1 1 New Method of delermiuing the Longitude. 



in this country, where we have no observatories, and so 

 few meridians fixed with much accuracy.* 



The author of this paper, after several pages of prehmi- 

 nary, historical, and explanatory remarks, proceeds to in- 

 vestigate, by the analytic method, a formula for solving the 

 problem under consideration. We need not follow him 

 through the several steps of the process, but only state the 

 final equation. 



In this formula, x denotes the correct difTerence of the 

 meridians of the two observatories ; t the difference be- 

 tween the time of the transit of the moon's iimb and the 

 star, at the most westerly observatory; r the same differ- 

 ence at the eastern observatory ; r the moon's true semi- 

 diameter, as seen from the earth, for the apparent lime of 

 her culmination at the western observatory ; d the moon's 

 declination at the same time ; ^ and <5, the same quantities 

 respectively, as the two last, for the time of the moon's 

 culmination at the eastern observatory ; s the true value 

 of a solar day in sidereal time, or 24 hours added to the 

 sun's daily increase in right ascension ; c the apparent 

 time of the moon's culmination at the western observatory, 

 reduced to the meridian for which the ephemeris made use 

 of was computed ; a the moon's true right ascension at 

 that time; h and b, the same quantities, respectively, as 

 the two last, as shown by the observation at the eastern 

 observatory. Where the ambiguous symbol + occurs in 

 the preceding equation, the upper sign is to be taken when 

 the first or western border of the moon is observed ; and the 

 lower sign, when the second or eastern border is observed. 

 But in all cases where the difference of meridians is not 



* A few years since, we observed several meridian transits of the moon 

 and stars, with a good theodolite and sextant, although the meridian was 

 not accurately settled : and we had it in view, to propose to our country- 

 men, (in the dearth of facilities among us for astronomical observations,) a 

 method of deducing the longitude from such observations with such instru- 

 ments, depending on equal altitudes for correcting the meridian, and on the 

 tables for the elements, instead of corresponding observations. But want 

 of time and health has prevented the execution of the plan; and since 

 reading the paper of Mr. Baily, and perceiving the much better mode of 

 corresponding observations likely to^be extensively practised we are inclin- 

 ed to dismiss our project sine die. 



