jio Mr. Herschel's account of a series of observations 



to this epoch, i. e. the difFerence they would have indicated if 

 instead of comparing them at the time A, they had been 

 compared at the time E. 



Every signal simultaneously observed at A and B, gives a 

 direct comparison of the clock and chronometer ; but it is 

 only when thus reduced to a fixed epoch that these compa- 

 risons become comparable inter se ; but when so reduced 

 their mean may be taken, and is of course preferable to the 

 fesult of any single comparison. Hence if we put 



P = mean of all the ( A — B) + /3 x mean of all the (A - E) 

 P will express the difference of the clock and chronometer 

 at the epoch more probably than any of the individual values 

 derived from single observations. 



It follows therefore that at any other sidereal time A', the 

 time indicated by the chronometer at B, (or B') may be cal- 

 culated from the expression 



B'= (A'^P) + /3 (A'— E) (a) 



more probably than it can be derived from any single actual 

 observation. This equation gives 



A'= ^^^^j^=^ = B' -f P — ^ (P + B' — E) 



neglecting squares and higher powers of jS, whence the 

 time by the clock at A becomes known at any instant in 

 terms of that shown by the watch at B. 



Now let a signal be made between B and C, and noted to 

 happen at the moment marked B' by the watch at B, and C 

 by that at C. Let )3 and y denote their respective rates on 

 sidereal time ; then since B' — jS (A'— E) and C— y (A'— -E) 

 are the times they would have marked had they kept strict 



