MOUNT WILSON OBSERVATORY. 



283 



Tactions give the more accurate result; if it is greater, the peculiar 

 motions are more reliable. 



Unless vitiated by some form of observational selection, the mean 

 parallax derived from 10 stars should have a probable error of less than 

 25 per cent of its own value, and be significant. These conclusions 

 Bre confirmed by a study of random groups of 10 stars of class B, 

 taken from Campbell's list. 



INVESTIGATIONS BY PROFESSOR KAPTEYN. 



The last of Professor Kapteyn's investigations mentioned in the 

 Year Book for 1920, p. 255, have been completed. The results, which 

 deviate somewhat from those previously considered probable, are per- 

 haps best appreciated from the accompanying table, which, though 

 confessedly crude, is believed to represent fairly what at present can 

 be learned about the arrangement of stars in distance. 



Limits in 'par sees within which the structure of the stellar system can be found. 



Method. 



Galactic latitude. 



0°-20'' 40°-90° 0°-90 



1. Direct parallax detennination 



2. Parallactic motion, now well known for stars to m = 10. 



3. The same, to m = 13 



4. Parallactic motion, stars to m=10 and ;u = 0T01 



5. The same, together with N^ (the latter to m= 14) 



6. The same, Nm to m = 17 



7. Extension according to Point IV, Nm to 7n= 14 



8. The same, N„ to m = 17 



320 

 (830) 

 400 

 1600 

 (4000) 

 3000 

 (8000) 



240 



(610) 



320 



800 



(1600) 



1000 



1700 



50 



300 



(720) 



360 



1200 



(2800) 



2000 



In another investigation, which has also been completed, a first 

 attempt is made at a complete theory of the arrangement and motion of 

 the whole stellar system. It was found that if, for the equidensity 

 surfaces derived in Contribution No. 188, we substitute a series of 

 concentric similar rotation ellipsoids, similarly situated, the observa- 

 tions are still tolerably well represented. This property makes it 

 highly probable that the total attraction of that part of the system 

 which lies outside ellipsoid X (major semiaxis = 8,465 parsecs; minor 

 semiaxis= 1,660 parsecs) on any point inside must be very small. 

 Since the distribution of the stars within this ellipsoid is known, we 

 can obtain a good approximation for the total attraction of the whole 

 system on any point inside elUpsoid X, expressed in terms of the 

 attraction of a star of average mass. 



It is then shown that the system, if at rest, can not be in equilibrium. 

 In order that the system may be in a steady state we must therefore 

 assume that the stars have a systematic motion. Observation shows 

 that such motion really exists and that it is parallel to the plane of the 

 Milky Way. It is the motion of the star-streams. We are thus led to 



