Hagen.] ^iU [Feb. 3, 



If we now compare this correction with lluit for the inclination of the hori 

 zontal rotation axis to the true horizon we find both coincide except their 

 constants. For if b denotes the elevation of the right-hand end of this 

 axis above the true horizon, the correction ot the azimuth is 

 f — for direct image. 

 d.^ = Tbcotz|_^ „ reflected" 



as may be found in any Manual of Spherical Astronomy. Joining both 

 corrections we have 



for direct image d A = — b cot z 

 " reflect. " d A = (3;5 + b) cot z = — (b — d) cot z. 

 if we put 



d = 2 (i3 + b) (3) 



Hence the usual formula for correcting azimuth observations is to be 

 modified for observations by reflection. For direct observations this form- 

 ula is 



a = A + J .-I — b cot z — c cosec z, (4) 



where a denotes the absolute azimuth of tbe observed object, A the actual 

 reading, J A the index correction of the circle, so that A -{- d A denotes 

 the azimuth counted from the meridian point of the circle, b denotes as 

 above the elevation of the right-hand end above the true horizon and 90*^ 

 -j- c is the angle formed by the axis of collimation with this same end. 

 Hence for observations by reflection we have 



a= A -{• A A — (b — d) cot z — c cosec z (5) 



where z is not the reading of the vertical circle, but the zenith distance of 

 the observed object. As we have defined the constant b as the inclination 

 of the horizontal rotation axis to the true horizon, we, of course, cannot 

 find it in the usual way with the striding level, this instrument being itself 

 inclined to the true horizon by the unknown angle fi. Hence we shall first 

 find the constant d = 2 (^J + ^)> which may be done in two ways, first by 

 tlie striding level applied to the horizontal axis, which will give us 



/5 + b = id, 

 and secondly by observing the direct and reflected images of stars. Let 

 g be the sidereal time, when the direct image of a star passes over a cer- 

 tain azimuth and (1^ the sidereal time, when the reflected image of the same 

 star passes over the same azimuth, then we have the two equations 

 direct image a ^= A -\- J A — b cot z — c cosec z. 

 reflect. " -a^ = A -\- J A — (b - d) cot z' — c cosec z^ 

 If now the observed star did not pass very near the zenith, we may ne- 

 glect the two quantities 



b (cot z — cot z^) and c (cosec z — cosec z') 

 as snmll of the second order and find by subtraction of the above equations 



d . a^ — a 



-r = 3 -uh— X tan 7,.. 



