OF ARTS AND SCIENCES. 179 



from his observations. The "Washington observations for 1845 were absolute 

 determinations. Here the positive and negative errors are pretty evenly dis- 

 tributed, but immediately upon the adoption of the differential system, with the 

 Nautical Almanac places as fundamental, the periodicity becomes strikingly 

 apparent. Johnson's St. Helena Catalogue contains far less evidence of perio- 

 dicity than we should expect, because he applied to his observations a system 

 of corrections by which the errors of single period were partially eliminated. In 

 Brinkley, Struve, and Argelander, and at Pulkowa, the errors in question are 

 very small, if they exist at all. 



The three cases which seem to form an exception to this general statement, 

 are, Bessel 1815, Bessel 1825, and Auwers' Cacciatore 1805. With respect to 

 Bessel's observations, it is to be remarked that they depend entirely upon the 

 places of a Aquilse and a Canis Minoris, the latter having an acknowledged 

 irregular proper motion. In the catalogue for 1815, the place of a Canis Minoris 

 was assumed .10^ too small, and if the Right Ascensions in this region were made 

 entirely dependent on the position of this star, the error should be distributed, not 

 over the whole arc, but over that part only in which the star was used as a 

 standard. In the catalogue for 1825, which is a combination by weights of the 

 results from each star, the periodicity is more marked than in either system 

 taken separately. In the catalogue for 1827, communicated to Pond, errors of 

 single period can hardly be said with certainty to exist. In Auwers' Cacciatore, 

 the periodicity is more marked, but as will be seen, there is apparently an accu- 

 mulation of accidental positive errors at about 15h, and we have here the only 

 instance (except Bessel), in which the coefficient of sin a has a large positive 

 value. This catalogue does not seem to depend in any way upon Leverrier's posi- 

 tions, with which it is compared, but it is rather curious that the coefficients, 

 VI and n, are nearly the same for the two catalogues. 



III. That the introduction of an excess of positive residuals between IS^ and 

 23^ is due to the inequality of the pivots of the new instrument with which 

 Pond began observations for Right Ascension in 1816. It seems to me that the 

 evidence on this point is decisive. These pivots were used till 1825, when steel 

 pivots were inserted, from which it is to be inferred that the first ones were not 

 made of this material. The new pivots not proving satisfactory, they were re- 

 ground in 1832. I give here, the coefficients a and b for the various catalogues 

 formed by Pond, and I add also, the values derived from the observations just 

 preceding the last correction of the pivots and those immediately following. It 

 is imfortunate for our purpose that the annual results do not appear in the voL 

 umes preceding 1829. 



EPOCH. a. b. 



1819 (1816-21) —.136' +.0213 



1820 (1816 ) —.142 +.021 



1823(1821-23) —.135 +.020 



1825 (1821-26) —.122 +.018 



1826 (182-5-28) —.092 +.015 



1830 (1816-33) —.087 +.022 



1829-30-31 +.099 —.015 



1833-34-35 —.059 +.00y 



