for determining the difference of meridians, &c. lis 



of B, and so for the rest) reducing and striking out all the 



terms which desti*oy each other. 



A = mean of A — mean ofB-{- mean ofB' — mean of C •{• 



+ mean of C" — mean of Z" 

 + (2 { mean of B—mean of BI-^- yimean ofC — mean of C\ 

 or simply, denoting by A, B, A', B', &c. no longer the indi- 

 vidual observed times (to which there will be no occasion 

 again to refer) but the means of all those which have cor- 

 responding observations. 



A = A — B+B'— C+ C — Z" 

 + i3(B-B')+y(C~C"( 



This expression is, as it obviously ought to be, independent 

 of the arbitrary epoch E, which may be assumed any number 

 of hours or days before or after the observations. 



The first line of this value of A may be regarded as an 

 approximate one ; the second as a correction depending on 

 the rates of the watches ; and it is clear that the several 

 portions of which this correction consists are the respective 

 gains of the chronometers on Sid. T. during the mean 

 amounts of the delay of the message between the several 

 stations, taking the expression in its algebraical sense, where 

 a negative delay corresponds to an anticipation. 



If all the signals succeeded, the coefficients of jS and y 

 would be each o** 5", and the amount of the correction would 

 be ( jQ + 7 ) •-|-T= ^^ • It would therefore require no less 

 a deviation of one of the chronometers from its assumed 

 rate than 29^" per diem, or of both of them i4j, and the same 

 way, to produce an uncertainty in the result to the amount 

 of a tenth of a second; deviations incompatible with the 



MDCCCXXVI. Q 



