago, September 8-11, 1920, five lectures were given on "Topics 

 from the Theory of Functions of Infinitely many Variables." These 

 lectures, which contained a large amount of original mateiial, will be 

 published by the American Mathematical Society. The titles of the 

 lectures and their synopses, as given in the program of the Colloquium 

 are as follows: 



I. Infinite Systems of Linear Equations. 



1. Completely reduced systems. Historical examples. 



2. The formal method of reduced systems. Historical examples. 



3. Normal infinite determinants. The Hill-Poincare form; the von Koch form. 



4. Infinite systems of linear equations having normal determinants and bounded right 



members. 



5. Absolutely convergent infinite determinants. 



6. Infinite systems of linear equations having absolutely converging determinants and 



bounded right members. 



7. Infinite systems of linear equations having absolutely converging determinants and 



coefficients analytic functions of a parameter. 



8. Irregular solutions of infinite systems of linear equations. Examples. 



9. The general theory of Schmidt. Solutions for which 



converges, including the limiting cases /> = 1, />= oo. 

 10. The method of successive approximations. 



II. On Properties of Functions of Infinitely Many Variables. 



1. Hilbert space (H-space) and parallelopipedon space (P-space). The mutual inde- 

 pendence of H-space and P-space. 



