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 motion corresponds a parallax of 0".0025, corresponding to the sphere of radius 400R.
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 absolute 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 certain 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 G 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 continuously 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
