Group of the Pleiades. 271 



It is possible to make an approximate estimate of the probable 

 errors of these scale values. According to Elkin the probable 

 errors of his final adjusted star places are ± o".o8 for either co- 

 ordinate, while those of the proper motions (Yale — Kbnigsberg) are 

 ± o".2o. But as we shall only use the proper motions during a 

 period of twelve years (1885-1873), we can take dz o".o5 as the 

 probable error of a proper motion. The probable error of the sum 

 of six heliometer distances, reduced to 1873.0, may therefore be 

 estimated as 



± T/6[(.o8) ! + (.o 5 ) 2 ]i=±o".2 3 . 



An examination of the Rutherfurd observation books shows that 

 the average probable error of a distance measure is zb o".o5, accord- 

 ing to the inter-agreement of the separate settings. The sum of 

 six distances will therefore have the probable error 



dz .05 |/6"= ±o".i5. 



Since the number of thousands in the sum of the six distances is 

 1 1.8, the probable error of the scale value will be 



i- 1 — [(.23) 2 -j- (.i 5 ) 2 ]*= ±o".o2 per 1000". 

 1 1.8 



This estimate of the probable error does not include the effect of 

 systematic errors of measurement due to imperfections of the photo- 

 graphic images, or possible distortions of the film,* or incorrect 

 division errors. It will be noticed in the table that the scale values 

 for the Western impressions exhibit a very small but well-marked 

 excess over those for the Eastern impressions. This may best be 

 explained as a result of the methods used in measuring the plates ; 

 but the discussion of this and several other important points must 

 form a part of the description of the measuring micrometer soon 

 to be issued. There does not appear to be any marked connection 

 between the scale values and the readings of the thermometer or 

 focal micrometer, as given in the table at the end of I. 



* In the American Journal of Science and Arts, vol. iv, Dec. 1872, Ruther- 

 furd showed that the distortion of his films during development was inappre- 

 ciable. 



Ankals N. Y. Acad. Sol, VI, March, 1892.— 19 



