523 



This result agrees with that found bj Kapteyn in 1893 and with 

 the conclusions, which Dyson and Thackeray found lately from a 

 discussion of the Greenwich 1910 catalogue. 



The mean parallaxes .t,„ „ for the whole sky and for the different 

 galactic zones have not been determined by us directly. In our opinion 

 they may be reduced for our investigation, preliminary as it is, with 

 sufficient accuracy from former researches. 



Kapteyn found in Publ. Groningen N°. 8 for these mean parallaxes 



in which a = 0".0038, «6 = 0.71 and « = 0.905. 



Use was made of the value 16.7 Kilometers a second for the 

 velocity of the sun. If we accept the modern value, 19.5 Kilometers 

 a second, the mean parallaxes rr,„, used by Kaptkyn in deducing his 

 formula, are lessened by 147o- If we now suppose — as Van Rhun 

 also does') — that this correction for the mean parallaxes jr,„ changes 

 only the value of a in jr„i,y, we find nf = 0".0032^ 



Kapteyn's parallaxes corrected in this way agree with the values, 

 deduced by Dr. Van Rhun in his dissertation in an investigation, 

 based on other and more modern data than those used by Kapteyn, 

 in which he partly also applied another method. Hence it follows that 

 the parallaxes .-^ „,,;,, as given in Publ. Groningen N". 8, are very reliable. 



In ordei' to derive from the parallaxes which may be applied to 

 the whole sky, the .t,,,„ for the different zones, we have assumed, 

 that the ^,n,,j. of the various galactic zones are related in the same 

 way as the .t,,, of these zones. 



This assumption is rather arbitrary. Most probably it cannot be 

 proved to be correct in all respects. There is reason to believe, 

 however, that the error, made in this way, is not very great. Therefore 

 we thought we might use this hypothesis in oui- preliminary research. 

 We have alieady mentioned that we were able to use, thanks to 

 the great kindness of Professor Kapteyn and Dr. Van Rhun, the 

 mean parallaxes of stars of determined magjiitude and galactic latitude, 

 which will soon be |)ublished in Publ Groningen N'. 29. These 

 parallaxes may be respresented by the following formulae: 



.1) Diss. Groningen 1915, p. 35. 



