498 BURNS— RELATIVE AND ABSOLUTE PARALLAXES. 



By this last-named method, the average parallax was computed 

 for each spectral class, using the data for all stars brighter than 

 mag. 5.6. The " First Catalogue of Radial Velocities " by Voute 

 was of great assistance in this work. It at once becomes evident 

 from an examination of the data that the selection of the fainter 

 stars for observation of the radial velocity has been largely influ- 

 enced by the consideration of large proper motion. In the case 

 of stars fainter than the sixth magnitude this effect is quite notice- 

 able, and it begins to be seen in Classes F and G, even among stars 

 of magnitude 5.2. The motions of the stars of large proper motion 

 are directed more nearly across the line of sight than would result 

 from random distribution, and so these data are not suited to studies 

 like the present investigation. The effects of this type of selection 

 are not of importance in the case of Classes other than F and G 

 when stars brighter than 6.0 are considered ; and the results for 

 stars brighter than 5.6 of Classes F and G are not greatly influenced 

 by selection. 



To obtain the average velocity and proper motion, these data 

 were plotted by spectral classes. The probability curve which best 

 represented each group was found, and the average value was 

 taken from the curve. The data in most cases fit the curve fairly 

 well, the departure being in the sense of too many large velocities 

 for the number of small ones. This excess may be due entirely to 

 the element of selection among the stars fainter than 5.0. In the 

 case of Class G the proper motions would suggest that we are 

 dealing with two distinct groups of stars, the larger group being at 

 about the distance of stars of Classes K and M of the same mag- 

 nitude. The smaller group, about ten per cent, of the whole, 

 appear to be much closer. Among stars of Class F there are just 

 as many large proper motions as in Class G but there is no break in 

 the curve. There are but few large velocities or motions among 

 stars of Classes K and Ma-c. The data for the latter class fit the 

 curves particularly well. The data for Class Md do not fit any 

 smooth curve and they were not included in the discussion. 



Taking the average values from the curves, the average parallax 

 was computed as outlined in a previous paragraph. The results 

 are given in column 2 of Table i, and may be compared with the 



