Asliommical and Naitlicul Collections. 361 



cension, in the ratio of tlie radius to the sine of the 

 orbital angle ; and the square of the nearest distance, being sub- 

 tracted from the square of the true distances, will give the 

 square of the distance from the point of the orbit nearest to the 

 star, the place of which in the orbit is found from the cosine of 

 the orbital angle. And in all these cases, the natural verse 

 sines, taken from a good table, will serve instead of the squares. 

 The time of immersion is found from the place in the orbit by 

 means of the hourly motion, and may be employed for correcting 

 the declination, and repeating the operation, when necessary. 



I. Example. Suppose the emersion of i^Jl to have been ob- 

 served at Paris, 1822, Feb. 8, 10" 9- IP: and the difference 

 of altitudes of the star and the moon's centre, either observed or 

 computed, to have been 2'36" : the semidiameter at the time 

 being 15' 18", and the parallax in altitude 52' 1", whence the 

 true difference of altitudes was 54' 37", the star being below the 

 moon's centre. 



II The semi-diameter 15 1 8 = 918 square 842724 

 True diff. alt. . . 54 37 = 3277 10738729 



DifF.app.alt. . . 2 36= 156 A.C. 99975664 



True distance . . 56 40 = 3400 11557117 



III, Now in order to find the point of the orbit nearest to the 

 star we take the difference of declination at the conjunction, 

 P.L. 41'58". _6324 ' !'; 



And add to it the log. cosec.l g^o 2' f ■^^'^^ 

 and the log. sec. J \ -3 289 



Hence the distance is 37' 4" .68631 



the motion in the orbit 19' 41" .9613J 



Then 37'.4" = 2224" square 4946176 



Subtracted from 1^557117 



Gives 42 51 =2571 6610941 



Deduct 19 41 



the remainder iFlO is the motion in the orbit, which, at 

 the rate of 31' 30" in an hour, gives 44" 8% to be added to the 

 time of emersion, 10*^9-" Us for the time of conjunction in 

 right ascension, making 10" 53"^ 19'; which differs only by a 

 second from the true term of conjunction, 10'' 53"' 18^ 



