COMPARISON-STARS. CXXi 



and all the meridian observations should be really portions of one system referred to the identical 

 co-ordinate plane, that the labor of an additional approximation for the better determination of 

 the personal equations in declination is trivial in comparison with the advantages to accrue 

 from a more trustworthy determination of the corrections to the scale of the standard observer. 

 These are, of course, accompanied by a slight increase in the precision of the adopted places of 

 comparison-stars. , 



Accordingly, the places deduced from all those authorities, for which the personal equation 

 has not been implicitly taken from the books, have been carefully compared with the table 

 alluded to, in order that the resultant equations, even if not so trustworthy as those deducible 

 from more extended comparisons and investigations, may at least possess an accuracy in 

 some degree proportionate to the influence which they must exert upon the resulting value of 

 the parallax. 



It is not to be expected, indeed, that the observations from Bessel and Argelander themselves 

 would indicate an absolute mean accordance with our final table ; but it is certainly to be 

 hoped that the positions of that table will be more accordant with the average places of Bessel 

 and A rgelander than would be the case for the limited number of stars taken from the zones of 

 these astronomers and here employed. 



The discussion of the personal equations soon made it manifest that the results for each planet- 

 series ought to be separately examined, the corrections being, at least in some cases, very 

 clearly more diiferent than may fairly be attributable to the mere difference of the declinations. 

 This was especially evident in the two meridian series at the Cape of Good Hope, but not less 

 distinctly in the stars from the Greenwich Catalogue for 1850. 



Thus, after incorporating the values given by some additional stars which, although not 

 employed for micrometic comparison, yet required investigation, on account of their import- 

 ance in determining the corrections of the meridian "series at the Cape and at Athens, we 

 have 



From twenty-three stars observed with the first Mars-series, 



Bessel Greenwich = -f- 1".09 0".995 ; 

 From eight stars observed with the second Mars-series, 

 Bessel Greenwich = 0".14 0".772. 



The table of definite places constructed from the materials already cited need not be given 

 here, as its employment was only provisional. The results of its comparison with the several 

 series of declinations afford the corrections to be employed in the new preparation of a table 

 precisely similar. These corrections afford a legitimate criterion for judging of the accuracy 

 attained and attainable. For they must, of course, be applied to the series of absolute meridian 

 determinations of the planet's place, as well as to the star-places derived from the same 

 authority, before incorporating them with their appropriate weight in the final list of star- 

 places. Only under such conditions would the combination of the absolute positions obtained 

 by meridian observation at different observatories be tolerable. And it so happens that neither 

 for any one of the four observatories which have furnished meridian observations of the planet, 

 nor for either of the other two on which drafts have been made for recent star-determinations, 

 is any sufficient determination of the personal equation in declination at hand. 



The places of the table are to be considered as representing the general standard of Bessel 

 for the northern, and Argelander for the southern stars. Their comparison with individual 

 authorities furnishes the following equations, in which T denotes the tabular declination : 



For stars observed with Mars I : 



T Greenwich = + 0".099 0".142 from 29 observ'ns, exclud'g three, (N M - 25, 35, 14.) 

 T Bessel = 0".287 0".259 from 24 observations, excluding one, (N- 2.) 



T Maclear = 0".591 0".188 from 14 observations. 

 T Washington = 0".517 0".096 from 14 observations. 

 E 



