64 BULLETIN OF THE UNIVERSITY OF WISCONSIN 



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

 OF REFRACTION. 



A useful application of the formulae 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 sum, 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. 1 



Denoting the refraction in declination by d and represent- 

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



_ _ r> -jp 



d = JR cos q = 2.99215 -r^- tan z cos q 

 L J 4oo -{- r 



(I) 



By applying the fundamental formulae of spherical trig- 

 onometry to the spherical triangle, Pole Zenith Sun, 

 and differentiating the equations, we find : 



dA 



= cos o cos q cosec z (2) 



Eliminating cos q between these equations, we obtain 



d = [2.992151 ,.f F sec d sin z tan z ^ (3) 



L J 4oo -\- r at 



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

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



dA 

 The numerical value of ~^- varies with the position of 



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 than 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 



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



