520 



We lia\e derived the numbers 7V„,,„ from the numbers of stars 

 of determined magnitude and galactic latitude by performing countings 

 in catalogues of stars with known proper motions. We have computed 

 these numbers xV,„ for the dilFerent zones from the tables in 

 Fabl. (rroninyen W. 18, as these ha\'e been corrected in Publ. 

 Groningen N°. 27. 



The results that Van Rhijn published in the work last-mentioned, 

 are veij reliable, as thev were confirmed by several independent 

 studies. The results of Nokt aiul Skakks, indeed, agree fairly well 

 with those of Van IIuun and the numbers of Chapman and Melotte 

 too cories|)on(l to the Groningen countings as soon as they shall 

 have been corrected for a mistake in the method of reduction wiiich 

 has been pointed out by Van Rhijn. 



In our countings the stars were divided according to their magni- 

 tudes iido groups of J — 2.9, 3.0—3.9,4.0—4.9, 12.0—12.9. 



According to their proper motions they were counted between the 

 limits 0— 2".9, 3".0— 4".9, 5".0— 7".9, 8".() -9".9, iO".0— 14".9, 15".0 — 

 J9".9, 20".0— 29".9, 30".0-49".9 and >49".9. 



The following catalogues have been used : 



1. L. Boss. Preliminary Catalogue of 6188 Stars, 1910. 



2. A. AuwERs. C/atalog der Astronomischen Gesellschaft, Zone 

 + 15° bis + 20°, 1896. 



3. W. G. Thackeray. Greenwich 1910 Catalogue of Stars, 

 Zone4-24°0' to + 32^0'. Analysis of Number and Peicentages of 

 Proper Motions. Monthhi Notices 77, 204— 2J 2, 1917. 



F. W. Dyson and W. G. Thackkkay. The Systematic Motions 

 of the Stars between Dec. + 24° and Dec. + 32°. Monthly Notices 77, 

 581—596, 19J7. 



4. F. W. Dyson and W. G. Thackeray. New Reduction of 

 Groombridge's Catalogue of Circumpolar Stars, 1905. 



5. J. C. Kapteyn and W. de Sitter. The Proper Motions of 

 3300 Stars of different Galactic Latitudes, derived from photographic 

 plates, pi-epared by Prof. Anders Donner. Puhl. Groningen N°. 19, 1908. 



6. J. C. Kapteyn. The Proper Motions of 3714 Stars derived 

 from plates taken at the observatories of Helsingfors and the Cape 

 of Good Hope. With the co-operation of Dr. H. A. Weersma. Publ. 

 Groningen N". 25, 1914. 



7. Dr. A. A. Rambaut. A photographic Determination of the 

 Proper Motion of 250 Stars in the Neighbourhood of ^ 443. Monthly 

 Notices 73, 616—630, 1913. 



8. A. van Maanen. Remarks on the Motion of the Stars in and 

 near the double Cluster in Perseus. Report of the Nineteenth Meeting 



