240-243] Stellar Motions in the Galactic Universe 237 



would obviously be of the same order of magnitude. This may be compared 

 with the possible period of rotation of 370,000,000 years for the Milky Way 

 referred to in 220. Thus after 10,000,000 years the path of the average 

 star will have undergone a deflection of only about 22 on account of the 

 description of its orbit under the attraction of the universe as a~ whole, while 

 encounters with near stars will, as we found in 228, have given it a cross- 

 velocity out of its orbit of the order of 16 metres a second. This velocity, for 

 a star moving with a velocity of 25 kms. a second, corresponds to a deflection 

 of only about 2'. 



Thus it appears that after an interval of 10,000,000 years the courses of 

 the stars will be but little altered ; their orbits over 10,000,000 years are not 

 far removed from the straight lines they would describe if gravitation were 

 suddenly annihilated. It is clear that the approach to a final steady state 

 is an excessively slow process. 



We must, however, bear in mind that the foregoing calculations have 

 been based upon numerical data derived from a consideration of the system 

 in its present state. Our conjecture that the system may have evolved out of 

 a rotating nebula of dimensions much less than those of the present system 

 compels us to suppose that conditions must have been very different in the 

 past. Adopting the conjectural figure arrived at in 221, we see that the 

 period of description of an orbit in the earliest stages of a star's life must have 

 approximated to 1 60,000 years, as compared with our estimated present value 

 of about 160,000,000 years. Here we have immediately a shortening of the 

 time-scale to about a thousandth part of its present value ; what gravitation 

 fails to accomplish now in 10,000,000 years may have been accomplished in 

 10,000 years when the system was young and the stars closely packed 

 together. 



243. A still more far-reaching change occurs when we turn back to 

 nebular conditions. 



In 220 we estimated that the density of stars in the nebular arms may 

 initially have lain between two limits. According to the first, stars were 

 7 ^ parsec apart, giving about 400,000 stars to the cubic parsec ; according to 

 the second, in which the stars were parsec apart, there would be 125 stars 

 to the cubic parsec. Either star-density is very high compared with that of 

 our present system which we have estimated as one star per 13 cubic parsecs. 

 Thus the quantity v which we have taken to be 10" 56 ' 5 must be increased at 

 least a thousand- fold, and perhaps a million-fold before our calculations can 

 apply to our system in its earliest stages. 



The effect on our previous calculations is profound. The times between 

 successive collisions and the time required for a star to be deflected appreciably 

 from its course by encounters with neighbouring stars are reduced enormously 



