OF AKT3 AND SCIENCES. 



181 



value derived from the whole system. Hence we should expect a general ten- 

 dency to positive residuals between 0^ and 12'>, wiien the corrections depending 

 on tlie pivots are applied. As a matter of fact, the resulting residuals for this 

 interval, are ahnost precisely represented by the expression, r sin a + r cos a. 

 And this relation should exist as long as the observations made with pivots of 

 different figure remain uncomhinrd. But this combination was made by Pond, 

 and it is on this account tliat he was unable to satisfy even his own earlier 

 observations. Hence for all observations previous to 1828, the accumulation of 

 positive residuals between O^and 12*', resulting from corrections through o and h, 

 must be distributed over this interval only, by the formula r sin a+r cos a, but 

 after that date, the errors become by combination so intermingled, that we must 

 distribute them over the whole arc of Right Ascension. In Table V., columns 

 1, 2, 3, 4, and 5, will be found the residuals previously given, corrected by the 

 values of a and b, given above. In column 6 will be fou'^d the corrected residuals 

 for Pond's General Catalogue (of 1112 stars). In the last column will be found 

 the mean of columns 1 to 5, corrected for errors of single period. The following 

 are the derived periodic equations. 



