NO. 6.] INTRODUCTION. CHRONOMETERS. XXXI 



If this last supposition should in some cases prove insufficient, the series 

 (a) will give the means for further corrections. The accuracy aimed at in the 

 reduction depends of course on the accuracy of the observations, but as this 

 is manifestly not great no such refined corrections have been found necessary. 



Now 



and on division by 



or, neglecting the second term and multiplying by x 



Similarly for another observation of the same phenomenon, made with a tele- 

 scope of aperture A^ at the moment T 2 



and by subtraction 



If the two observations have been made with the Planet at the distance 



/-D'\4- 

 D' instead of D, x is to be replaced by |-yr I x, and consequently if 



. (D\l 

 c a 



*() 



then x may be found by the equation 



-/> __ n 1 I Ffl fjl \ /"(' * I 



CTiC ~ K \ JL o J. * I ** \^/ 



expressed in the same units as w, T 2 2*i being given in seconds. 



As soon as x has been determined in this manner by pairs of observa- 

 tions, every observed moment 2" found by means of an aperture A' at dis- 



