CATALOGUE OF POLAR STAKS. 



229 



Encke has suggested a form of equation (4) which is well adapted for logarithmic 

 computation. (See Danckwortt, Vierteljahrsschrift der Astronomischen Gescllschaft, 

 XVI., 1881, p. 10.) 



Let 



m .sin 3r— sin (t, 



m cos M= cos 8 cos A, 



whence 



,,. tan 8 



tan M — J . 



cos A 



Substituting in (2) we have 



cos (5' sin A' = cos 8 sin A, 

 cos 8' cos A' = m cos (J/ + 6), 

 sin 8' ~ in sin (J/ + 0), 



whence 



tan A cos M 



Then 



tan 8' = tan (J/ + d) cos ^' j 

 a' = ^' + (a'- A'). 



(6) 



For the computation of the quantities s, z , and Q, we have the following general 

 equations (see Chauvenet, Vol. I. p. 613) : 



whence 



cos \ sin J (s' + g) = sin ^ (i/j' — ^) cos 1 (?/ + fj) 



cos ^ d* cos \ {?J + s) = cos \ (ijj' — ifi) cos h (f/ — fj) 



sin i- d sin i (s' — z) = cos A^ (i/;' — i<A sin i Cf.' — f.') 



sin' J 9 cos ^ (z' — z) — ' ' ' ' 



- t|;) sin ^ (f/ - f,) 

 5 (•/'' - V) sin i («/ + ^i) 



(7) 



tan ^ (s' + £•) = tan i (ip' — rf.') cos A (f/ + f,) 



i .,-_ .^ ^ iW_ZJ^ 



^ ^ ■■'' ~ tan i (V;' - ip) sin J («/ + c,) 



sin J 9 = sin ^ (xp' — xp) sin J (e^' + ?,) 



(8) 



In which the constants of Struve and Peters for the epoch 1800 are to be employed. 

 They are as follows : 



6„ = 23 27 54.22 



e, =i, + 0.00000735 i^ 



0.4738 t - 0.0000014 1- 



0.15119 < - 0.00024186 «' 



V; — 50.3708 t - 0.0001084 t^ 



