176 CARNEGIE INSTITUTION OF WASHINGTON. 



combination of distributions, there must be more than two of them, or else 

 one of them at least must be skew; there is, therefore, no point in resolving it. 



The skewness explains a number of difficulties relating to stellar motions. 

 For example, it is found that the solar motion derived from stars of large 

 velocity is greater than that derived from the low-velocity stars. This 

 results from the juxtaposition of the axis of greatest excess and the antapex of 

 solar motion. Since it does not coincide with the antapex, the direction of 

 the solar motion will be shifted when derived from small or large velocities, 

 the latter tending toward the point whose galactic coordinates are L = 45° and 

 B = 0°. The principle that the solar motion derived from proper-motions is 

 proportional to the mean parallax must, therefore, be applied with caution. 

 The determination of the direction of preferential motion will also be affected. 

 Consequently, determinations of either solar or preferential motion based 

 upon proper-motions and upon radial velocities, respectively, will not be 

 strictly comparable, since the radial velocities can be and are assorted before- 

 hand into large and small real motions with but little indetermination, while 

 proper-motions can not. The geometry of the case is such that for small 

 motions the radial-velocity apex should be south of the proper-motion value 

 and north for large motions. 



SYSTEMATIC ERRORS OF PROPER-MOTIONS. 



Mr. Raymond has investigated Kapteyn's^ proposed correction of +1''30 

 times the cosine of the declination to the centennial proper-motions in 

 declination of the Preliminary General Catalogue. His study, though incom- 

 plete, has gone far enough to show that such an error very probablj- exists, 

 but that its value is only about a third that assigned by Kapteyn. 



Three methods of approach at once suggest themselves. One is through 

 a comparison of the results for solar motion derived from proper-motions 

 with those based on radial velocities, from which such corrections may be 

 devised as will force an agreement in the declination of the apex. The second 

 depends on the use of landmarks, which can be regarded as fixed or whose 

 motions may be determined beforehand, and which can be compared with 

 the stars. Such are the declinations of the planets, whose deviations from 

 the tables will be zero in the long run, or the latitude of a fixed observatory, 

 the changes of which are determinable. For the third we may have recourse 

 to meridian observations. 



With regard to the first alternative, as is shown from the investigation 

 of velocity distribution, perfect agreement is not to be expected because of 

 skewness, not to mention possible source of error in the radial velocities. 

 The quantity proposed by Kapteyn is at least twice too large for the correction 

 required to bring Boss's determination of the declination of the apex from 

 -f34° to -f 25°. The correction derived from small proper-motions amounts 

 to +0'f65. For the larger motions there are no good radial-velocity deter- 

 minations of the Sun's apex, but real-motion results indicate about +45° 

 as against Boss's value of +34?5. Using this data, the correction becomes 

 — 7". This illustrates the effect of skew distribution. 



To illustrate the second method, two results by others may be set down for 

 comparison. Lambert, in an analysis of the latitudes of the International 

 Latitude stations, obtains a correction of +0''55 to Cohn's motions, which, 

 combined with Schlesinger's computation of Cohn minus Preliminary General 



^ Bulletin Astronomical Institute of the Netherlands, No. 17. 



