270 The Origin and Evolution of the Solar System [CH. xn 



For compressible and non-homogeneous masses, rotational break-up can 

 occur in two, and only two, ways by fission or by equatorial ejection of 

 matter. Fission can only begin after the configuration has passed the point 

 of bifurcation at which the pseudo-spheroidal form gives place to the pseudo- 

 ellipsoidal. The value of a> z /27ryp at this point depends naturally on the 

 structure of the mass. For a gas in adiabatic equilibrium, the possible limits 

 have been found to be 



0-18712 <^< 0-31. 



The limits for equatorial break-up for a mass in adiabatic equilibrium 

 have similarly been found to be 



0-31 <~^< 0-36075. 



In both these sets of limits the entry 0*31 is subject to considerable error, 

 but this is immaterial to our present purpose. It seems quite certain that a 

 mass of gas in adiabatic equilibrium cannot break up rotationally unless the 

 value of o> 2 /27T7p has exceeded the value 0-18712. 



A natural mass of gas differs from a mass in adiabatic equilibrium in two 

 respects the quantity k, or plp y , will not be constant throughout the mass, 

 and the chemical structure will not be constant throughout the mass. For 

 stability, k must increase on passing outwards along a radius, and the heaviest 

 molecules or atoms must sink towards the centre. Both of these departures 

 from the adiabatic arrangement tend to increase the degree of central con- 

 densation of mass. The mass approaches more closely to Roche's model, and 

 the critical value of o> 2 /27r7J5 approaches more closely to the value 0-36075. 

 Thus we seem fully justified in supposing that no mass can break up rota- 

 tionally until after a) 2 /27ryp has exceeded the value 0'18712. 



In particular, if our solar system has been formed by the rotational 

 break-up of a primitive mass of any kind whatever, the value of a) 2 /27ryp for 

 this body must have been greater than 0'18712 before break-up commenced. 



285. Babinet's criterion ( 14) proceeds on the suppositions that the mass 

 of this primitive body must have been equal to the total mass of the present 

 solar system, and that the angular momentum of this body must have been 

 equal to the total angular momentum, rotational and orbital, of the solar 

 system. 



Neither of these suppositions is altogether justifiable. The supposition 

 that the angular momentum has remained constant requires us to suppose 

 that our system has remained entirely undisturbed by encounters with other 

 systems ever since its birth. This is in opposition to the results reached in 

 the two last chapters, where we came to the conclusion that most stars, with 

 the exception of B- type and some A -type stars, shew evidence of having 

 experienced considerable disturbance by other systems; there is no reason 



