106 Mr, Herschel's account of a series of observations 



chronometer ; then, if the observations were perfect, the 

 difference of the clock at A, and the chronometer at B, would 

 become exactly known. Let this be denoted by A — B. 

 A short time after, let a signal be made at 6, and observed by 

 the chronometers at B and C, whose difference (which we 

 will in like manner denote by B — C,) becomes thus precisely 

 known at the time of making the signal. In the same manner 

 may the difference C — Z of the chronometer at C and the 

 sidereal clock at Z be known at the moment of explosion of 

 a signal at c ; and so on, if there be more intermediate 

 stations. 



Now, the clocks at A and Z being all along supposed to 

 keep strict sidereal time, if the watches at B, C, did the same, 

 it is manifest that the difference between any two of them 

 determined at one moment would be the same at every 

 other ; and therefore the intervals elapsed between the 

 signals would be out of the question, and the observations 

 might all be regarded as simultaneous ; so that the sum of 

 the differences (A — B) + (B — C)+ (C — -Z) =A — Z 

 would express strictly the difference of the true sidereal times 

 at the extreme points, /. e, their difference of longitudes ex- 

 pressed in time, without any further calculation or reduction. 



It is equally evident that, whatever be the rates of the 

 watches, if the intervals elapsed between the signals were 

 infinitely small, so as to reduce their gain or loss in these 

 times to nothing, the same would hold good. Since this 

 however cannot be the case, it is obvious that the difference 

 of longitudes so obtained will be affected by the rates of the 

 watches and the intervals of the signals, which must accord- 



