1 88 REPORTS ON INVESTIGATIONS AND PROJECTS. 



carrying them out we shall obtain a good idea of the importance of 

 these processes in cosmical evolution. 



In all the orbits so far treated the disturbing sun, which we shall 

 call S', was supposed to have the same mass as our sun. It was 

 supposed that it moved around our sun, S, in a parabolic orbit. In 

 the first case it was supposed that the perihelion distance of S' was 

 five astronomical units, or nearly the distance of Jupiter. The ejec- 

 tion was supposed to have taken place when S' lacked 90° of being 

 at the perihelion of its orbit. The ejection was supposed to have 

 been both toward and from S' with velocities sufficient to carry the 

 material, if it were undisturbed by S', out to 10 astronomical units. 



lyet us consider first the material ejected toward S'. Its deviation 

 from a straight Hue was slight until its distance was about six astro- 

 nomical units. At this time it was moving in an hyperbolic orbit 

 with respect to S. Then its direction of motion was rapidly changed 

 by the perturbations of S', and the eccentricity of its orbit rapidly 

 decreased. By the time S' had reached its perihelion the ejected 

 material had moved through a heliocentric angle of about 40°, the 

 eccentricity of its orbit had become small, and it was near the peri- 

 helion of its orbit. A little later its orbit became exactly circular. 

 Then it became again elliptic with the ejected material near the 

 aphelion ; that is, the aphelion and perihelion had changed ends by 

 the orbit passing through the circular form. The perturbations 

 turned the orbit in more and more toward the sun until the eccen- 

 tricity had increased to 0.97 and the perihelion distance had shrunk 

 to 6,500,000 miles. At this point the effect of S' became negligibly 

 small. The large eccentricity was produced by an excess of per- 

 turbation by S'. It would have been smaller if the mass of S' had 

 been taken less, if S' had been moving in a hyperbolic orbit, or if 

 the ejection had occurred when S' was nearer its perihelion. 



The particle which was ejected in the direction opposite to vS' went 

 in nearly a straight line until it had receded eight astronomical units. 

 All of this time S' was tending to increase its velocity. Then it began 

 to curve off in the direction in which S' was traveling around S, but 

 S' continued to accelerate its speed. The result of this acceleration 

 was that the orbit became hj^perbolic with an eccentricity at one 

 time probably exceeding 2.0 ; but when S' got about 115° beyond the 

 perihelion its effect on the eccentricity was reversed and it steadily 

 decreased until it was 0.98. While the perturbations of S' were still 

 sensible, it was not thought anything of value would be learned by 

 pursuing this case further. The major axis was over 1,500 astro- 

 nomical units and the perihelion distance was about 20. The major 



