220, 221] The Galactic System 223 



number, will increase the density to a quite unknown extent, so that the 

 estimates only provide lower limits to the true density. 



Assuming these estimates to be somewhere near to the truth, a com- 

 parison with our previous estimate of the density of the primitive nebular 

 arms shews that the system must have expanded very largely in its passage 

 from nebula to star-cluster. Even the lower estimate of p = 10~ 20 requires an 

 expansion of about six linear diameters. The necessity for some such ex- 

 pansion can be seen without detailed calculations. Our estimate of p. 217 has 

 already suggested that the mass of the Andromeda nebula is about equal to 

 that of our galactic universe, so that we may think of it as a picture of the 

 primaeval nebula out of which we are conjecturing that our universe has 

 been formed. But the Andromeda nebula subtends an angle of less than 2 

 from the centre of our universe, whereas our universe probably subtends 

 about 30 when seen from the Andromeda nebula. 



The idea of such an expansion will probably present no difficulties to the 

 observational astronomer. The general appearance of the spiral nebulae is 

 certainly not unfavourable to the view that they are in an expanding state, 

 and this view is confirmed by the measurements of van Maanen and Kostinsky 

 already referred to ( 4) ; the matter in the nebular arms appears to be moving 

 away from the nucleus with no inconsiderable velocity. 



221. For further calculations, let us assume the density of the original 

 nucleus to have been 10~ 17 , corresponding ( 214) to a period of rotation of 

 160,000 years. The mass of the whole system being supposed to be 5 x 10 42 gms., 

 the volume of the nucleus before disintegration commenced must have been 

 5 x 10 59 cubic centimetres say a figure of radius 30 parsecs in its equatorial 

 plane and of radius 10 parsecs perpendicular to this. 



We suppose that this figure has expanded until its equatorial radius is 

 about 2000 parsecs say 66 times that of the original nucleus. During this 

 expansion the angular momentum Mko) must remain constant. The value of 

 k* may be supposed to have increased about (66) 2 times or say 4000 times, so 

 that the mean value of o> will have decreased to one four-thousandth of its 

 former value, and the final period of rotation will be about 640,000,000 years. 

 Thus our whole system may be expected to average one rotation in 640,000,000 

 years, or about 0'0020" per annum. The rotation calculated in this way 

 depends only very slightly on the initially assumed value of p, being in point 

 of fact proportional to p*. 



In this connection it may be mentioned that Charlier* has found that 

 the node of the invariable plane of the Solar System has a direct motion 

 on the plane of the Milky Way amounting to 0-003528" per year, or a revo- 

 lution in about 370,000,000 years. This, as Eddingtonf has remarked, might 

 equally well be interpreted as a retrograde rotation of the Milky Way in space. 



* Lund Meddelanden, u 9, p. 78. t Stellar Movements, p. 260. 



