CHAP. XIV.] CHRONOMETRIC MERIDIAN DISTANCES 347 



on arrival at B on the 20th and 27th, we should take the mean 

 of the two Errors on 2nd and 8th, and call it the Error at A 

 on the 5th, and similarly at B on the 23rd-5, and use the 

 interval between these two epochs for the multiplication of the 

 mean rate. 



The formula given by Tiarks, and generally adopted, for Tiaiks' 

 calculating the meridian distance between two places by rates '<'™^"^^- 

 at departure and arrival, without any consideration of tempera- 

 ture, is — 



Where M is meridian distance required, 



X the Error at mean epoch of departure, 

 X^ „ ,, ,, arrival, 



t the interval between the two epochs, 

 a the rate at departure, 

 b the difference between rate at departure and arrival. 



In calculating t, the difference of time, due to difference of Caicuiat- 

 longitude between the two places, must not be forgotten ; but, interval, 

 being reduced to the decimal of a day, must be added or sub- 

 tracted to the interval between the epochs, according as we 

 have moved westward or eastward. 



Thus, if our mean epoch at A is at noon on the 20th, and 

 at another place, B, 30° to the westward, at noon on the 

 30th, the interval of time for accumulated rate will not be ten 

 days, but ten plus the difference of longitude of the two places, 

 or 10-08 days ; for the sun, having completed tlie ten days by 

 returning to the meridian of A, will take yet another -08 of a 

 day to be on the meridian of B. 



Similarly, in calculating sea rate from observations at 

 different places where longitude is known, we must allow for 

 this difference of time. 



Thus, having taken sights at A at noon on the 2nd, and at 

 B, 20° eastward, on the 11th at noon, the interval with which 

 to divide the difference of Error at A (corrected for difference 

 of longitude) and Error at B, to ascertain the daily rate, will 

 be 8-94 days, as the sun will be on the meridian at B 06 of a 

 day earlier than at A. 



