64 BULLETIN OF THE UNIVERSITY OP WISCONSIN 



II.-TO CORRECT THE SUN'S DECLINATION FOR THE EFFECT 



OF REFRACTION. 



A useful application of the formulaB of the preceding 

 section occurs in connection with the use of the solar com- 

 pass. It is here required to set off upon a certain divided 

 arc the apparent declination of the sun, i. e. the true de- 

 clination corrected for the effect of refraction. This cor- 

 rection is usually interpolated from rather cumbrous tables 

 of double entry.' 



Denoting the refraction in declination by d and represent- 

 ing by q the parallactic angle of the sun, we have : 



d = Rcosq = [2.992151 ^^g , , tan z cos q (1) 



By applying the fundamental formulae of spherical trig- 

 onometry to the spherical triangle, Pole — Zenith — Sun, 

 and differentiating the equations, we find: 



— — = cos 8 cos q cosec z (2 ) 



Eliminating cos q between these equations, we obtain 



d = 12. 99215 1 -— sec S sin z tan z -r- (3) 



L J 4:5b -(- r at 



where z, A, s and t represent respectively the zenith dis- 

 tance, azimuth, declination, and hour angle of the sun. 



The numerical value of -^ varies with the position of 



dt 



the sun in the heavens, but may be readily determined at 

 any time as follows : Let the horizontal circle of the solar 

 compass or transit be set to read some integral 10' and the 

 telescope be then pointed upon the sun by rotating the in- 

 strument about the lower motion. The sun having been 

 brought into the field of view, the^ earth's diurnal motion 



1 See Johnson's Theory and Practice of Surveying, pp. 47, 48. 



