OF ARTS AND SCIENCES. 183 



catalogue fell between the first and the third quadrants. Had Mr. Johnson used 

 the Greenwich clock stars for the same year, he would not have detected the 

 inequality mentioned in the volume for 1841. We find here also an explanation 

 of the difference often found between day and night observations. In January 

 and July the residuals reach their maximum value, but with opposite signs. 

 During these months, therefore, the difference between day and night observa- 

 tions may amount to nearly .lO^. On the other hand, in Ma^^nd No /ember, 

 no appreciable difference will be observed, the observations for these months 

 being near the zero points. It may be found also that the large difference in 

 the values of a and /3 from the Washington observations of 1866 and 1867, as 

 determined by Professor Newcomb, may be due to the difference in the relative 

 number of observations made in corresponding months of different years. 



Under the second head, the most marked cases in more modern observations 

 are Paris, Edinburgh, Washington II., and Harvard College, though in the last 

 case, the coefficients, depending on an average of 6 observations for each star, 

 must be considered as only approximately correct. As has been already re- 

 marked, the errors of single period from this cause are in some cases diminished ; 

 in others augmented. 



To conclude briefly : — 



I. The periodic errors of single period existing in observed Eight Ascensions, 

 are in no sense inherent in the observations themselves, but are entirely trans- 

 ferred from the provisional places of the clock stars on which they depend. 



II. The accumulation of positive residuals in the region of 18*>, is due to the 

 unequal pivots of the Greenwich Transit, erected in 1816. 



III. The accumulation of negative residuals in the region of 6'» is due, partly 

 to the general drift in the direction of the motion of Sirius and Procyon, and 

 partly to errors developed indirectly from the combination of observations made 

 with unequal or irregular pivots. 



IV. The errors thus accumulated are distributed over the whole are of 

 Eight Ascension by means of the formulae : — 



m sin a -\- n cos a. 

 vi' sin 2a + n' cos 2a. 



If the resulis which I have reached, are accepted as true, it is evident that 

 the speedy return to absolute determinations of Eight Ascension is a matter of 

 vital consequence. I venture to suggest that the time has come when astrono- 

 mers should, by concurrent action, determine which stars shall be regarded as 

 fundamental. If the true. elements of e.<j. 100 stars, properly distributed in De- 

 clination, could be decided by recognized authority, and then if all differential 

 observations could be made to depend on these stars only, it would be possible 

 to reach a degree of accuracy unattainable under the present system. For the 

 future, we ought not to be compelled to depend on theory in order to harmonize 

 observations. Theory may be useful in making available, data already accumu- 

 lated, but observation must be the last resort. 



