Principles of the Nebular Theory. 269 



leaving a system of stars with no central sun. We may sup- 

 pose, for instance, our solar nebula to have been expanded 

 originally to less than half the distance to the nearest fixed 

 star, say to 3500 times the distance of Neptune. Then much 

 less than the 40,000,000,000th of the entire mass would have 

 been within the present orbit of Neptune. All the matter 

 exterior to that orbit would have been abandoned as equatorial 

 rings ; and even the matter at that orbit, and some within, 

 would have been so abandoned. This appears as follows. 

 We have just seen that the velocity of a planet in its orbit is 

 to a fall from infinite distance as 1 is to the square root of 2. 

 We take the velocity of Mercury in its orbit as 110,000 miles 

 per hour, and that of Neptune as 12,500 miles per hour; 

 therefore 



1 : VI : : 110,000 : 154,000 



1: x/2:: 12,500: 17,625 

 Difference . 136,375 

 Therefore a full from the orbit of Neptune to that of Mer- 

 cury would gain a velocity of 136,375 miles per hour, which 

 is far more than that of Mercury. Hence a nebula rotating 

 through all its interior, and contracting through a distance 

 from Neptune to Mercury, would gain a velocity great enough 

 to separate by centrifugal force nearly all of its interior matter ; 

 and therefore all its matter exterior to that orbit would be sepa- 

 rated, leaving an excessively small amount to subside at the 

 centre. With so small an amount of matter within that orbit, 

 the force of gravity toward the centre would be very small, 

 and the consequent velocity of rotation and centrifugal force 

 very small. But the proportion between the centrifugal and 

 centripetal forces would remain the same, and the equipoise 

 between the two would occur at the same distance from the 

 centre, as if they were both large. 



Corollary 1. — An ancient nebula vastly expanded, whose 

 primitive rotation pervaded its entire mass, might gain a cen- 

 trifugal force to abandon nearly all its materials as rings far 

 away from its centre ; and as contraction continued, those 

 rings would break and condense into stars forming an annular 

 system like that in Lyra, or like our own sidereal system, whose 

 stars are chiefly in the galactic ring or rings. 



Cor. 2. — A nebula with a smaller amount of rotation in its 

 interior at the beginning, would not abandon its chief materials 

 so far from the centre. But it might abandon its materials 

 evenly from the circumference to the centre, and thus form a 

 sidereal system which would appear in the vast distance like 

 what are called planetary nebulae. 



