Astronomical and Nautical Collections. 345 



proposed to substitute the reduction of the parallax to the moon's 

 orbit, as employed by Dr. Young in the calculation of a predicted 

 occultation, and as explained in the following Rules : 



I. Compute the altitude of the star for the time of observation, 

 and from the reduced or geocentric latitude of the place, as shown 

 in the Nautical Almanac for 1826, Add. P. 1 ; and find the paral- 

 lactic angle P -)f Z, the sine of which is equal to the secant of the 

 altitude multiplied by the cosine of the reduced latitude, and by the 

 sine of the horary angle : this angle having- the sign + before the 

 star has passed the meridian, and — afterwards. The complement 

 to 90° of the moon's orbital angle P J J) ' is to have the sign — , 

 when the moon's nearest approach to the star and the orbital angle 

 have the same denomination N. or S., and + when they are of 

 diflferent denominations. The sum of these two angles is the 

 complement of the parallactic orbital angle Z J J ', or the comple- 

 mentary angle, with its proper sign. 



Example: — In the case of 5;^, the star's reduced altitude has 

 been found 29° 22' 48", N. A. 1826. Add. P. 7 ; then, 



Log. sec. alt. . . , 0.05979 Orb. A. . .65 29 N.E. J N. 

 cos, red. lat. . . 9.79609 Compl. . —24 31 

 sin. H. A. . . 9.25669 Par. A. . - 7 27 - ^^ W. of Mer. 

 sin. Par. A. 7° 27' 9.11257 C. P. O. A. —31 58 

 Remark 1. The parallactic angle must always be reckoned from 

 that pole of the equator, which is either north or south, accord- 

 ingly as the nearest approach is marked N. or S. in the Elements 

 of the Occultation; and therefore, when this pole is of a contrary 

 denomination to that of the latitude of the place, the parallactic 

 angle is to be takeo obtuse, or equal to the supplement of the angle 

 found by the above rule. But when the latitude is less than the 

 star's declination, and of the same denomination, an ambiguity may 

 arise, respecting the magnitude of the parallactic angle, in pro- 

 ceeding by the rule above. This ambiguity may be removed by 

 resolving, according to the common rules of spherical trigonometry, 

 the triangle P -^ Z, formed by the reduced zenith, the star, and the 

 proper pole of the equator. 



Vol. XVIII. 2 A 



