toao 



[ZEKTTH TBIBR' 



The reductions from the apparent to tho mean place* 

 re performed in a manner similar to that previously ex- 

 plained for right ascension. . 

 ^he other comvti.'Mt for rin-lo observations, viz., <lo- 

 fective illumination of Moon and Venus, etc., aresofully 

 in tho Intn-liu-tion to the Orttnwich Obtcrtar 

 fcoiw, that a short investigation will only be nocewary.* 



OOEKECTIOX FOB DMFwrrmi ILUJMWATIOH. The fol- 

 lowing is the investigation of the correction for the defec- 

 tive illumination of the moon in the right ascension : 



he the place of the sun, M that of the 

 moon if the sun were at S' both limbs of the moon 



would be full 12h. v> apparent time of moon's transit = 

 B P Q = arc B Q, but B Q x cos. SB = SS = SMS' 

 = O M n = arc O n. This is the arc on the moon's disc, 

 which is not illuminated, and its versed sin. is the part of 

 the surface not enlightened. 

 Moon's gemi-diameter X versed sine S S' = correction . 



Defective Illumination in N. P. D. Moon gibbous. 

 Let E Q (Fig. 221) be the equator, P the pole, E M= 

 Fig. 1. 



P 



M 



E O M S'O B - D the moon's declination. If the 

 sun were at S' both limbs of the moon would be enlight- 

 ened. E P S -* sun's hour angle = the difference between 

 the times of passage of the sun and moon without regard 

 to sign. Then in O B = cot. B O S' X tan. B S'. 

 .'. tan. B8 - sin. O B tan. D = sin. (E P S - 90) 



tan. D = 

 oos. sun's hour angle X tan. moon's apparent 



declination. 



: < called the new declination. 



New declination nun's declination = angle required. 

 When this angle is positive, the north limb is full. 

 From 8' let fall the perpendicular arc 8 A, then cos. 



B O 8' -oos. B 8' sin. B S' O.\ sin. B S'O-^ 8 ^- 

 sin. 8 A - sin. S 8' sin. AS'S - sin. SS'; sin. AS' S - sin. 



c - Ba '- 8 A 



Th robject of ptnlUx hw mlr-nutr txwn eiunlnrd, In nfrrraco to the 

 . moon. t.. M put 9M: to which UM muter it referral for the 

 ltal tff>}**tlom at Ik* prurtlng roamrlu ud (ormate. 



called the new angle, therefore sine now angle - cos. 

 app. dccl. X sec. new decL X sine n 



Tin- now angle, or S A, is taken for tho measure of 

 S M A or p M x, the a illumination. 



,'. in If. P. D. Afoon horned. 

 Mean time of passage 3h. to Oh. 



Let 8 (Fig. 222) be tho sun, M the moon on the meri- 

 dian, a c perpendicular to S M. Join M O, D E M 

 su. 



the moon's apparent declination, d = the sun's apparent 

 declination. Tho angle M P S = T = the difference be- 

 tween tho moan times of passage of the sun and moon ; 

 the ancle S M O is the angle of defective illumination = 

 90 PMS. 



sin. T 



= cos.Dtan.d sin. D cos. T 



cos. D tan. d sin. D cos. T 

 tan. SMO=cot. PMS= ^-^ gill T 



THK ZENITH TELESCOPE. Tho instrument employed 

 in measuring the difference of tho zenith distance and 

 KIT. 223. 



hour, called the zenith telescope, may bo doscril* 

 although it is scarcely the proper place for it. A A (Fig. 



