CATALOGUE OF POLAR STAKS. 



220 



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

 computation. (See Danckwortt, Vierteljahreschrift der Astronomischen C jchaft, 

 XVI., 1881, p. 10.) 



Let 



whence 



m sin M— sin 8, 



m cos M = cos 8 cos A, 



tan M 



Substituting in (2) we have 



tan 8 



cos .. 1 ' 



cos 8' sin A' = cos 8 -in A. 



cos 5' cos A' 



sin 5' 



whe 



m cos (31 + 0), 



»» sin (J/+ 0), 



nee 



tan A' 

 tan 5' 



tan yl cos M 



cos ( J/ + 0) 



tan (J/ + 0) cos A' 



Then 



a 



; 



-4' + {z! 



V). 



(6) 



For the computation of the quantities z, z\ and 0, we have the folio 

 quations (see Chauvenet, Vol. L p. 613): 



whence 



cos \ sin i (z 1 + z) 



sin 



HV 



U') cos J (*/ + * x ) ] 



COS £ COS I (2' + Z) = COS £ (t// — 1/;) COS £ (>/ 



sin 



£ 5 sili 



1 

 2 



v 



sin' J 5 cos £ (^ 



1 



2 





COS 



sin 



2 



(v 



' 



'1) 



HV 



V) sin J («/ - 

 V) sin £ ( f i' + f i) 



tan I (2' + z) = tan J (ii/ — ti-) cos £ (*/ + e^ 



i(*' 



*) 



K'.' 



O 



tan £ (1// — xp) sin £ (c/ + e x ) 



sin £ 5 = sin £ (V — i/>) sin i (*/ + f 2 ) 



(") 



(8) 



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

 They are as follows : 







e 



f 



X 



O / // 



23 27 54.22 



* ft + 0.00000735 i 



tr 



// 



e - 0.4738 t - 0.0000014 1 2 

 0.15119 t - 0.00024186 t 2 



V 



// 



// 



50.3798 t 



0.0001084 t 



