THE ORIGIN OF THE EARTH. 



57 



a b 



relative to it would be revolutionary. To follow out even approximately 

 the actual motions of the sun and the protuberances in a given case of 

 this kind is extremely difficult and laborious. 

 It is obvious, furthermore, that in any given 

 instance a succession of protuberances follow- 

 ing one another at different stages of ap- 

 proach must probably have taken place, and 

 hence the formation of a nebula presents a 

 series of such extremely difficult problems. 

 Dr. Moulton has worked out the selected case 

 of two opposite protuberances, in which the 

 mass of the passing star is assumed to be 

 equal to that of the sun, and the protuber- 

 ances are assumed to be shot out to twice 

 the star's perihelion distance (Fig. 22). It 

 is further obvious upon consideration that 

 the number of possible cases that might arise 

 from the varying ratios of the masses and 

 from the varying distances of their approach, 

 is very large, and that immense labor is in- 

 volved in covering the whole ground and find- 

 ing out what cases are applicable to the 

 problem of the solar nebula, but in the course 

 of the series now being worked out under the 

 direction of Dr. Moulton, it is hoped that a 

 close approximation to the solar nebula may 

 be found, a hope which seems to be war- 

 ranted by the results thus far obtained. 

 Analytical considerations have seemed to 

 show that if the disturbing star were equal 

 to or more massive than the sun, and were 

 to pass very near to it, a large portion of the 

 sun would be dispersed with great velocity, 

 and the resulting nebulae would probably re- 

 semble those immensely expanded ones which are chiefly represented 

 in the foregoing illustrations. A more distant approach in which the 

 protuberances are small relative to the mass of the sun seems to be 

 more in consonance with the demands of the solar problem. It will be 



Fig. 22. — Diagram illustrating 

 the courses pursued by par- 

 ticles, P and P' , shot out 

 from the sun, S, on opposite 

 sides under the disturbing 

 influence of a passing star, 

 S', when at the position S/. 

 The successive positions of 

 the disturbing star are in- 

 dicated by S/, S 2 ' . . . S/, 

 assumed at successive time- 

 intervals. When S' was at 

 the position &/, the par- 

 ticles P and P' were shot 

 out from S with velocities 

 such that if not disturbed 

 they would have reached 

 to distances twice AS. 

 P 2 . . . P 1 and P 2 ' . . . P/ 

 are the successive positions 

 assumed by these particles 

 at the successive times, a-b 

 is the acceleration at unit 

 distance. (After F. R. 

 Moulton.) 



