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Read before the Academy, April 28, 1919

The motion in space of the stars of very high radial velocity is of exceptional interest because such stars are usually of comparatively low intrinsic brightness and probably of small mass as well. It might, therefore, be expected that these stars would show the effects of stream motion strongly and that the components of their velocities might be related to the fundamental plane of the stellar galaxy.

As a basis for the study we selected all stars with radial velocities exceeding 80 km. per second for which proper motions and parallaxes are available. This gave a total of 37 stars with velocities ranging between 81 and 339 km., the latter the highest stellar radial velocity so far known. It is of interest to note that the largest velocities of approach and of recession are very nearly equal. The parallaxes of all but five of these stars have been derived by the spectroscopic method, the trigonometric values being used for the remainder.

After elimination of the solar motion the velocity-components and the apices of the stars relative to the centroid of the stellar system were determined by the aid of their proper motions, parallaxes and radial velocities. These components were in turn reduced to the plane of the galaxy and the galactic coördinates of the apices and the total velocities were calculated for all the stars.

Some of the results of the investigation are shown graphically in the accompanying figure. The plane is that of the galaxy with the apices shown in projection. Vectors drawn to the origin represent the direction and amount of motion in this plane.

A few of the more important conclusions may be indicated briefly. 1. The highest velocity in space magnitude star A. G. Berlin 1366. show values of nearly this amount.

found for any star is 494 km. for the ninth Several other stars with larger parallaxes In all cases the components of motion in

the plane of the galaxy exceed greatly those at right angles to it.

2. For the stars as a whole we find the two components in the galactic plane very nearly equal and more than two and one-half times as great as the component perpendicular to it. We find a similar result from a consideration of the latitudes of the apices. Only 6 out of the 37 stars have apices with latitudes exceeding 30°. It is clear, therefore, that the influence of the galactic condensation is very marked upon the motion of these stars.

3. Nearly an entire hemisphere in longitude is devoid of apices, the values all lying between 131° and 322°.

4. The velocity of the centroid of these stars is remarkably high. Thus even if we omit total velocities greater than 300 km. we find a value for the centroid of 74 km. This motion is almost wholly in the galactic plane.

5. The effect of stream motion among these stars is very marked. The axes for which the sum of the squares of the projected velocities is a maximum and a minimum have longitudes of 141° and 61°, respectively, and latitudes of +9° and -49°. The projections of these axes upon the galactic plane are

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The vectors drawn from the origin represent the projected velocities in km per sec. The axes of the ellipse of intersection of the velocity-ellipsoid with the galactic plane are indicated by the two arrow-headed lines.

indicated in the figure. The mean square dispersion along the major axis is over twice that along the minor axis. The value for the major axis is in close agreement with that found by Strömberg from a discussion of the radial velocities of 260 dwarf stars, and with that of Raymond from 559 stars of large proper motion. All of these investigations indicate that the galactic longitude of the principal vertex for the stars of high velocity is considerably less than that for stars in general.

6. There appears to be some tendency for the stars to move along a line of galactic longitude about 260°, allowance being made for the motion of the centroid. This direction coincides nearly with that of the greatest star density as determined by various observers.

7. The stars of highest velocity, over 300 km., also appear to move along a line parallel to that of the major axis when the motion is referred to their common center. This is shown in the figure by the positions of the apices.

8. The average galactic latitude of the apices of the stars of high luminosity is nearly twice as great as that of the fainter stars, the values being 26° and 14°. The latitudes of the apices of only four of the fainter stars exceed 26°. 9. The average space-velocity of the stars of low luminosity is much larger than that of the brighter stars. Twenty-eight stars of average absolute magnitude 5.9 show a velocity of 216 km. Nine stars of absolute magnitude 0.4 a velocity of 130 km.

10. An extraordinarily large proportion of the stars in this list, 26 out of 37, are of types F and G. The successive types F, G, K and M show average space-velocities of 307, 156, 122 and 121 km. respectively, the weight of the determination for the last two types being rather low. Among the stars of type F those of earlier spectral type show the larger velocities. Thus the six stars with spectra between Fo and F5 inclusive have an average velocity of 365 km. as against 307 km. for all stars of the F type.

