The present writer, in a determination of the precessional motion, incidentally determined the solar motion from 2527 stars contained in Bradley's Catalogue which had small proper motions, and from about 600 more having larger proper motions. Of the latter the declinations only were used. sults were:

The re

From small motions: A
From large motions:

274°.2 ; D = +31°.2

276°.9

31°.4

Quite recently Campbell has made a determination of the position of apex from the radial motions of 280 stars, mostly measured by himself. The result is:

From all these results it would seem that the most likely apex of the solar motion is toward a point in

The

This point is situated in the constellation Lyra, about 4° from the first-magnitude star Vega. uncertainty of the result is as much as this difference, 4° or 5° at least. We may therefore state the con

clusion in this form:

The apex of the solar motion is in the general direction of the constellation Lyra, and perhaps near the star Vega, the brightest of that constellation.

It must be admitted that the wide difference between the positions of the apex from large and from small proper motions, as found by Porter, Boss, and Stumpe, requires explanation. Since the apparent

motions of the stars are less the greater their distance, these results, if accepted as real, would lead to the conclusion that the position of the solar apex derived from stars near to us was much farther south than when derived from more distant stars. This, again, would indicate that our sun is one of a cluster or group of stars having, in the general average, a different proper motion from the more distant stars. But this conclusion is not to be accepted as real until the subject has been more fully investigated. The result may depend on the selection of the stars; and there is, as yet, no general agreement among investigators as to the best way of making the determination.

The next question which arises is that of the velocity of the solar motion. The data for this determination are more meagre and doubtful than those for the direction of the motion. The most obvious and direct method is to determine the parallactic motion of the stars of known parallax. Regarding any star 90° from the apex of the solar motion as in a state of absolute rest, we have the obvious rule that the quotient of its parallactic motion during any period, say a century, divided by its parallax, gives the solar motion during that period, in units of the earth's distance from the sun. In fact, by a motion of the sun through one such unit, the star would have an apparent motion in the opposite direction equal to its annual parallax. If the star is not 90° from the apex we can easily reduce its observed parallactic motion by dividing it by the sine of its actual distance from the apex.

Since every star has, presumably, a proper motion of its own, we can draw no conclusion from the apparent motion of any one star, owing to the impossibility of distinguishing its actual from its parallactic motion. We should, therefore, base our conclusion on the mean result from a great number of stars, whose average position or centre of mass we might assume to be at rest. Here we meet the difficulty that the stars measured for parallax are generally those having a proper motion away from the apex. This will make the result derived in this way too large.

A second method is based on measures of the motion of stars in the line of sight. A star at rest in the direction of the solar apex would be apparently moving towards us with a velocity equal to that of the solar motion. Assuming the centre of mass of all the stars observed to be at rest, we should get the solar motion from the mean of all. In the investigation just referred to, Campbell has derived the velocity, 19.89 kilometres per second, with a probable error of 1.52 kilometres. A speed of 19 kilometres per second would carry our system over almost exactly four radii of the earth's orbit in a year, and we may regard this as the most likely value of the speed in question.

IT

CHAPTER VII

VARIABLE STARS

-And the moist star

Was sick almost to doomsday with eclipse.-Shakespeare.

T is a curious fact that the ancient astronomers, notwithstanding the care with which they observed the heavens, never noticed that any of the stars changed in brightness. The earliest record of such an observation dates from 1596, when the periodical disappearance of Omicron Ceti was noticed. After this, nearly two centuries elapsed before another case of variability in a star was recorded. During the first half of the nineteenth century Argelander so systematised the study of variable stars as to make it a new branch of astronomy. In recent years it has become of capital interest and importance through the development of spectroscopic research.

Students who are interested in the subject will find the most complete information attainable in the catalogues of variable stars published from time to time by Chandler in the Astronomical Journal. His third catalogue, which appeared in 1896, comprises more than three hundred stars whose variability has been

66

well established, while there is always a long list of suspected variables"-whose cases are still to be tried. The number to be included in the established list is continually increasing at such a rate that it is impossible to state it with any approximation to exactness. The possibility of such a statement has been yet further curtailed by the recent discovery at the Harvard Observatory that certain clusters of stars contain an extraordinary proportion of variables. Altogether at the time of the latest publication, 509 such stars were found in twenty-three clusters. The total number of these objects in clusters, therefore, exceeds the number known in the rest of the sky. They will be described more fully in a subsequent chapter. For the present we are obliged to leave this rich field out of consideration and confine our study to the isolated variable stars which are found in every region of the heavens.

Variable stars are of several classes, which, however, run into each other by gradations so slight that a sharp separation cannot always be made between them. Yet there are distinguishing features, each of which marks so considerable a number of these stars as to show some radical difference in the causes on which the variations depend.

We have first to distinguish the two great classes of irregular and periodic stars. The irregular ones increase and diminish in so fitful a way that no law of their change can be laid down. To this class belong the so-called "new stars," which at various periods in history have blazed out in the heavens, and then in