CHAPTERS ON THE STARS. 465 



a vague idea of the actual parallaxes. Let us take, for example, the 

 stars of the sixth magnitude. A few of these are, doubtless, quite 

 near to us and have a parallax several times greater than that of the 

 table. Excluding these from the mean, an important fraction of the 

 remainder will have a parallax much smaller than that of the table. 



We get a slightly more definite result by studying another feature 

 of the proper motions. We may consider the Bradley stars, whose 

 motions have been investigated, as typical, in the general average, of 

 stars of the sixth magnitude. By a process of reasoning from the 

 statistics, of which I need not go into the details at present, it is shown 

 that the parallactic motion of a large number of these stars, probably 

 one-eighth of the whole, is about 1" per century or less. To this mo- 

 tion corresponds a parallax of 0".0025, corresponding to the sphere of 

 radius 400K. 



The statistics of cross-motions lead to a similar conclusion. One- 

 half the Bradley stars have a cross-motion of less than 2 ".5 per century. 

 To this motion would correspond a sphere of radius 200R and a parallax 

 of 0".005. Stars at this distance must be hundreds of times the abso- 

 lute brightness of the sun to be seen as of the sixth magnitude. Yet the 

 conclusion seems unavoidable that the sphere of lucid stars extends 

 much beyond 400R. 



Granting the star density we have supposed, a sphere of radius 

 400R would contain 8,000,000 stars. As we see many more than this 

 number with the telescope, we have no reason to suppose the boundary 

 of the stellar system, if boundary it has, to be anywhere near this limit. 



All the facts we have collected lead to the belief that, out to a cer- 

 tain distance, the stars are scattered without any great and well-marked 

 deviation from uniformity. But the phenomena of the Milky Way 

 show that there is a distance at which this ceases to be true. Let S 

 be the sun, R a portion of the surface of the outer sphere of uniform 

 distribution, and R2 and R3 two contiguous spheres passing through 

 the galactic region G, of which the pole is in the direction P. It is 

 quite certain that the star-density is greater around Gr than around P. 

 This may arise either from the density at G being greater, or from that 

 at P being less, than the density within the sphere R. From the 

 enormous number of stars collected in the galactic regions, we can 

 scarcely doubt that the former alternative is the correct one. But 

 there must be a sphere at which the second alternative is also correct, 

 because we find the number of stars, even of the lucid ones, to con- 

 tinuously increase from P toward G. 



Can we form any idea where this difference begins, or what is 



the nearest sphere which will contain an important number of galactic 



stars? A precise idea, no; a vague one, yes. We have seen that the 



galactic agglomerations contain quite a number of lucid stars, and 



vol. lviii.— 30 



