z 



246 Trans. Acad. Sci. of St. Louis. 



Az = h'^\\iz + a'GOQZ + h"%\x\'2z + a"cos22! ... * 



in which 6', 6", a', a" are constants independent of z. In 

 practice no attempt is usually made to take account of the 

 terms in sin22j and cos22! and the expression reduces to 



Az = b'siuz + a'cosz, 



in which b' is the constant of sine flexure and a' the constant of 

 cosine flexure, so called. f Or b' is the flexure at the horizon 

 and a' that at the nadir and zenith. Now if we assume that 

 the horizontal flexures, object-glass north and object-glass 



south, are the same, the con- 

 stants b' and a' may be de- 

 termined from observations 

 of the nadir and of leveled 

 collimators. 



In Figure 3 let ZSZ'N 



be the plane of the meridian, 



S the south collimator and 



iV the north collimator. The 



collimators beingr leveled and 



their lines of coUimation 



-^ -^ made parallel, the line 8N 



^^^' ^' is horizontal. 



Let B" be the reading on the north collimator, It' that on 



the south collimator, and R" the reading on the nadir. Let 



8 OB' =■- NOB" = b' and B"'OZ' = a'. We then have 



R _ R" = 90° — b' — a' and R" — B" = 90° — b' + a' 



whence, 



A' _ QAO R — B" , R + R" 



— \j\j — _ ana a =R" — x 



If the horizontal flexures, object-glass north and object- 



s 



-*a' 



* See Sawitsch, AhrUs der Praktischen Astronomie, p. 209. 

 t We shall show later on that there is in theory a reason for the existence 

 of the term b"Bin2z. See Equations (16) and (37). 



