up by Boss of the Dudley Observatory, Albany, New York. By the recent study of several thousand of the brighter stars included in his Preliminary General Catalogue, Professor Boss has deduced their proper motions with a high degree of accuracy. Campbell found from 180 of these stars resembling our sun in spectral type that their average cross proper motion in the sky, from the values derived by Boss, was about 0.11 second of arc per annum, while at the same time their average speed in the line of sight shown by the spectrograph at Lick Observatory was 8.9 miles per second, or two hundred and eighty million miles a year. Having the average motion in the line of sight, in absolute units, and the average cross proper motion in seconds of arc, it is easy to find how far away a base line of 280 million miles would have to be to subtend an angle of 0.11 of a second of arc. It turns out to be ninety-two light-years.

In this way it is possible to get the average distances of large groups of stars. Here are some of the results found by Campbell.

This table contains the most important results of the CampbellBoss method of obtaining average distances for large groups of stars. It need scarcely be remarked that its significance can hardly be overrated. But whilst the average values given are quite trustworthy, the method is of course inapplicable to the individual stars; and if their distances are to be found recourse would have to be had to the standard method of parallaxes, or to the spectroscopic method in the case of visual binaries.

85. SOME OF THE DISTANCES OF THE REMOTEST STARS AS HERETOFORE CALCULATED BY ASTRONOMERS.

1. Sir William Herschel, Phil. Trans., 1802, p. 498, "almost 2,000,000 lightyears."

2. Sir John Herschel, "Outlines," edition of 1869, p. 583, “upwards of 2,000 light-years."

3. Guillemin, "The Heavens," trans. by Lockyer, 1867, p. 433, “upwards of 20,000 light-years."

4. Bartlett, "Spherical Astronomy," 1874, p. 149, "upwards of 2,437.5 lightyears."

5. Newcomb, "Popular Astronomy," edition of 1878, p. 481, "about 14,000 light-years" (for the Herschel stars).

6. Clerke, “System of the Stars," 1890, p. 314, “less than 36,000 light-years." 7. Ranyard, “Old and New Astronomy," 1892, p. 748, “less than 70,000 lightyears."

8. Young, "General Astronomy," edition of 1904, p. 563, "10,000 to 20,000 light-years."

9. Newcomb, “The Stars," 1908, p. 319, “at least 3,000 light-years." 10. See, "Researches," Vol. II., 1910, p. 638, “4,500,000 light-years."

From this table it will be seen that there was a great falling off in the distances following the epoch of Sir William Herschel; and that the present writer was the first to recognize the fallacy of the recent estimates of distance, and to restore the large values used by that unrivaled astronomer one hundred and ten years ago. Here we have a good illustration of the retrogradation of opinion in astronomy, under the cultivation of inferior genius. Sir John Herschel's preference for such small distances over the large values used by his father is indeed remarkable and very regrettable. Evidently the small value used by Newcomb is simply an echo of the reduction in distance made by Sir John Herschel. The absurdity of these small values-not over five times that of the helium stars of 4.14 magnitude investigated at Lick Observatory-ought to impress us with the small importance to be attached to any opinion merely because it is currently accepted. Thus we have a clear case of misleading tradition transmitted from the second Herschel, and the amazing spectacle of the whole world using values about a thousand times too small, for the greater part of a century, in times which were supposed to be very enlightened! Strange indeed that the correct work

of the great Sir William Herschel should have been neglected all this time! Will it seem credible to future ages that such a remarkable retrogradation of opinion could have occurred and persisted during the nineteenth and twentieth centuries? If so, it must be attributed to the narrowing effects of extreme specialization, which, with the advance of science, has been difficult to avoid in our time, and yet is utterly disastrous to the growth of true natural philosophy as the study of nature in the widest sense.

§6. OTHER METHODS FOR CONFIRMING THE GREAT DEPTH OF THE MILKY WAY.

