346 Astronomical and Nautical Collections. 



2. It may sometimes happen that the complementary angle 

 exceeds 180°: in this case its supplement to 360°, with the sign 

 reversed, is to be used. 



II. Add together the proportional logarithm of the moon's 

 reduced horizontal parallax, the logarithmic secant of the star's 

 altitude, and the logarithmic cosecant of the complementary angle; 

 the sum will be the proportional logarithm of the orbital parallax, 

 •which must have the same sign as the complementary angle. To this 

 logarithm add the logarithmic tangent of the complementary 

 angle ; the sum will be the proportional logarithm of the perpen- 

 dicular parallax, which must have the contrary sign to that of the 

 moon's nearest approach, when the complementary angle is less 

 than 90°, and the same sign when it is greater ; considering + as 

 belonging to the moon's distance, when she is N. of the star, and 

 —when S. 



Example: — The P. L. of the reduced horizontal parallax is 5225. 

 (SeeN. A. 1826. Add. P. 4.) 



P. L. red. H. P 5225 



Log. sec. Alt 0598 



cosec. corapl. A 2762 



P. L. ... - 24' 56" O. P. .8585 



Log. tan. comp. A 9.7952 



P. L. ... - 39' 57" P. P. .6537 



III. The sum of the moon's nearest approach and the perpendi- 

 cular parallax may be considered as one of the sides, and the moon's 

 semidiameter, without augmentation, as the hypotenuse of a right- 

 angled plane triangle, of which the other side is to be ascertained : 

 it will have the sign + in the case of an immersion, and — in that 

 of an emersion. The sum of this quantity and the orbital parallax 

 being reduced to time, by means of the moon's horary motion, and 

 then applied to the time of observation by addition or subtraction, 

 accordingly as it bears the sign + or — , will give the time of the 

 nearest approach, reckoned according to the meridian of the place 



