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



jz = b's\nz + a'cosz + b"s\n2z + a"cos2z ... * 



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

 practice no attempt is usually made to take account of the 

 terms in sin2z and cos2z and the expression reduces to 



Az = 6'sins + 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 

 he the plane of the meridian, 

 S the south collimator and 

 iVthe north collimator. The 

 collimators being leveled and 

 their lines of collimation 

 made parallel, the line SN 

 is horizontal. 



Let R" be the reading on the north collimator, R that on 

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

 SOR' = NOR" = b' and R'"OZ' = a'. We then have 



R' — R' = 9(T — b' — a' and R"' — R" = 90° — b' + a' 



whence, 



h' - 90° R — R ' i - t>., R + R " 

 — yu — _ ana a =R" — s u * 



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



* See Sawitsch, Abriss 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"s\n2z. See Equations (16) and (37). 



