ON OCCULTATION, ETC. 59 



"We have thus a coustructiou foi- liudiug the moon's displaeemeut. 

 The application of this coustructiou, and the final détermination of the occultation 

 will be best understood from an explanatory example. 



For the occultation of the star 54 Arietis, as seen at Greenwich on Oct. 9th, 1881, we 

 have the following elements : — 



3)'s horizontal parallax - - - - - - -- ;r= 57"6 



2)'s semi-diameter s = 15"7 



3's hourly motion in E. A. if = 350 



3'8 " " " dec - - /t =^ e-t N 



3's declination at mean conjunction â ^ 19°-2 N 



Mean time of corijunction T := 12''-75 



2) north of 7)6 at conjunction .-.--.- d ^ 48-8 



Project for the hours f = IT' 12" 13" 



Corresponding sid. time = 0" 14'" 46" 1" 14'" 56' 2" 16"» 6' 



3's E. A « = 2 57 38 2 59 57 3 2 17 



Corresponding hour angle, a, in time 2 42 52 1 45 1 47 11 



in arc 40°-7 26°-3 ll°-8 



The latitude of Grreenwich is ip = 51°'5 N. 



Construct the figure already described having the angle POG = 51°'5 and 

 OP = 5t-6. Take the angles PQA, PQB, PQC = 40°-*7, 26°-3 and ll°-8 respectivelJ^ 



In this figure QP represents the meridian of the place and A, B, C, the positions 

 of the moon at the hours XI, XII aud XIII respectively ; and since the moon is approach- 

 iug the meridian, it is east of the meridian at the hour named. Hence the horizontal 

 displacement of the moon is eastward, or from right to left in the plot. 



Draw OH to make the angle GOH ô = 19'^'2 ; aud as the declination is north 

 OH lies above OG. For south declination OH will lie below OG. 



Take OH = H=^ 350 and draw HGh perpendicular to OG, and make Gh = /t = 6"'7. 

 When the moon is moviug northwards Gh is to be taken downwards, and upwards 

 when the moon is moving southwards. 

 Draw Oh and produce both ways. 



OH is the moon's hourly motion in E. A. ; OG its hourly motion along its circle 

 of declination ; and Oh its hourly motion in its path as seen from the earth's centre. 

 If O denotes the time of mean conjunction, we take Off equal to three- fourths, (T — 12), 

 Oh, aud make KJ and /t'L.each equal to Oh. J, K, L are the positions of the moon's 

 centre at the hours XI, XII, aud XIII as seen from the earth's centre. 



At these hours set off the displacements, parallel to OQ, viz. : — JJ = ad , Kk = W, 

 LI = cc' ; and at j, k, I set off the displacements perpendicular to OQ, viz. : /XI =Aa, 

 A-XII = Bb and Z XIII = Cc. 



XI, XII, and XIII are the apparent positions of the moon's centre at these hours res- 

 pectively. 



Lastly, take OS ^ d ^ éS'8. S is the apparent position of the star. 

 With S as centre aud a radius = s = 15"7 describe an arc cutting the line drawn 

 through XI, XII, and XIII, in D and R. D is the time of disappearance of the star, or the 

 beginning of the occultation, and R is the time of reappearance, or the end of the 

 occultation. These are in the present example about 11'' 52'" for the begiuuing aud 

 12" 30'" for the end. 



