is, u] Theories of Cosmogony 15 



luminous and remain so until the mass bursts into incandescence as a giant 

 M star. But, as we shall see later, Russell's theory does not destroy, but 

 actually strengthens, the belief that a star starts with a very low density, and 

 this virtually brings us back by a different path to the theory of nebulous 

 origin. 



The Rotational Theory 



14. The main outline of what we are now calling the rotational theory has 

 been sufficiently explained already. This theory originated in an effort to 

 explain the origin of the solar system. In its application to this particular 

 problem it has been subjected to many criticisms, one of which in particular 

 has seemed to many to be unanswerable. 



In 1861 Babinet* suggested that a criterion as to the tenability of the 

 general rotational theory was provided by a calculation of 'the present total 

 angular momentum of the solar system. He argued that if the planets had 

 been thrown off by rotation the moment of momentum of the original rotating 

 mass must have been exactly equal to the total moment of momentum of the 

 present system. The mass of the original body must also have been equal 

 to the total mass of the present system, so that on assuming a reasonable 

 size for this original body, the dynamical conditions of the mass can to some 

 extent be reconstructed, and in particular we can calculate the amount of 

 rotation with which it must have been endowed. Babinet pointed out that 

 the aggregate moment of momentum in the solar system is far too small for 

 the original mass to have been broken up by rotation alone. 



A simple calculation will shew that the greater part of the present moment 

 of momentum of the solar system resides in the orbital motion of Jupiter. 

 Taking the moment of momentum of the sun's present axial rotation as 

 unity, the moment of momentum of the orbital momentum of Jupiter is found 

 to 'be about 37, that of Saturn about 14, that of Neptune about 4*8, that of 

 Uranus about 3'3, and the aggregate arising from all the other planets, 

 asteroids, satellites, etc., is less than O'l. Thus the total is roughly 60 times 

 the present moment of momentum of the sun's rotationf. 



Now imagine the whole mass of the solar system concentrated in the sun, 

 which can be done with only an inappreciable increase (about '0013) of its 

 mass, and imagine the whole moment of momentum of the present solar 

 system concentrated in this one mass. The moment of momentum being 



* Comptes Renduis, 52 (1861), p. 481. See also Moulton, Astrophys. Journ. (1900), p. 103. 



t These are the figures given by T. J. J. See (Ast. Nach. 4053). See makes special assump- 

 tions as to the interior constitution of the sun, but any other reasonable assumption would lead 

 to similar figures. Fouche (C. E. 99, p. 903 (24 Nov. 1884)) calculates the total momentum to 

 be 28 '2 times that of the sun, but he assumes the sun to be homogeneous. Lord Kelvin has 

 given a well-known estimate (Popular Lectures, i. p. 420) according to which the ratio in question 

 is only 18, but he assumes the sun to be homogeneous, and also neglects the contributions from 

 Saturn, Uranus, Neptune, etc., this latter procedure being clearly erroneous. 