(a) The girdle of helium stars about our sun, according to the Lick determination, has a mean distance of 540 light-years, or a mean diameter of 1,080 light-years. If this be one twentieth of the average thickness of the Milky Way stratum, as one may infer from the appearance of certain clusters in the constellation Sagittarius, which are near enough to be studied intelligently, then we have 21,600 light-years for the average thickness of the Milky Way.

Now when we traverse the Milky Way from Centaurus to Cepheus, over an arc of 180° in length, the central band appears to the naked eye to have a width of 3° or 4°, as was long ago remarked also by Herschel and Struve. This is an extension along the circle of the Galaxy of about 60 times its thickness. If then the thickness be 21,600 light-years, the double depth of the stratum in both directions becomes about two thirds of 21,600 X 60=864,000 light-years. And if only the faint or distant telescopic stars be considered, the width of their belt of distribution is narrower, and the depth would be found several times greater yet. Wherefore it seems certain that the profundity of the Milky Way, considerably exceeds a million light-years, and may be several times that depth.

(b) Accordingly if we make the very moderate hypothesis that the width of 3° or 4°, which was also noticed by Herschel and Struve, represents chiefly the nearer portion of the Galaxy; and that the remoter portion has a width not exceeding 1°, we should conclude that the depth may be found by multiplying the thickness

or apparent angular width of 21,600 light-years by the number of degrees in the radius, 57.3. This gives for the depth 1,237,680 lightyears, and this value might be considerably increased by adjustments in the data which are not improbable.

(c) In addition to these general arguments, founded on the principles of geometry, we might introduce another based on actual measurement. The Lick helium stars, of average brightness 4.14 mag., were found to have an average distance of 540 light-years. If they were brought near enough to us to appear of 1st magnitude, this distance would have to be divided by 4V (2.512)3, and thus we find for the first magnitude helium stars a distance of 135 light-years.

Now in calculating the plan of the construction of the heavens, from the apparent breadth of the Milky Way, Herschel arrived at the conclusion that the thickness of the stratum is about 80 times greater than the diameter of the sphere including the first magnitude stars represented by Sirius (Phil. Trans., 1785, p. 254). And if the average distance of these stars be taken as 135 light-years, the mean diameter of the shell in which they are included will be 270 lightyears. This would give exactly 21,600 light-years for the thickness of the stratum of the Milky Way, as before.

It is true that Herschel classed all first magnitude stars in one group, and took no account of the fact that the helium stars are the more remote and the more brilliant; yet regarding the Galaxy as a stratum of stars chiefly of the helium type, which certainly is true of all the more distant portions of that magnificent collection of stars, we may consider the reasoning of this great astronomer as still valid. And the argument in regard to the depth of the Milky Way is thus the same as that given above under (a) and (b).

87. THE EFFECTS OF THE EXTINCTION OF LIGHT IN SPACE.

This problem has been treated with some detail in the 23d chapter of my "Researches," Vol. II., 1910, but we shall here examine the subject with greater care, especially as to the most probable average value of the coefficient of extinction. The light was shown.

by Struve to be defined by the equation

I

(0.990651) -1,

(1)

where is the distance of the star, in units of AV (2.512)" and n is the difference in magnitude. At very great distances nearly all the light is cut off, and it therefore becomes a question of high importance to determine as accurately as possible the proper value for the coefficient of extinction.

Struve's value, used in the above formula, seems to be too large, and I have therefore calculated a new table, to show the effect of decreasing the coefficient. In justification of this course it should be recalled that Sir William Herschel ignored extinction entirely; but while this procedure obviously is defective, it is pretty clear, from the aspects of the Milky Way as now made known by modern research, that Struve's coefficient is decidedly too large. The following table shows the effects of varying the coefficient, upon stars 17 magnitudes fainter, corresponding to a distance 2,512 times larger, where r -I =2,511.

From the study of this table, we perceive that at the distance