io8 Mr. Herschel’s account of a series of observations 
the Fairlight chronometer, and at i8 h 4i m 7 s . 11 true sidereal 
time at Greenwich. The calculation then stands thus 
+ A = -f 18 39 52 ’50. — B ~ - 10 4941-00 
-J-B'rr-fio 54 53-20 — C'“ —10 4637-50 
4 C' = +10 51 59-40 •— Z"— —18 41 7*ii 
Sum = +3S h 144 ”i65 s -io — 3 8h X36 m 85 3 -6i 
B' — B + o 5 12-20 
C"- — C'ss + o 5 21-90 
Sum o 10 34-10 
— o h 8 m 79*'49 or ~o h 9“ 195.49 the uncorrected value of A 
Reduction from mean to 1 
Sid. T. for an interval 1 = -f- 1*73 
of io m 34 s> io . . J — - 
o 9 21-22 ~ a 
the corrected difference of longitudes. 
Such is the result of the transmission of a single signal 
along the line, and such the whole calculation required to 
deduce it. It is chosen at random from among the observa- 
tions, yet is probably entitled to at least as much confidence 
as any value hitherto previously obtained ; a circumstance 
which sets the excellence of this method in a very strong 
light. 
Such would be the process of calculation in the simplest 
state of the data, viz. when the signals are seen along the 
whole line without a failure, so that each message so trans- 
mitted arrives at its destination and gives a complete result. 
But this (in the present instance at least) has not been always, 
oFgenerally the case. It has much more commonly happened 
that a signal made at one station (a for instance, has not been 
simultaneously observed, or not observed at all, at A and at B, 
while the other signals, at b, c, See. have been regularly seen 
and registered. In every such case (of which endless combi- 
nations may occur) a link of the chain fails, and no result can 
be obtained from this series of observations taken singly. A 
very slight consideration will suffice to show that were we 
