236 



REPORT 1866. 



Lihrations of Centre. 



Having found the apparent right ascension and declination of the moon, also 

 the apparent N.P.D. of the centre, and the angle A, we proceed to compute 

 the following quantities : — 



1' = the selenographical longitude of the apparent centre = libra tion in longi- 

 tude*. 

 b'=the selenographical latitude of the apparent centre = a — 90°= libra- 



tion in latitudef. 

 C = the angle which the meridian of the middle of the moon's disk makes 

 with the declination circle. See section 4 et seq., and figs, 3 and 11. 

 For the formulae see section 11. 



Angle C and b'. 





11 27 47 

 33 44 31 



68 42 48-5 



log cos |A 

 logsin|(2?'— i) 



sum (1) 



sum (2) 



9-55996 

 9-57877 



9-13873 

 9-82034 



difr.=logtan|(B-C) 9-31839 



log cos |A 9-55996 



logcos|(y— i) 9-96630 



sum (3) 9-52626 



sum (4) 9-81723 



diff.=logtan|(B + C) 9-70903 



sum (2) 

 log cos |(B— C) 

 1, 



diff.=logsin^a 



9-82034 

 9-99079 



9-82955 



O / // 



22 16 44 

 45 12 18 



log sin |A 

 logsinKp'+i) 9-85103 



sum (2) 9-82034 



9-96931 



log sin |A 

 log cos g(p' + i) 



sum (4) 



KB-C) 

 KB + C) 



B 



c 



9-96931 



9-84792 



9-81723 



11 45 31 



27 5 59 



38 51 30 

 -15 20 28 



42 29 5 



84 58 10 



- 5 1 50 



For the selenographical longitude of the moon's apparent centre, we have 

 r^L — L', where L= the selenocentric longitude of the moon's appai-ent cen- 

 tre, and L' = 1 -1- supplement of a . See Section 22. Now 



L=270°— E-A, Sup. £3 = 



o 



67 



8 20 



A + B 



L=270°-B-A 

 L'=l+ sup. S 



L-L'=r 



270 

 148 29 3(5 



A 



B 



109 38 6 

 38 51 30 



L' 



124 43 21 



* + wlien W. of the first meridian, 

 t + wlien N. of equator, — wlien S. 



when E. 



