280 ON FINDING THE LONGITUDE FROM 



rithm of the rate of change of declination for one minute of 

 time, the remainder will be the logarithm of the correction in 

 seconds. 



EXAMPLE. 



Given the moon's greatest altitude near the meridian, cor- 

 rected from the effects of paral. and refraction, 45° 40' 20" 59; 

 the latitude of the place, 32° 29' 25", and therefore the moon's 

 declination (nearly) is 11° 50' 14" 41. 



Constant logarithm. . . .8651414 Change in declination for 1' of time 12" 86 



Decl. 11° 50' 14" 41 cosine. 9.9906648 Logarithm of ditto. . . . 1.1092412 



X 2 



Lat. 32 29 25 cosine. 9.9260761 Square of change of decl. Log. 2.2184820 



Alt. 45 40 20 59 cos. ar. co. .1556719 4 times the depression. Log.— .9375542 



Log. of 4 times the depression. .9375542 Cor. for mer. alt. 19" 096 Log. 1.2809278 



The. correction being found by the foregoing formula, is to 

 be subtracted from the greatest altitude, cleared of the effects 

 of refraction and parallax, the remainder will be the true alti- 

 tude of the moon, when she was on the meridian. The dif- 

 ference between the corrected altitude of the moon's centre on 

 the meridian and the colatitude, will be the moon's true decli- 

 nation, when on the meridian : the time at Greenwich, when 

 the moon had that declination, being found, and also the time 

 of the moon's transit over the meridian of Greenwich, take 

 their difference, take also the difference of the increase of the 

 A. R. of the J and © for the interval of time elapsed in passing 

 the two meridians, which last difference being subtracted from 

 the first difference, the remainder will be longitude in time. 



In order to calculate with sufficient accuracy, the times cor- 

 responding to the moon's declination, and her transit over the 

 meridian of Greenwich, it will be necessary to prepare four 

 right ascensions and four declinations of the moon to seconds, 

 which in the nautical almanac, are set down to minutes only, 

 by the aid of which, with the tables of second differences, we 

 can find very correctly the times which are sought, and in re- 

 gard to the moon's declination, the effects of aberration and 

 nutation should not be omitted, because an error of seconds in 



