27S ON FINDING THE LONGITUDE FROM 



chronometer or good watch, to a single observer, and as time- 

 pieces of a delicate construction are liable to derangement, the 

 discovery of a method, by which one observer without a know- 

 ledge of the precise time, may be enabled to ascertain his lon- 

 gitude, becomes a desideratum of value. 



There are two portions of time during each lunation, when 

 the moon's change of declination is sufficiently rapid to afford 

 the means of solving this useful problem; those times are, when 

 the moon is on or near the celestial equator, and may be ex- 

 tended to four or five clays at least, i. e. two before and two 

 after the day on which the moon crosses the equator: the moon's 

 change of declination in the most favourable circumstances, 

 exceeds 6° in twenty-four hours, or 15" in one minute of time 

 and although this is scarcely half the moon's motion in longi- 

 tude, yet it is to be remembered, that this method is no other 

 than a meridian altitude, which may be taken to a degree of 

 precision, never to be attained in the usual manner of taking 

 the moon's distance from a star, and if the altitude be taken at 

 land, with the aid of a mercurial horizon, the double angle 

 will place this method on a footing of equality (nearly) with 

 the usual mode, in respect to the moon's change of place, other 

 circumstances being in its favour. The accuracy of this me- 

 thod, depends upon the correctness of the lunar meridian alti- 

 tude, and the precision with which the latitude of the place 

 of observation has been ascertained. 



At sea, this method cannot always be used to advantage, 

 on account of the ship's change of place, which might ren- 

 der the latitude doubtful to several minutes, and thereby affect 

 the longitude an equal number of degrees. 



The moon's greatest altitude being taken, a correction be- 

 comes necessary, because the greatest altitude is not on the 

 meridian, but to the east or west, according as the moon is in- 

 creasing or diminishing, by change of declination, her zenith 

 distance, and which may be calculated as follows. — Having 

 cleared the moon's apparent altitude from the effects of refrac- 

 tion and parallax, the difference between it and the co-latitude 

 of the place of observation, will give the moon's declination 

 nearly, from which by even proportion may be found, the ap- 



