for determining the difference of meridians , &c. 113 
of B, and so for the rest) reducing and striking out all the 
terms which destroy each other. 
A = mean of A — mean of B + mean of B' — mean of O + 
+ mean of C" — mean of Z" 
+ # { mean of B— mean of B j -j" 7 | mean of C' — 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 + O' — Z" 
+ ]S(B-B / ) + 7 (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 jQ and y 
would be each o h 5 m , and the amount of the correction would 
be ( /3 + 7) r=: • It would therefore require no less 
a deviation of one of the chronometers from its assumed 
rate than 29 sec per diem, or of both of them 14^, 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. O 
