ASTRONOMICAL NOTES

THE EVOLUTION OF BINARY SYSTEMS.- It is a fundamental fact of stellar dynamics that adjacent stars interfere to only an infinitesimal extent with one another's motion; the alterations in a star's motion must be ascribed to the gravitational forces of the universe as a whole. These latter forces can have only an infinitesimal effect on a star's angular momentum, whence it follows that the angular momentum of a star, or stellar system, must remain very approximately constant.

Assuming this constancy of angular momentum, it is well known that the angular momentum of our solar system is too small for the system to have broken up by rotation. This difficulty has been amply discussed; the present paper deals with a similar difficulty which has hardly been discussed at all, namely, that the angular momentum of the majority of binary systems is too large for them to have broken up by rotation.

At this stage only two hypotheses seem to be consistent with dynamical theory:

(A) The periods and dimensions of orbits of binary stars are permanently fixed, and have retained approximately their present values through the whole of the star's life.

(B) The periods and dimensions of orbits of binary stars, although now definitely fixed, have been determined as the result of interactions with other stars in some past epoch in which these interactions were not negligible.

Conclusion.We have found that there is only one hypothesis which is capable of reconciling the facts of observational

astronomy with dynamical theory. It is that the present epoch in the history of our universe was preceded by one in which the stars were much more closely packed than they now are, so that stellar encounters at fairly close distances, instead of being rare events of negligible frequency, were events of comparatively common occurrence. Such encounters must have increased the eccentricities and periods of our long-period binaries to their present values; from now on the periods both of these and of the short-period binaries are likely to vary but little.

The main hypothesis, that the stars were formerly closer together than now, is not difficult to accept. If we suppose the stars to have been formed by a process of nebular condensation, it becomes almost inevitable. If the stars, with their present spacing, were redissolved into a continuous nebular mass, the mean density of this nebular would be of the order of 10-23 only. Now the average mass of stars formed by gravitational condensation out of a continuous nebular mass depends upon the density of the nebula, and masses comparable with those of our sun and stars would be formed out of a nebula of density of the order of 10-19. The hypothesis of nebulous origin commits us to the supposition that our universe must have expanded by at least about ten diameters since its nebular stage. It is open to question whether this expansion is not still going on. The observed positive excess of radial velocities of stars of all types, particularly the 5 kms. a sec. excess velocity of the B-type stars, is most naturally interpreted as an expansion taking place now before our eyes.

We suppose the longest period binaries to have lived through sufficient of this earlier epoch for equipartition of energy to have been established, or approximately established, in their internal degree of freedom. It follows that equipartition ought also to have been established as regards their motion of translation in space. This is probably the case; the dwarf M-stars have velocities which show no preference for particular directions in space, and there seems to be no correlation between the magnitude of their velocities and the parts of the universe they occupy.

The old objection that the present spacing of the stars leads to a "time of relaxation" of the order of 10 or 10 years is removed by our main hypothesis.

On the other hand, the short-period binaries, which are mainly early type stars, cannot have lived through this earlier period as binary stars. The circumstance that they largely fall into undissolved moving clusters of stars having a common velocity in space leads us still further and suggests that these early type stars cannot have existed at all during the early period. We are led to regard the B type stars and short-period binaries as of more recent birth; neither in their velocity of translation nor in their internal motions do they show evidence of encounters with other stars. They are mainly still close to the galactic plane in which we must suppose them to have been born; they were perhaps the last stars to be born out of the rotating nebula which we may suppose to have been the parent of our system of stars.-J. H. JEANS, M.A., F.R.S., Monthly Notices, Royal Astronomical Society, December, 1918.

THE GEGENSCHEIN OR AFTERGLOW.-The gegenschein is always best seen in September, October and November. It is then largest and brightest.

These positions show quite clearly that the gegenschein is on the ecliptic and exactly (180°) opposite the sun. My previous observations also proved this fact. It is not probable that this condition can exist for any celestial body. It seems certain from this exact opposition to the sun that the phenomenon is in no sense a celestial one, and that its explanation must rest alone in the earth and the sun.

The more familiar one becomes with it the larger it appears. I have seen it 40°, 50° and even 60° in diameter when it would seem to fade insensibly into the night. Under these conditions it has been round and very gradually a little brighter towards the centre.

The gegenschien has always seemed to me to be due in some way to a concentration of the sun's light by refraction in the

atmosphere (opposite the sun) as if the atmosphere acted as a spherical lens. If this is so then the gegenschein has no more interest than twilight or dawn. To this theory is opposed the question of parallax. As projected on the landscape the rainbow has a great parallax but if it were seen against the stars it would have only the parallax of the sun. May not there be in some way a similar effect (though the two things must be entirely different) in the case of the gegenschien that would account for the want of any large parallax? I do not believe that any one else has ever offered this explanation. The only other theory that seems plausible from the conditions is that of a tail to the earth, a theory that was offered, I believe, by Mr. Evershed. The parallax objection holds also in this case.

Apparently there is one other drawback to the atmospheric theory of the gegenschein. I have a great many records which show that it is not always round, but sometimes seems much elongated. This apparent elongation repeats itself each year at about the same time- in the latter part of October.

The best explanation of the cause of the gegenschein from a mathematical standpoint is given in a paper by Dr. F. R. Moulton in the Astronomical Journal, Vol. 21 (1900), 17, where he shows that it may be due to the accumulation of meteoric matter some 930,000 miles outside the earth's orbit, through the attraction of the earth and moon and the sun.

While this ingenious theory could account for the gegenschein, I do not think it is the true explanation-E. E. BARNARD, Popular Astronomy, February, 1919.

stars.

THE DARK MARKINGS OF THE SKY.-It would be unwise to assume that all the dark places shown on photographs of the sky are due to intervening opaque masses between us and the In a considerable number of cases no other explanation seems possible, but some of them are doubtless only vacancies. I do not think it necessary to urge the fact that there are obscuring masses of matter in space. This has been quite definitely proved in my former papers on this subject. If any doubt

remains of this it will perhaps be readily dispelled by a close examination of the photographs previously printed. The conclusive ones I think are:

The photograph of the nebula about Nu Scorpii which clearly shows partial and complete obscuration by the great wing-like nebula that covers much of the immediate region of Nu Scorpii and extends southward to the great nebula of Rho Ophiuchi.

The region of Rho Ophiuchi, where a blotted out by a great and beautiful nebula.

large space of sky is

The fact of obscur

ation is clearly evident here, for wherever a trace of the nebula extends, especially to the west, the general background of small stars is sharply blotted out.

To me these are all conclusive evidence that masses of obscuring matter exist in space and are readily shown on photographs with the ordinary portrait lenses, What the nature of this matter may be is quite another thing. Slipher has shown spectroscopically that the great nebula about Rho Ophiuchi is probably not gaseous; that is, it does not have the regular spectrum of a gaseous nebula. The word "nebula" nevertheless, remains unchanged by this fact, so that we are free to speak of these objects as nebulæ. For our purpose it is immaterial whether they are gaseous or non-gaseous, as we are dealing only with the question of obscuration.

Then follows a descriptive catalogue of 175 of these objects. This catalogue is necessarily incomplete; it is constantly being added to. Later, a more complete list will be printed. The places are closely approximate. An effort was made to measure the positions with exactness, but on account of the nature of the objects it was found to be practical to do this in only a few cases.-E. E. BARNARD, Astrophysical Journal, January, 1919.

ATMOSPHERIC TIDES. -Sir Napier Shaw took the chair at last week's geophysical meeting at Burlington House. Dr. Wedderburn opened a discussion on seiches, or rhythmic varia