l86 RKPORTS ON INVESTIGATIONS AND PROJECTS. 



REPORT OF F. R. MOULTON, 

 University of Chicago. 



During the past year I have been engaged in two general lines of 

 inquiry. The first has been to find out whether our solar system 

 could have developed out of a " planetesimal nebula" having a few 

 nuclei of considerable dimensions. The test has been made with 

 respect to all the more important features of the system, such as the 

 rotation and equatorial acceleration of the sun, the direction of 

 revolution of the planets and the small relative inclinations of their 

 orbits, the small eccentricities of the planetary orbits, the directions 

 of rotation of the planets, the origin of satellites and their directions 

 of revolution, the eccentricities of the orbits of the satellites, and the 

 orbits of the asteroids. Although several of the.se questions had 

 been considered by Professor Chamberlin, it seemed advisable to go 

 more fully into the dynamics of the whole theory in order to be per- 

 fectly sure that it would justify the undertaking of the extensive com- 

 putations which we are now carrying out. The results obtained have 

 been in all cases qualitatively favorable to the theory. In order to 

 test the theory quantitatively it seems to be necessary to make some 

 assumptions respecting the eccentricities of the orbits of the original 

 nuclei and of the great number of small bodies which they have swept 

 up. The necessity of making these assumptions has driven me to 

 the second line of inquiry. The details of the results obtained in the 

 first line of inquiry may, I think, be more profitabl)^ withheld until 

 they shall have had complete quantitative application. 



The second line of inquiry is respecting the possibility of a plan- 

 etesimal nebula originating from the matter ejected by one sun while 

 another sun is passing near it. A rough preliminary examination, 

 something like the one made by Professor Chamberlin, showed that 

 there is a strong probability that planetesimal nebulas may originate 

 in this way. While it is a simple matter to find the character of the 

 disturbing forces for any relative positions of the two suns and the 

 ejected material, it is a very laborious task to compute the continued 

 effects of these forces, for they are not only large, but they vary in a 

 most complicated manner. In some cases it has been necessary to 

 follow the perturbations for more than twenty years. 



The problem of three bodies of the type considered here is not 

 susceptible of general treatment by the mathematical processes now 

 in use, and it has been necessary to go to the examination of special 

 typical cases by numerical processes. In this work I have had the 

 very efficient assistance of Mr. Elton James Moulton, who has car- 



