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ASTRONOMY

All three of these agree in the general conclusion that the smaller the proper motions used the greater the declination of the resulting apex, and, in a less degree, the greater its right ascension. • But this conclusion needs farther examination before it can be accepted as fully established. Some doubt is thrown upon it by the fact that the position of the solar apex from all the stars of Bradley’s catalogues having a small proper motion is A = 274*2°; D= +31*2°. The discrepancy, especially in the declination of the apex, is far outside the normal limits of error on any probable hypothesis, and suggests the necessity of a more thorough examination of the question than has been made. The general conclusion which may be drawn from these results is that our system is moving toward the constellation Lyra, not Hercules. The point is probably near right ascension 280° and declination + 38°; but there is an uncertainty of several degrees in this position which cannot be removed until an improved method is applied. An important and interesting point is that of the speed of the motion. The most obvious method of determining this is through the apparent parallactic motion ot of the stars whose parallaxes have been actually measured. When we see a star at a motion. known distance moving away from the sun’s apex with a given angular velocity, the transformation of this given velocity into a linear velocity is extremely simple, and gives the relative velocity between the sun and star. The measure of these results from all the stars included will give the speed of the sun relative to their mean position. In this way, from the list of stars whose parallaxes have already been given, it would follow that the speed in question was 6 radii of the earth’s orbit in a year, which would correspond to nearly 28 kilometres per second, about that of the earth in its orbit. But this result has an unavoidable defect arising from the fact that the stars selected for measures of parallax have been those having large apparent proper motions. A star whose actual motion is in the opposite direction to that of the sun will have a large apparent motion, while one moving towards the solar apex may have little or no apparent motion, though its actual angular motion may be the same. In consequence, the selection is biased by including mainly those stars whose absolute motion is away from the apex. Consequently, the result is too large. The speed in question can also be derived from the observed motions in the line of sight or radial motions. Kapteyn has done this by a statistical method. From a study of the apparent angular motions of the stars can be derived the ratio between the velocity of the sun and the mean velocity of the stars in general. This mean velocity is found in linear measure from the observed motions in the line of sight, and its product into the ratio derived from the angular motions gives the actual linear velocity of the sun. The resulting speed of the sun’s motion was, in round numbers, 16 kilometres, or 10 English miles, per second. This result is now superseded by a recent research of Campbell, based on 280 radial motions (Astrophys. Group I. (551 stars) A=287*4 ; D=+45-0 Jour. January 1901), giving a speed of 19*89 ± 1*92 km. ,, II. (339 „ ) 287*2; 43'5 This speed is almost exactly 4 radii of the earth’s orbit ,, III. (106 „ ) 280*2; 33*5 per year. It will be seen that the apparent proper motion of a Porter (Ast. Jour. xii. p. 89) divided his proper motions into four groups : I., those less than 30" ; II., those be- star is made up of two components—the actual motion tween 30" and 60" ; III., those between 60" and 120" ; relative to the mean of all the stars, sometimes called the motus peculiar is ^ and the parallactic motion, which is only IV., those exceeding 120". The results were ;— apparent, being due to the motion of the sun. It has been shown by Stumpe that, when we take a large number Group I. (570 stars) A = 281 *9 D= +53*7 of stars and classify them according to their total proper „ II. (533 „ ) 280*7 40*1 motions, the ratio of the parallactic motion to that peculiar ,, III. (142 „ ) 285*2 34*0 „ IV. (70 „ ) 277*0 to each star is nearly the same for large and for small 34*9

contain any of the sixteen stars, except at their limits. This may be attributed to the effect of the solar motion in exaggerating the apparent motion of stars far from its apex. A desideratum of the present time is an exact knowledge of how many stars in the heavens have a measurable proper motion, or, in greater detail, how many have proper motions of each order of magnitude. The data for completely solving this question are still wanting, but the most complete attempt in this direction is that of Auwers, who observed the zone of the “ Astronomische Gesellschaft,” 15°-20°, at Berlin. He made a comparison of the 8000 stars in his zone with the older observations as far as they were available, and the result was the discovery that 1200 of the stars had proper motions large enough to be detected. Assuming that in the whole heavens the number is proportional to the area, we may regard it as probable that 20,000 stars have a proper motion, extending 5" per century. Several astronomers have made catalogues of stars having exceptionally large proper motion; the most thoroughly worked up of these catalogues is that of Porter for 1890, Publications of the Cincinnati Observatory, No. 12, but Bossert’s in the Paris Observations for 1890 contains more stars—2675 in all. That our sun is to be included among the stars having a proper motion has long been inferred from an apparent motion of the stars in the opposite direction, motion called the parallactic motion. If we regard the general mean position of the mass of stars as at rest, our solar system is relatively to this mean moving toward a point, now known as the Solar Apex, which was long supposed to be situated in the constellation Hercules. Although the approximate situation of this point has been known since the time of the elder Herschel, yet its exact determination is a matter of extreme difficulty, owing to the diversity of the actual motions of the stars and the irregular distribution of those which have been determined. In the following summary of the results of recent researches, we put A for the right ascension of the apex and D for its declination. Professor Lewis Boss, from 279 stars of large proper motion in the zone 1° to 5°, derived A= 283'3°; D = + 44‘1°. This result might be seriously influenced by the introduction of stars of abnormally large motions; had he excluded twenty-six motions exceeding 40" per century, the result would have been A = 288'7°; D= +5P50. Porter of Cincinnati, and Stumpe of Berlin, have each made determinations based on all the welldetermined proper motions available at the time. Porter’s list included 1300 stars, Stumpe’s 996, the greater number of the stars being common to the two lists. Each investigator classified his material according to the proper motions of the stars. Stumne excluded all motions less than 16" or greater than 128" per century. Between these limits they were divided into three groups: Group L, from 16" to 32" ; II., from 32" to 64" ; III., from 64" to 128". The separate results were :—