80 THE TRANSATLANTIC LONGITUDE. 



Naval Observatory, to the centre of the dome of which the preceding value refers, 



we have as their longitudes from Greenwich — 



Seaton Station, 5'' Y^SO'-OT 



Capitol, 6 8 2.22 



XII. 

 TRANSMISSION-TIME OF THE SIGNALS. 



We have seen in Chapter VII how an interchange of signals gives the numerical 

 measure of the time consumed in their transmission and registration, upon com- 

 parison of the records at the two stations. Representing the clock-time and its 

 needful correction by T and A^, denoting the signals from Valencia and from New- 

 foundland by the subjacent figures 1 and 2 respectively, and distinguishing by an 

 accent those quantities which depend upon the Newfoundland clock, we have (since 

 the Valencia signals preceded) — 



x,^x^= {T,— T,) — {T,'— T,') + (At, — At,) — {At^— At,') 

 or, in words : the sum of the transmission-times for westward and eastward signals, 

 each increased by the error incurred in the process of recording, is equal to the 

 excess of the recorded interval upon the chronograph at the station whence the 

 first signal was given, increased by the excess in the loss of time by the clock at 

 that station during the interval. 



In our experiments the interval in question rarely amounted to so much as 160 

 seconds, and the clock-rates were small. The correction due to difference of rates 

 appears never to have surpassed the thousandth of a second ; and, since it is cer- 

 tainly a quantity of the second order in comparison with the variation in personal 

 error, we may disregard it, and consider the quantity x^ + Xo as the excess, in the 

 record upon the eastern chronograph, of the interval between the westward and 

 eastward signals. Or, otherwise stated, it is the excess, for eastward signals above 

 westward ones, of the difference of time recorded upon the two chronographs. 



Half of this excess would measure the time required for the transmission and 

 record of a signal, assuming the velocity to be the same in each direction, could we 

 assume the personal error in noting to be equal for the two observers. This we 

 have in Chapter IX found not to be the case, but happily we have trustworthy 

 values of the absolute amount of the error for each observer. Deducting the sum 

 of the two errors from the quantity Xi + x.2, we have determinations of the actual 

 time consumed in one westward and one eastward transmission ; or, if w^e assume 

 the velocity in each direction to be the same, we have the measure of twice the 

 time required for the transmission of a signal through the length of the telegraphic 

 cable. 



The transmission-time as determined for the dates of the several longitude-deter- 

 minations has been deduced in Chapter VII, subject to a correction for the mean 

 personal error in noting signals, which correction we have in Chapter IX found to 

 be 0'.303. Applying this to the results obtained, we have the following values for 

 the mean time of transmission of signals, upon the five nights Avhen the longitude 

 was determined: — 



