354 SEE— ORIGIN OF ZORE OF ASTEROIDS. [November 4, 



the remoter parts of the nebula, at a great distance from the center, 

 it will be doubly obvious that these insignificant secondary nuclei in 

 the outer parts of the nebula could not have rotated rapidly enough 

 to detach their satellites. This is emphasized also by the retrograde 

 motions of the outer satellites of Jupiter and Saturn, which are 

 entirely inconsistent with any theory of detachment. Such a view 

 would be nothing less than absurd. The relatively greater energy 

 of axial rotation of some of the planets is to be explained by the 

 capture of nebulous matter circulating as a vortex in the powerful 

 field of the sun's attraction, owing to its immense mass, which gives 

 the particles impinging against the planet great relative moment of 

 momentum. 



7. The column of the accompanying table designated "centrifugal 

 force "' gives the fractional part of the centrifugal force due to rota- 

 tion, when the central bodies are expanded to fill the orbits of their 

 attendant bodies as imagined by Laplace. In this table the unit in 

 each case is the amount of centrifugal force required to set the 

 body revolving in its present orbit. The excessively small value of 

 the centrifugal force due t the rotation of the expanded central 

 mass is very remarkable ; ai I emphasizes strongly the untenability 

 of the view that the attend nt bodies were thrown off. Nothing 

 more misleading than this traditional view ever became current in 

 the literature of science ; and yet it still circulates in all old works on 

 astronomy, and probably it will take many years to get it eliminated 

 from the current thought of our times. 



8. There is another impressive way of illustrating the unten- 

 ability of the now abandoned detachment theory, as follows : It is 

 shown in works on celestial mechanics that 



^r-=,k^l■^m){2/r~l/a), (i) 



where k- is the constant of attraction, ;;; the mass of the attendant 

 body, that of the central mass being unity, r is the radius vector, 

 a the semi-axis major, and z! the velocity. This gives for an at- 

 tendant body of insensible mass 



a = ^^- (2) 



