DETERMINING THE LONGITUDE. g43 



corresponding to thisARn., in other words, at what apparent time the moon's 

 limb was on the meridian. First, compute from the Ephemeris, the right 

 ascension of the sun at noon, at the phice of observation, which subtract from 

 the A Rn. moon's limb, as above found, the remainder is the approximate time 

 of transit. From this quantity, subtract the proportional part of the sun's 

 daily increase of right ascension, according to the number of hours and 

 minutes elapsed, and the second remainder is the apparent time of the transit 

 of the moon's limb, true to the fraction of a second. 



Rule 2d.- — In order to find the ARn. of the moon's centre at this appa- 

 rent time, take out the semi-diameter, as given in the Ephemeris, and either 

 multiply it by the natural secant of the moon's declination, or if there be no 

 table of natural secants present, then, to the Logm. of the horizontal semi- 

 diameter, add the Logm. secant of the moon's declination, the sum is the 

 Logm. of the semi-diameter in ARn., which added to, or subtracted from 

 the observed ARn. of her limb, gives the ARn. of her centre, when her 

 limb was on the meridian. 



Rule 3d.- — Having thus found the right ascension of her centre, the next 

 and last process is, to compute from the Ephemeris, at what apparent time at 

 , Greenwich, the moon's centre had the observed right ascension; the difference 

 of these apparent times is the difference between the right ascension of the 

 meridian of the place of observation, when the moon's limb passed it, and that 

 of the meridian of Greenwich, at the same instant of time^;: to the angle at the 

 pole, formed by the two meridians, measured on the equatorrz the difference 

 of these meridians in sidereal timez: to the loneritude from the first meridian. 



o 



A few examples will render the method perfectly intelligible to any per- 

 son who has the slightest knowledge of nautical astronomy. I shall first 

 compute one transit, observed near Calcutta. 



