82 



Sven Wickseil 



33. We have in this investigation found that many circumstances point to- 

 wards a value 0.75 for q . A question of interest in stellar astronomy is: what 

 value of the constant \ conies out of this value for q ? 



We remind of the equation 



q = a, e r , 



ocj = 0.88; a 2 = 0.43. 



Clearly the value of X 1 depends on what value is to be taken for the dispersion 

 of the apparent magnitudes /.-, of which, on the whole, we only know that it has 

 a value of about 3 or 4. 



For q = 0.75 the above equation may be written 



Taking & 2 and X 3 as coordinates of a Cartesian system this equation is repre- 

 sented by the curve drawn up in rig. 8, from which it is seen that for Jc = 3.0 we 

 have X L = 0.87 and for Jc = 4, Xj = 0.94. Now the values of the factor 0.88 and the 

 term 0.43 depends on our having regarded the stars brighter than 6.0 as being 

 chiefly of magnitudes fainter than 3.0. As it has been necessary to have a lower 

 limit of the magnitudes when discussing the relation between Xj and q' , it is im- 

 possible to say if it is chosen too high or too low. Taking a higher limit, a 1 will 

 be found greater and a 2 smaller and vice versa. Thus if the lower limit is taken 

 higher up, the curve will be lifted upwards, and taking a yet lower limit the curve 

 will lie nearer to the X-axis. The effect on the order of magnitude of X t for h 

 about 3 and 4 will however be small and hence we conclude that X 1 has a value of 

 about. O.g. 



Before finishing this memoir I grasp the opportunity to express my sincere 

 gratitude to Professor C. V. L. Charlier for the many fertile impulses that I have 

 received during the planning and preparation of this investigation by his always 

 intent interest for the questions here inquired into. Especially I wish also to express 

 my hearthiest thanks for the kind readiness with which he has placed at my disposal 

 as yet unpublished material of a character to greatly facilitate my work. 



It is further with sincere pleasure that I acknowledge the obligations in which 

 I stand to Mr. K. A. W. Gyllenberg for many useful suggestions received during 

 our daily conversations on these and related subjects and especially for his kindness 

 to permit me to use the results of his own investigations of the radial velocities. 



To the Royal Physiographic Society of Lund I also wish to express my thanks 

 for pecuniary support granted me out of the Anders Jahan Retzius' Minnesfond. 



