48 



If it is required to make the computation within 1" then, 

 for observations more than 18 minutes from elongation, the 

 value of A^ — A given by formula (7) should be corrected by 

 being decreased by the amount 



cos2 ]} 2 sin^ i (^'o-^O 



sin 2 .4, ^—^ (8) 



sin- h sin 1" 



2 sin^ ^ (h^-h) 



As the expression has to be evaluated in 



sin 1" 



the reduction of circum-meridian observations for latitude, 

 tables of the values of the expression and its logarithm have 

 been prepared, and are available in Chauvenet's Astronomy, 

 Close's Trigonometrical Surveying, and other works. Similar 



2 sin* h (h^-h) 



tables for are also available. The computa- 



sin 1" 



tion by any one of these formulae is much facilitated by the 

 use of these tables. Five-figure logs, are sufficient. 



2 sinn (/?„-//) 



Writing tan Aq cos^ P = ^, m = , 



sin 1" 

 (6) becomes 



Aq — A=B m, where ^ is a constant. 



Thus for each observation we get Af^ = A+B m, and, 

 averaging the whole series, 



mean value of Aq = mean value of .1 + ^ x mean value of m. 



Therefore, mean angle between R.M. and star at elongation = 

 mean observed angle between R.M. and star ±B x mean value 

 of m. 



Example. 

 In the following example the method is applied to the 

 reduction of a series of observations taken by Mr. Calder, 

 surveyor, upon Canopus near elongation: — 



Star observed — Canopus. 

 Place — Rendelsham . 

 Ric/ht Ascension — 6h. 22m. 06s. 

 Latitude— ^r 32' 40" S. 

 Declination— b2° 38' 43" S. 

 Longitude— 9h. 20m. 40s. E. 

 Z^a*^'— December 9, 1914. 

 Standard Meridian — 9h. 30m. E. 



