COMSTOCK — STUDIES IX ASTRONOMY 



69 



azimuth circle of the theodolite and the readings of the 

 level bubble upon its scale, let the accompanying figure 



represent a portion of the celestial sphere adjacent to the 

 zenith, Z, and let V and S be the points in which the axis 

 of the theodolite, and the line drawn from the center of 

 curvature of the level tube through the middle of the bubble, 

 respectively, intersect the sphere. The arc SV is the in- 

 tersection with the celestial sphere of a plane passing 

 through S, V, and the center of curvature of the level 

 tube, and if the adjustment of the level above referred to 

 is approximately made, VS may be considered as the inter- 

 section with the sphere of the plane in which the curva- 

 ture of the level tube lies, so that as the bubble moves in 

 its tube its successive positions, when projected upon the 

 sphere will lie along VS, and any position may be indenti- 

 fied by its distance from V. represented in the figure by p. 

 Since the bubble always stands at the highest part of the 

 tube, its position, S, and the corresponding value of 2^ are 

 found by letting fall a perpendicular from the zenith upon 

 the arc VS, and in the right angled spherical triangle thus 

 formed we have the relation, 



tan p = tan y cos t 



where r. as it appears from the figure, is the angle by 



