Ill 
for determining the difference of meridians , &c. 
sidereal time since the epoch, their difference reduced to the 
fixed epoch will be 
(B'-C')-(/3 -y) (A' — E) 
in which, substituting for A its value above found, we get 
(B' — C') — (/3 — y) (P + B' — E) 
neglecting powers and products of j3 and y. Putting then 
Q=mean of all the{ B' — C') — (/3— <y) — mean of all the (P+B' — E) 
we get the most probable value of the difference of the 
chronometers at the epoch which can be obtained from any 
number of such comparisons. 
Finally, if we make a comparison at anytime A" ( Paris 
Sid. T. ) between the watch at C and the clock at z, and call 
their indications at that moment C" and Z", their apparent 
difference will beC" — Z", and their difference reduced to the 
epoch will be 
(C"— Z") — y (A" — E ) . 
But Q being the most probable difference between the chro- 
nometers B and C at the epoch, and (jG — y) the difference 
of their rates 
Q + (0 — y) (A" — E) 
will be their difference at any other moment A"; hence 
B" — C"= Q + <j3 — 7 ) (A" — E). 
But by the equation (a) since B" and A" are correspond- 
ing times, we have 
B"=A"-P + /3 (A"— E). 
Consequently substituting this for B /7 we get 
C"= A P — . Q + y ( A"-E) 
whence A"= P -]_ Q _j_ C /f — y ( A" — E) 
= P + Q + C"-y(P + Q + C"_E) 
neglecting the square and higher powers of y : 
