THE TRANSATLANTIC LONGITUDE. 55 



tude by /I ; and if furtliermore we distinguish those quantities which pertain to 

 Valencia signals by a subjacent 1, and similarly those belonging to Newfoundland 

 signals by the subjacent figure 2, it is manifest that, if we include in x the personal 

 error of noting signals, then 



the signals given and recorded at Valencia at the time T-^ will be registered 



upon the Newfoundland record at T^ = 7\ + A^i — A^/ — 7^ + x^ 



and the signals given and recorded at Newfoundland at T^ will be registered 



upon the Valencia record at T^, = T^' + At^' — A^o + ^ + X2 



Thus the comparison of the records of Valencia signals, at the two stations, gives 



T,— T,' = At/ — At, + ^ — x, 

 while the comparison of the records of Newfoundland signals gives 



T^— Ti = Ati — At^ + ;H- X2 

 and consequently 



2A = ( 1; — 7;') + ( 7; — 7\') + (A«3 — A^/) + (A^i — A^i' ) + (iKi — iCa) 

 X, + a;2= (T;— T:) — {T,— T/) + {At^ — At.{)—{At, — At/) 

 If we assume the personal error of noting to be the same for the two observers, 

 and the signals to travel with equal velocity in the two directions, the term x, — x^ 

 will disappear from the first equation, while the second will give a measure of the 

 sum of the transmission-times and the personal errors of noting. 



From the time-determinations in Chapters IV and V we may obtain the clock- 

 corrections as follows, for the periods in which longitude-signals were exchanged. 

 They are iirst given for those epochs for which they were determined, and the 

 interpolated values follow for intervals of five minutes during the period of the 

 exchanges. 



, On November 5, a double weight is assigned to the first time-determination, on 

 account of the much smaller value of the azimuth error ; this having been largely 

 changed by an accident (due to no carelessness of the observer) which interrupted 

 the first series of observations. 



