214 The Evolution of Rotating Nebulae [CH. ix 



as the centre of gravity of the nebula, and terms beyond S 2 may be omitted 

 as being numerically small in comparison with S 2 . Thus V T may be sup- 

 posed to reduce to the single term S 2 , and the total potential fl (cf. equation 

 (390)) assumes the form 



n==F M + S 2 +ift> 2 (^ + 2/ 2 ) (538). 



When the external potential S 2 is omitted, the condition for a break-up 

 n 0) becomes 



- 



Sr 



and the break-up commences simultaneously at all points of the cross-section 

 in the plane of xy. But when the term S 2 is included in H the cross-section 

 in the plane of xy can no longer be circular ; it becomes slightly elliptical and 

 obviously the break-up will occur first at the two -ends of the major-axis of 

 this ellipse. Thus instead of a ring of matter being thrown off, we see that 

 matter will be thrown off initially only at two antipodal points. 



The first elements of matter thrown off from these two points form in 

 themselves a tide-generating system whose potential must now be included 

 in the general tide-generating potential V T . The effect of this addition will 

 clearly be to reinforce the value of the second harmonic term in V T , so that 

 when matter has once started coming off from two antipodal points, the region 

 of ejection will concentrate more and more at two points as the motion 

 proceeds. Under ideal conditions we may expect to have matter thrown off 

 uniformly from all round the equator ; under actual conditions we must expect 

 two streams of matter issuing from antipodal points. 



213. At this stage it will be profitable to pause again in our theoretical 

 investigation to compare theory with astronomical observation. 



Theory predicts the existence of rotating masses of gas of a lenticular 

 form having sharp edges in their equatorial plane. These we have already 

 ( 207) found reasons for identifying, at least provisionally, with the so-called 

 " lenticular " nebulae of which examples are illustrated in Plate III. 



Theory further predicts that an emission of matter ought to take place 

 in the equatorial plane : most of the examples illustrated in Plate III shew 

 an extension of figure in the equatorial plane which may very reasonably be 

 interpreted as matter ejected from this plane. The dark band in nebula 

 N.G.C. 5866, lying as it does along the equator*, strongly suggests darker 

 and cooler matter which has cooled after ejection, while still more pro- 

 nounced dark bands are shewn in the three subsequent nebulae on Plate III. 

 Theory predicts that the ejection of matter from the equator ought to continue 

 almost indefinitely, so that the extensions in the equatorial plane ought to 

 extend further and further as the evolution of the nebulae proceeds. Theory 



* Pease (I.e. ante) describes the dark streak as making an angle of 3 with the major-axis of 

 the nebula. 



