16 Introductory Chapter [CH. i 



increased 60-fold, and the mass remaining substantially the same, it follows 

 that the angular velocity will be about 60 times what it is now, and instead 

 of having a period of rotation of 25 days, the new sun will have a period of 

 about 10 hours roughly the same as that of Jupiter. The mean density of 

 the sun (1'36) is roughly equal to that of Jupiter (T30) so that the primitive 

 sun reconstituted in this way will be very similar to the present Jupiter, only 

 of greater mass. The mass of a body, as we shall see later, has almost no 

 influence on its tendency to break-up rotationally ; this depends almost 

 entirely on its angular velocity and mean density. Now Jupiter shews an 

 ellipticity of only about 3^, and is to all appearances very far from breaking 

 up under the influence of its rotation, so that we cannot suppose our primitive 

 sun to have broken up by rotation. 



In this we have supposed the primitive sun to be of about the same size 

 as our own sun ; it must certainly have been larger, and this makes the result 

 still more certainly true. The rotational theory asserts that shrinkage is the 

 primary cause of the inset of instability which results in the throwing off of 

 a satellite ; if the primitive sun, when shrunk to the size of our present sun, 

 does not throw off a satellite, it certainly cannot have thrown off a satellite as 

 the result of rotation before the shrinkage took place, when its dimensions 

 may have been a thousand or a hundred thousand times what they now are. 



The discussion of whether or not this criticism of the rotational theory is 

 valid will naturally be deferred until our mathematical investigations have 

 provided evidence on which to base a judgment. 



II. THE TIDAL-ACTION THEORY 



15. Suggestions have at various times been made that tidal forces may 

 play the preponderating part in effecting the birth of satellites, for it is obvious 

 that, when subjected to tidal forces of sufficient intensity a mass of fluid may 

 reach a breaking point at which it divides into two or more detached masses. 

 The most complete form of tidal-action theory is found in the " Planetesimal 

 Theory" of Chamberlin and Moulton*. 



A non-rotating mass will in general assume a spherical shape under the 

 action of its own gravitational forces, but will depart from this form when a 

 second body approaches near enough for its tidal influence to be perceptible. 

 At the approach of a second body, the spherical shape will at first give place 

 to a spheroid of small ellipticity, owing to tides being raised directly under 

 and directly away from the tide-raising body. With the closer approach of 

 this body the tides continually rise in height, and Chamberlin and Moulton 

 suppose that ultimately two jets of matter rush out from the two antipodal 



* A summary of a comprehensive kind will be found in Chamberlin's Origin of the. Kartli 

 (Univ. of Chicago Press, 1916). 



