ON THE FORMULAE FOR CALCULATING 



c, the complement of the Latitude of th« place of observation, ov c zz — X; 



b, the polar distance of the star ; B the angle of Azimuth, and a the Zenith 

 distance : consequently, if f denote the seconds of sidereal time, the above 

 equations are transformed to 



1st. cos — tan >^ 's Pol. dist X tan X 



2nd. sin * 's Azimuth — sin >^ 's Pol. dist X seel. 

 3rd. sin * s Altitude = sec * 's Pol. dist X sin x 



If t' be required in mean solar time, it must be diminished in the ratio 



H. M. S. 



of twenty-four hours to 23 56 4, or if denote the seconds in mean solar 



time, then we have Log. — Log. t' -f- Const. 1*9988127. 



The corrections are also easily obtained from tables constructed on 

 purpose. 



To take an example of this ; let the time of the greatest Western 

 Azimuth of the Pole-star be required on the 4th May, 18.30, in Latitude 

 24° 0' 0^ as also the Azimuth and Altitude at that instant; the Longitude 

 being 78° East of Greenwich, and the Polar distance 1° 36' 0"". 



Hour Angle, Azimuth. Altitude. 



Pol. dist 1° 36' 0'^ tan 8,4461103 sin 8.4459409 sec 0.0001694 



Lat. ....24° 0' 0''' fa?i 9,6485831 5ec 0.0392698 9.6093133 



Space 89° 17' 14.'''8 cos 8.0946934 sin 8.4852107 sin 9.6094827 





1° 45' 5.'''37 



24° 0' 35.^83. 



4 







5 57 8.98 Siderial time. Refraction + 2 9.83. 



22 16 3.19 A.R (* — ©) at noon. 



Appt. Altde 24 2 45.66. 



16 18 54.21 Sid. time 

 — 2 40.37 Corr". 



16 16 13.84 Mean Solar Time. 



