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



the Fairlight chronometer, and at 18^ 41"" 7M1 true sidereal 

 time at Greenwich. The calculation then stands thus 



+ A = +i8 39 52 '50. — B = — 10 4941-00 

 + B'=+io 54 53-20 — €'=— 10 4637-50 

 + C"=+io 51 59-40 — Z"=:— 18 41 7-11 



B' — B rz + o 5 i2'2o 

 C"— C'= + o 5 21-90 



Sum o 10 34-10 



Sum = +38" i44°i65s-io —^S^ i36"858.6i 



r: o'' 8° 79*-49 or rso" 9" 198.49 the uncorrected value of A 



Reduction from mean to ^ 

 Sid. T. for an interval y= + 1*73 



of io"» 34»-io . . J — — — — 



o 9 21-22 r= 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, 

 or'generally 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 6, c, &c. 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 



