112 Mr. Herschel’s account of a series of observations 
Consequently, still neglecting the same things we get 
C" — Z"— y { P+ Q +C"_E } 
for the difference of the timekeepers C and Z reduced to the 
epoch, and putting 
R= mean of all the (C" - Z") - y.mean of all the (P-f Q-j-C"— E) 
R will be their most probable difference reduced to the fixed 
epoch. 
P, Q, and R, being thus obtained, we must obviously have 
for the correct difference of longitudes, 
A = P + Q + R* 
Now, substituting for P, Q, R, their values, this gives 
A = mean of (A — B) -f- mean of ( B' — C) mean of (C" — Z") 
+/ i.mean of (A — E) 
+ (o' — / 3 ) .mean «/( P + B'-E) 
— y.mean of (P -f- Q -f- C" — E) 
that is, reducing, 
A = mean of (A — B) -f mean of ( B' — C') -f mean of (C" — Z") 
-j- (3. mean of A -f* ( y — (3). mean of B' — y. mean of C" 
— P/3 -Qy- 
This value of A is however susceptible of still further 
reduction by substituting for P and Q their values ; which if 
done, and the powers and products of (3 and y neglected, as 
has all along been done, we get 
A = mean of (A. — B) -f- mean o/(B'_C) + mean of (C /; — Z") 
-f- /3 .mean of A -J- (7 — /3) mean of B' — y. mean of C " 
— (3. mean of( A-B)-y. mean 0f{ B'- C') 
that is, finally (since the numbers of the observations of 
A and of B are necessarily equal, and therefore the mean of 
the values of A — B is equal to the mean of A — the mean 
