(54(f) PHILOSOPHICAL TRANSACTIONS. [aNNO 17(52. 



be found at an hour's interval after the time assumed at Greenwich, by adding 

 the horary motions to the longitude and latitude computed ; and by the applica- 

 tion of the rules, the distance of the star from the moon must be found again at 

 the end of that hour ; which gives the horary motion to or from the star as 

 required. 



It is to be observed that the longitude thus found is that of the ship, at 

 the instant when the altitude of the sun or star was taken, by which the watch 

 was regulated, and not at the time of the observation of the distance of the star 

 from the moon ; for the watch being supposed not to vary considerably during 

 that interval of time, must continue to indicate the time according to the meri- 

 dian by which it was corrected; and the observation of the distance of the moon 

 from the star showing the time at Greenwich, the difference must show tiie dif- 

 ference of longitude between that meridian and Greenwich. 



Perhaps the following method of deducing the longitude from the observations 

 may be least liable to mistake ; — Find what the longitude by account was, at the 

 instant of taking the sun 6r star's altitude, for the regulation of the watch ; which 

 being turned into time, at the rate of one hour for every 1 5°, and 4 minutes for 

 every degree, add to the correct time from noon, when the distance of the star 

 from the moon was taken, if the ship is to the west of Greenwich, or subtract 

 from it, if it be to the east ; this gives the apparent time at Greenwich by account ; 

 and the mean time is found, by applying the equation of time ; to which time, 

 compute the moon's longitude and latitude from the tables, and the distance of 

 the star from the moon by the rules, and find by proportion as befoie, u hat time 

 the moon will take to run over the difference between the distance computed, and 

 that resulting from the observation ; this turned into degrees and minutes of the 

 equator, will show the error of the ship's account ; and the following rules will 

 show whether the ship is to the east or west of its account. 



If the distance of the moon observed east of a star (or the sun in the first quar- 

 ter) is greater than that computed, the ship is west of the longitude by account ; 

 but if the distance observed is less than that computed, it is east of account. If 

 the distance of the moon observed west of a star (or the sun in the last quarter) 

 is greater than computed, the ship is east of account ; but if the distance observed 

 is less than computed, it is west of account. 



The horary motion of the moon in the eclipt'c, may be thus made out very 

 expeditiously from Mayer's equations, by the help of the principal arguments used 

 in the computations of the moon's place. Call a, b, c, and d, the differences of 

 the equations of the centre, evection, and variation, and reduction to the cciiptic, 

 for 1° addition to their arguments; where it must be noted, that they must liave 

 the same sign as the equation, if it is increasing, but a contrary sign, if it is 

 decreasing. Compute the value of 32' 5& -|- a X ii X tV-o + b X 4 X -f-f, 

 Tvhich put = H, and the true horary motion of the moon in her orbit = h -f- c 



