500 PROFESSOR CHALLIS, ON THE DETERMINATION OF THE LONGITUDE 



No. 78, B's observation was doubtful on account of noise. 



No. 97, D's signal-time is 2 s in defect, as appears by T's and B's. 



Batches I., III., XIV., XV. and XVI. are respectively transits of 16 Librae, B.A.C. 4941, 

 10 Serpentis, 1 1 Serpentis and A' Serpentis across the wires of the Greenwich Transit-Circle. 



The omissions in Nos. 8, 63, 71 and 131 are due apparently to the same accidents as those 

 which occurred on May 17- 



Some inferences may be drawn from the noted signal-times before reducing them to the 

 sidereal times of the Observatories. In the first place, we may compare the times of the 

 same signals as recorded by two observers. By 147 comparisons of the signal-times noted 

 at Cambridge on May 17, it appears that Mr Breen observed later than Mr Todd by the 

 mean interval s ,0l6. On May 18, some of Mr Breen's signal-times in Batch V. appear to be 

 anomalous, possibly by mistakes of half a second. If this batch be excluded, the mean result 

 of 130 comparisons is, that Mr Breen observed later than Mr Dunkin by S ,020. It seems, 

 therefore, that Mr Dunkin's and Mr Todd's observations of signals agree very closely, and 

 that little difference exists between the three observers in that kind of observation. This 

 result is the more to be remarked because a decided difference of personal equation exists 

 between Mr Breen's transits and those of Mr Todd. In the year 1848 Mr Breen observed 

 earlier than Mr Todd by 8 ,35. (See the Cambridge Observations, Vol. xvn. p. 55). By 

 transits taken in 1853, on May 17 and May 19, the differences of the personal equations of 

 these two observers were 0",17 and 8 ,19, and by transits taken on May 18 and May 19, the 

 differences of the personal equations of Mr Dunkin and Mr Breen were 8 ,14 and s , 18, 

 Mr Breen's observations being the earlier in each instance. It follows, therefore, that there 

 is not necessarily the same personal equation in observing signals as in observing transits. If 

 such were the case, the determination of longitude by signals would plainly not be affected 

 by personal equation, provided the transits for clock-errors and the signals were observed 

 by the same observer. 



Again, from the unreduced signal-times, the interval occupied by the transmission of the 

 galvanic action between Greenwich and Cambridge may be ascertained, if it be of sensible 

 amount. In order to get a result independent of the rates of the time-pieces used for 

 recording the signal-times, and of the comparisons of chronometers, the mean excess of 

 the Cambridge signal-times above the Greenwich signal-times, as derived from the first and 

 third sets, will be compared with the mean excess derived from the second set, and the mean 

 excess of the Cambridge above the Greenwich signal-times given by the second and fourth 

 sets will be compared with the excess given by the third set. It will only be necessary to 

 indicate the fractional parts of these excesses. Let G,, G 3 represent the fractional parts of 

 the mean excess of the Cambridge above the Greenwich signal-times for the first and third 

 sets of signals, or those given at Greenwich, and C 2 , C 4 represent the like quantities for the 

 second and fourth sets, or those given at Cambridge. Then the following results may be 

 obtained. 



