Astronomical and Nautical Collections. 437 



Example, 



Log. cosec. hor. angle . . , 0*0168 



N. P. D. of Zenith . . 0-5871 



sineC ..... 9*4928 



secant com p^ angle . . . 0-038S 



Prop. log. reduced hor. par. . . . 0*4861 



perpendicular parallax = - 48' 20" 0*5711 



Log. cotang. comp^ ang. . . . 0*8575 



A. C. Prop. log. 35' 20" IL M. . . 9*2929 



Constant log. . . . . .0-4771 



H. M. 8. 



Prop. log. -f SO 2 0*6986 



Time of observation 6 9 17 

 Time corrected 6 45 19 



3. The nearest approach will have the sign + or — , 

 accordingly as the diflference of declination at the conjunction 

 is marked N. or S. The sum of the nearest approach and 

 perpendicular parallax is the star's distance from the appa- 

 rent orbit, which add to and subtract from the moon's hori- 

 zontal semidiameter without augmentation. To half the 

 prop. log. of the sum add half the prop. log. of the differ- 

 ence, the arithmetical complement of the prop. log. of the 

 moon's horary motion, and the constant log. 0-4771, the 

 sum is the prop. log. of another portion of time, which, 

 added to or subtracted from the time corrected, accordingly 

 as an immersion or emersion has been observed, gives the time 

 of the nearest approach for the meridian of the place of obser- 

 vation ; which being compared with the Greenwich time set 

 down in the Elements, the difference of longitude is obtained. 



Remark. — In some rare cases, when the star's distance from the apparent 

 orbit is nearly equal to the semidiameter, the portion of time will have to be 

 applied in a contrary manner to that here directed. This will happen when the 

 immersion takes place after, or the emersion before^ the apparent conjunction. 



Example. 



Time of nearest approach 7 12 18 

 Ditto for Greenwich 1 3 8 3 



Longitude of Port Bowen 5 55 45 west of Greenwich. 



