206 The Evolution of Rotating Nebulae [CH. ix 



205. In two cases we have calculated the value of a) 2 /2?rp at which the 

 sharp edge forms on the equator of a rotating mass of gas. In 152, dis- 

 cussing Roche's model, or an adiabatic gas for which 7 = 1J, we found the 

 critical value of a> 2 /27r/5 to be given by 



L = 0-36075. 



27T/5 



And in 183, discussing a mass of adiabatic gas for which 7 had the highest 

 value consistent with the formation of a sharp edge, namely 2^, we found the 

 critical value of a> 2 /27r/o to be given, approximately, by 



-- = 0-31. 



These limits for 7 are much wider than those which can occur in an actual 

 mass of gas, for which 7 must be greater than 1J and less than If. The 

 critical values of a) 2 /2?r^ are so comparatively close together that it seems safe 

 to assume that for an actual gas the critical value must be somewhere between 

 the two theoretical critical values, and probably considerably nearer to the 

 former than to the latter. For purposes of rough calculation we shall suppose 

 that the critical value is given by 



^4 = 0-35 .............................. (534). 



Comparison with Observation 



206. The course of events in our typical nebulous mass of gas may now 

 be briefly recapitulated. It has been supposed to come in to. existence in an 

 entirely unknown way, probably forming at first an irregular mass of com- 

 paratively cold gas at a very low density. This will contract under its own 

 gravitation and would in time assume a spherical form except that it is 

 repeatedly being disturbed by tidal forces from passing masses. The effect 

 of these is to set up a slow rotation which continually increases as the mass 

 contracts. The mass assumes at first a spheroidal form, then a pseudo- 

 spheroidal form, until, when the rotation reaches an amount given by equation 

 (534), a sharp edge is formed round the equator. The figure of the mass is 

 now lenticular in shape, and any further contraction results in matter being 

 thrown off from the periphery or equator of the lens. 



Fig. 41 shews the theoretical cross-sections which have been found for 

 two rotating masses of gas at the instant at which the sharp edge is first 

 formed, the two figures corresponding to the two extreme values of 7, 7= 1 

 and 7 = 2 respectively. The next stage in the motion will consist of the 

 ejection of streams of matter from the sharp edge. 



On comparing these figures with those of actual nebulae shewn on Plate III, 

 we at once notice the similarity in the cross-sections of the two sets of figures, 



