248 CAENEGIE INSTITUTION OF WASHINGTON. 



The application of the systematic corrections to latitude and of the 

 tangent term leaves the residuals which form table B. While the curve 

 drawn to represent the observed corrections to the Preliminary Gen- 

 eral Catalogue is on the whole very smooth, there is an abrupt break 

 at about —60°. No explanation has developed to account for this 

 sudden break. 



The duplicate copies of the reductions of the San Luis observations 

 in right ascension have been reconciled, and the observations of the 

 fundamental stars drawn off for discussion. 



Mr. Varnum separated the observations of each star according as 

 they were taken with the instrument in the position clamp east or 

 clamp west. The mean position in each clamp was then compared 

 with the place given in the Prehminary General Catalogue. The 

 residuals thus formed were drawn off in the order of the dechnation of 

 the stars, and means were taken for each degree. These means from 

 clamp east and clamp west indicate the correction to the Preliminary 

 General Catalogue to reduce it to the system of the San Luis obser- 

 vations and should yield similar results; but, when plotted, a very 

 anomalous region appeared, so striking as to make it evident that the 

 observations must require an additional correction for pivot. 



As a preliminary to determining the outstanding pivot factor, the 

 residuals were freed approximately from the effect of error dependent 

 on declination, by means of a curve wliich represented the mean of 

 clamp east and clamp west. The outstanding residuals were then 

 treated as dependent upon uncorrected inequahty and irregularity of 

 pivots. The inequality of pivots introduces errors in the colhmation, 

 the level, and the azimuth. These assume the form of 



C-^a sin R+b cos R 



where R refers to the circle-reading on the same circle both clamp east 

 and clamp west. The equation was solved from the data by least 

 squares and then was applied to the residuals. 



This left a well-defined periodic term due to irregularity of pivots^ 

 and represented by the formula 



c sin QR+d cos 6/? 



It was found, however, that the agreement between observed and 

 computed values did not extend bej^ond R = SIS°. Therefore a sepa- 

 rate solution was made for the region from 7^ = 318° to 278°. 



By successive approximations the following formulas were deduced 

 as representing outstanding pivot correction: 



For clamp east from dechnation +8?7 to —64° S. P.: 



+ ?0176+ '0063 sinR- «0296 cosR- ?0028 sin QR - «0084 cos 6R 



For clamp east from declination 4-8?7 to -F50°: 



+ ?0176+ '0063 sin R - «0296 cos R + ?0078 sin QR -}- ?0071 cos 6R 



