BURNS— RELATIVE AND ABSOLUTE PARALLAXES. 501 



smaller. This is not the case, yet the number of stars is too small 

 to permit a definite conclusion. The larger correction is supported 

 l)y the number of very small and negative parallaxes that have been 

 found. This fact was checked by applying various corrections to 

 the observed parallaxes and computing the cross velocities by means 

 of the proper motions. Making the greatest permissible allowance 

 for probable error in the parallax determinations and in the proper 

 motions, and for the possible range of the distances of the com- 

 parison stars, the smallest value of the correction that would make 

 the cross motions comparable with the radial velocities was found 

 to be o".CK)9. 



About one half of the comparison stars used in determining the 

 parallaxes discussed in this paper are of visual magnitude 9.7 or 

 brighter on the Harvard scale. The number in each magnitude class 

 was found by counting representative fields. Taking account of 

 the number of stars in each magnitude class, the mean proper 

 motion of the group was derived from the values given in Gronin- 

 gen Publications No. 30, page 99. Using this value, about ©".030, 

 and the most probable value of the mean radial velocity, 14.5 km., 

 the mean parallax of the group becomes o".oo7. 



It should be borne in mind that these data refer to the fields 

 of the brighter stars, and that the fainter stars have been compared 

 with fainter fields on the average. In a definitive treatment of the 

 subject it would be necessary to take account of the magnitude of 

 the comparison stars in each field in applying the correction to re- 

 duce from relative to absolute parallax. It will also be borne in 

 mind that a larger number of data, insuring greater freedom from 

 accidental and systematic error, may modify these results to some 

 extent. Yet it is quite unlikely that a correction of less than 

 o".oo7 will be found for the fields in which the comparison stars 

 are all brighter than 9.5 visual. 



It is perhaps not fully recognized that the value generally sug- 

 gested for this correction to reduce relative to absolute parallaxes 

 (i.e., a correction of o".oo3 to o"oo5) corresponds with a mean 

 velocity of the comparison stars sixty per cent., or more, greater 

 than that of the stars whose velocities we know. This value of the 

 mean velocity results from the comparison of the mean proper mo- 



