124 TUCKER— EFFECT OF DIURNAL VARIATION 



Both classes of error can be eliminated by observing the same 

 stars in each hour of right ascension, and closing a cycle of observa- 

 tions in which every hour has been included. Also some systematic 

 errors of observation, such as that due to magnitude equation, are 

 eliminated in the cycle. 



The average systematic error of Newcomb's right ascensions at 

 this date is not far from dz 0^.02 per hour. 



The average difference between two consecutive hours is smaller 

 than the average per hour, since the systematic errors are periodic in 

 character, approximately of the form, — o^02 cos a -|- o^oi sin a. A 

 comparison of the right ascensions of Newcomb in the American 

 Ephenieris with those of Boss in his Preliminary General Catalogue 

 gives an indication of the character of the systematic errors to be 

 anticipated. 



For 325 stars at present under observation here, between 37° 

 north declination and 30° south, the average difference is ± o^022 

 per star. In hourly groups the average difference is ±: o^oo6 per 

 hour. Differences between individual stars are evidently mainly 

 fortuitous.* This does not imply an absence of systematic errors, but 

 does indicate that the systematic errors of the two authorities are 

 similar. The average difference between two consecutive hours is 

 d= o^0IO for the two lists. 



If we use the right ascensions of Boss, the computed hourly rate 

 of a clock will differ C'.oiq from the hourly rate computed with 

 Newcomb's right ascensions, in the average, and may differ more 

 than twice that amount. The right ascensions of Boss appear to 

 have the relative weight 3 : i, as regards accidental errors, and weight 

 2:1, for systematic errors. 



The later fundamental system of Auwers appears to be as precise 

 as that of Boss, both as regards accidental errors and systematic 

 errors. 



Newcomers system antedates the other two by about ten years. 

 If we include as clock stars only those within 15° of the equator, 317 

 in number, the average differences between Newcomb and Boss are 



* The difference 0^.006 for an average of 13 stars per hour corresponds 

 to the average difference of 0^.022 per star. 



