DEPARTMENT OF MERIDIAN ASTROMETRY. 175 



lack of a better method, the mean parallax of stars of any particular 

 class is used. Various tables have been constructed for this purpose. 

 In general the mean parallaxes have seemed too large, so an attempt 

 has been made to prepare new values. The new tables are based upon 

 magnitude effects and the effect of galactic latitude upon mean paral- 

 lax. Account should be taken of the type of the comparison stars, 

 but in the present investigation this has been omitted mainly because 

 the types of the comparison stars are in many cases unknown. 



As Adams parallaxes are so numerous they are apt to exert a pre- 

 ponderating influence upon the system, and consequently it seemed 

 advisable to test their systematic accuracy. Residuals were formed, 

 Adams minus author, which yield both the constant difference between 

 Adams and the author and the probable error of a parallax determined 

 by the author. These results were compared with a more independent 

 method of obtaining the same quantities. Where three or more 

 authorities have furnished parallaxes for any particular star their 

 results have been combined according to an arbitrary system of weights 

 depending in part upon the probable errors. Comparisons of the 

 results obtained in this way with the results derived from a comparison 

 with Adams show a remarkable agreement and thus serve as proof 

 of the systematic excellence of Adams results. 



A second approximation to a system was therefore attempted for 

 which all stars were used where two or more values of the parallax 

 are given. These results were treated not only for constant systematic 

 corrections, but also for a term dependent upon sine and cosine of the 

 right-ascension, and sine and cosine of double the right-ascension. 

 The expressions for systematic parallax obtained in this way fit the 

 observed results remarkably well in most cases. A digression from 

 this rule was made in the case of the first set of parallaxes published 

 by Flint. It was found that after the rejection of abnormally dis- 

 cordant parallaxes the remainder are excellently represented by a 

 term depending upon the sine and cosine of triple the right-ascension. 

 As the second approximation fits the observed results most satisfac- 

 torily, another approximation was deemed unnecessary. 



A system of weights was formed dependent upon a com.parison 

 between the computed and observed weights of the parallaxes. Since 

 the formation of this system the Director has been generously offered 

 the unpublished results of a large number of parallaxes, which will 

 be used to revise the system before publication. 



Two features of the investigation were quite unexpected. First, 

 the probable error of Adams parallaxes should theoretically approach 

 zero with decrease in the parallaxes toward zero, whereas the actual 

 probable error seems to be constant for parallaxes under 0"A, with a 

 considerable increase past this limit. Secondly, the gain in accuracy 

 for any particular parallax through the employment of more than 

 one plate in its determination is scarcely appreciable. 