The most important result of this brief investigation is the evidence for the marked influence of the condensation of matter in the plane of the stellar galaxy upon the motions of these relatively faint stars. Their susceptibility to stream motion is perhaps another result of the same general influence which is, no doubt, gravitational in character. Probably the most peculiar fact in connection with these stars is the spectral type of the stars of highest velocity. That a type which we are accustomed to consider as intermediate in the scale of stellar development should contain so large a proportion of the most rapidly moving stars is difficult of explanation unless we may assume that these stars. are of exceptionally small mass. Since the relationship of velocity to absolute magnitude seems to be fairly well established this hypothesis may be worthy of consideration.


Communicated by G. E. Hale. Read before the Academy, April 28, 1919

A communication to the Academy in 19171 describes the method used for the location of the sun's magnetic axis and gives values for the inclination, the period of revolution about the solar axis of rotation, and the epoch when the magnetic pole was on the central meridian. These results were based upon observations made on 63 days between June 8 and September 25, 1914. In the meantime the spectrograms of 11 additional days within the limits of this interval have been measured and reduced, and the elements defining the position of the axis have been revised with the following results (appended quantities are probable errors):

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The modifications produced by the revision are unimportant, and, so far as the 1914 series of observations is concerned, these values may be accepted as final.

The uncertainty in the period is naturally large, for it has been derived from data covering less than four complete revolutions of the magnetic axis. Moreover, this limitation prevents any conclusion as to the constancy of the period. An improvement of the results in these particulars therefore requires additional observations, which should be distributed over a long interval. A beginning in this direction was made with a short series in September, 1916, which should reduce the uncertainty in the period well below a tenth of a day and make it possible to carry the longitude of the pole forward, without ambiguity as to the number of revolutions, to the coming sun-spot minimum, when further observations can be undertaken wihout risk of interference from the magnetic fields of spots.

The 1916 observations are now under discussion, and the indications are that the longitudes to be derived from them will agree closely with those calculated from the 1914 results. The period given above is therefore probably near the true value.

All discussions thus far described rest upon the assumption that the sun's general field is that of a uniformly magnetized sphere. The example of the earth, however, suggests that this hypothesis may be justified only to some rough degree of approximation, and that the field may not possess the uniformity hitherto presupposed.

We have therefore rediscussed the data from this standpoint, with results which seem to be conclusive. The investigation has had to meet the difficulty that the percentage errors in the data, in the nature of the case, are large; but there seems no doubt that there are irregularities in the field-strength at least, which cannot be accounted for on the basis of systematic or accidental error. In order that the numerical quantities involved in the above solution-which we may refer to as the uniform-field solution-might be utilized as completely as possible, we have based the discussion upon the formulae there used, namely, Ax+ By A

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y k-1 sin i cos
y/x = tan i cos


A and B are known quantities, functions of the heliographic latitudes of the sun's center and the points observed; ▲ is the observed displacement of the spectral line; and i and λ are the inclination of the magnetic axis and the longitude of the magnetic pole. Y is a function of i and X, whose value is calculated for each day from all the measured A's for that day. The discussion of the resulting series of Y's then leads to the required values of i, to, P, and finally to k, which is connected with Hp, the field-strength at the ple, by the relation

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in which C is a constant depending on the spectral line employed.

For the uniform-field solution, the values of I were calculated separately for three different lines. For the investigation of the deviations from the uniform field, the measures of the three lines were combined (this is possible since the values of x for the three lines are sensibly equal) and the entire collection of data then subdivided according to zones of heliographic latitude as follows: I ❤ > +10°

II +10° -10°
III < -10°

The outer limites for forces I and III vary somewhat, but are approximately 45°

To the data within these limits we have applied equations (1), much as described above. In other words, we have derived separate uniform-field solutions for each of the zones. Had the three series of results agreed within the uncertainties affecting their determination, we could only have concluded that there is no evidence for the existence of appreciable deviations from the uniform field originally presupposed. As a matter of fact, we have found a large difference for k, which leads to the conclusion expressed above.

Certain details require comment. The fundamental equation-the first of (1)-cannot be applied directly to either zones I or III, because of the numeri

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