no 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 
result of any single comparison. Hence if we put 
P = mean of all the ( A — B) -j- /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) -f /3 (A'—E) (a) 
more probably than it can be derived from any single actual 
observation. This equation gives 
A' = - ' *4 + / E == B' + P — (P + B'— E) 
neglecting squares and higher powers of jG, 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' — /3 (A' — E) and C — y (A' — E) 
are the times they would have marked had they kept strict 
