252 On eliminating the Signs in Star-Redtictions. 



< 1+ — sec 8 sin a +14'^ 53"" 14.s >- 



+ 32^-937 \ 1 + — tan 8 sin a +T4M8m^s \ 



- SEp= - 308^-392 + 55^-422 { 1 + sin© +42° 32' 4"} 

 + 1 -324(1+ sin 2© +55° 29'} 



(J.) 



+ 30'5(1— ^) + 21'254{l+ sin 53 +60° 30' 44"} 

 + 0-2l7{l+ sin 2 £3 +235° 52'}. 



Sum =2Art—2E^=— 387^*386 + periodical terms. 

 II. North Polar Distance, // = 2, (7' = 2, >'' = 30-5 5 — 2. 



2Pp'— 2^P= — 74"'849 + 1 2"-476 cos 8 + 41"'912 



(K.) 



{1+ sin 8 sin a + 8^1 53°^ 14^} 



+ 32"-937{l+ sin a +8^18'"49s} 



>. 



-XW 



= _?^=_S 



15 



308"-392 + &c. 



(J'.) 

 (K'.) 



Sum =SAa — 2Ee=— 383"-241+ periodical terms. 



Now if we add to (J.) and (J'.) the constant 180, and to 

 (K.) the constant 420 seconds, there will be only positive 

 quantities, and we shall have merely to subtract 10°^ or 10' 

 from the mean place ; the corrections being 



E=28'75- 18-732 cos © 



<?=2+ 7^ cos a sec 8 

 lo 



e' = 2 — •434COS 8 + sin a sin 8 



1 



y= 2 + — sin a sec 8 



F=30'5 — 20-420 sin © 



y' = 2— cosasin 8 

 l0G = 13-5 + 10^-3-43sina&c. 0-lfl:=3-35706 + 0-1337sinatan8 



0-lg'= 3-05 - 2-0055 cos a 

 1 



H = 20 — 9-250 cosQ &c. 



h-. 



; 2 + :^ cos a tan 8 

 15 



: 2 + sm « 



It follows that the index of the first set in logarithms is 

 constantly unity, and that of the third set constantly zero, 

 permitting the omission of the latter. From 86° 10' S. dec. to 

 88° 50' N. dec. e,f, g, h will have their values range between 

 1 and 10, and their indices therefore always zero; these may 

 also be omitted. Now of the 8377 British Association Ca- 



