238 



d' 8 3 n* 



CATALOGUE OF POLAR STARS. 



C n^ m 



18n»m 



tan' 



[sin* « — 4 sin- u cos- «] + p^ tan- 5 sin « -f — z;^ — tan- S sin « cos- a 



7 «2 wi- 3 71- m^ n* „ . , » . 



+ — ;;7- tan fi sin= « — — .^ tan d + ^^ tan o (sin* « — 8 snr a cos^ «) 



~n m (m^ -I- »i°) 



6 «' »« 



li' 



(23) 



;^i sin u - -^ sni « cos- «J 



«&c., &c., &c. 



For the computation of the numerical coefficients, we have the following con- 

 stants for 1875.0. (See Pub. XIV., p. 51.) 



For the reduction in Rit^ht Ascension, 



logi2 = 4.1383338 

 logif^= 8.276C676 

 Xoc'E'^ 12.4150014 



For the retUiction in Declination, 



m =: 46.08307 

 logwi = 1.6635471 

 lo<j)/r= 3.3270942 



n = 20.05423 

 logM = 1.3022060 

 log«== 2.6044120 

 logn'= 3.9066180 

 lo!iM*= 5.2088240 



m'= +0.0002849 

 log m' = 6.4540924 



n'= -0.0000863 

 loir n' = 5.9300108« 



log 7? = 5.3144251 

 log^-= 10.0288502 

 los Ji^= 15.9432753 



Substituting in the preceding equations, we have : 



da 



dt 



= + 3.072245 + [0.1261147] tan 5 sin a. 



(24) 



^' = + 0.00001899 + [6.1138956] tan^ 8 sin 2 « + [6.4752367] tan 5 cos a + [5.8128656] sin 2 a 



+ [4.7599145«] tan if sin a. 



(25) 



~dt- 



= + 0.0000000145 + [2.4027065] tan' 5 sin 3 « + [2.9401389] tan= d cos 2 « + [2.2777078] tan 8 sin 3 a 

 + [2.7811577;/] tan 8 sin a + [2.6391089] cos 2u + [0.8598285n] tan 8 cos a (26) 

 + [1.2248167?)] tan-2 5 sin 2 a + [0.9237867] sin 2 «. 



