CHAP. XIV.] CHRONOMETRIC MERIDIAN DISTANCES 343 



The algebraic formula for meridian distance by above Formula 

 method of uniform sea rate is — po^iaSo" 



Mi = Ai-A+T . 



t 



Where M is meridian distance between the terminal points A 

 and K of the voyage. 

 Ml is meridian distance between port of departure and 



a port B touched at on the voyage. 

 X is error at A on leaving. 

 Ai is ,, B on touching. 

 A 2 is ,, K on arriving. 

 t is interval between observations at A and K. 

 T ,, ,, ,, A and B. 



In any case of a ship's calling at a place as an intermediate 

 port on her voyage between two other places, it may be well 

 to send home, beside the meridian distance obtained in the 

 ordinary manner, the information which would enable the 

 office, if or when it j)0ssesses the true difference of longitude 

 hetiveen the terminal ports, to calculate the difference of longi- 

 tude of the intermediate place by the last formula. 



This necessary information Avill be — 



A, Ai, Ao, t, and r. 



In transmitting this information, we could, for the facilita- Meaning 

 tion of computation afterwards, give only the mean of the t^^Errors 

 Errors of all the chronometers, instead of the individual error 

 of each, or, in other words, assume an imaginary watch, the 

 result of which Avill give the same meridian distance at the mean 

 of the meridian distances by each chronometer ; but the adop- 

 tion of this method will of course preclude any estimation of 

 the value of the distance by the concurrence of individual 

 results, and should be therefore only adopted when we have 

 reason to believe from intercomparisons during the voyage 

 that the watches have been going well together.* 



There is another adaptation of the methods of sea rates as 

 obtained by Error at two places whose longitude is known, 

 which is often useful. 



* This method of interpolation is not recognised as being as vahiable as 

 I believe it to be, and the remarks on it must be taken as my private opinion 

 only.— W. J. L. W. 



