MAGNETIC OBSERVATIONS. 27 



was computed, and applying it to the sun's true bearing the true bearing of the 

 terrestrial object at once became known. 



The formulae employed were as follows. Let 



T = mean of observed chronometer times. 



dt = correction of chronometer to reduce the reading of its face to local mean 

 time. 



t = equation of time. 



t = sun's hour angle, or the apparent time. 



£l = mean of observed angular distances between the sun's limb and the ter- 

 restrial object. 



o = index correction of sextant. 



s = sun's semi-diameter. 



a = apparent zenith distance of sun's centre. 



b = zenith distance of terrestrial object. 



c = true angular distance between the sun's centre and the terrestrial object. 



C = horizontal angle included between the sun's centre and the terrestrial object. 



<£ = latitude of the place of observation. 



A = azimuth, or true bearing, of sun's centre. 



£ = true zenith distance of sun's centre. 



& — sun's declination. 



r = refraction due to apparent altitude of sun's limb. 



B = true bearing of terrestrial object. 



Then we have 



t = T + dt + t 



tan 8 



tan M — 



tan A = 



cos t 



tan t cos M 



sin ($ — M) 



tan (<£ — M) 



tan C = A — 



3 cos A 



where A is to be taken greater or less than 180°, according as t is greater or less 



than 180°. 



a = £ — r 



c = D. + a + s 



If b is exactly 90°, we have 



, , cos c 



cos 0=— — 



sin a 



But if b is either greater or less than 90°, Ave have 



. hin (S- a) sin (S-b) 



tM1 5° = 'Nl S i n S sin (S - c) 



Finally 



} B=A± C 



