TABLE 25.-TRIGONOMETRIC FORMULAS FOR THE SOLUTION OF STADIA 

 MEASUREMENTS, OBSERVATIONS FOR TIME, LATITUDE AND AZI- 

 MUTH, AND PROBLEMS IN CONVERGENCE 



NOTATION. 



"THE EPHEMER1S." 



"Ephemeris of the Sun and Polaris, and Tables of Azimuths of Polaris," pre- 

 pared under the direction of the Commissioner of the General Land Office. 

 "T>": The symbol for approximation. 



"v." 



Observed vertical angle; in altitude observations on the sun, the reductions to the 

 sun'scenter both vertically and horizontally, as well as instrumental errors, are elimi- 

 nated by taking direct and reversed observations on the opposite limbs of the sun, 

 and the mean observed vertical angle to the sun'scenter is to be considered "it" in the 

 notation. In single observations the vertical reduction to the sun's center= 16'; a 

 refinement is had by referring to the Ephemeris for the value of the sun's semidiam- 

 eter for the date of observation. 



"ft." 



True vertical angle to the sun's center, or to Polaris, in altitude observations, after 

 correction for refraction: ft = v refraction in zenith distance; a refinement is had in 

 altitude observations on the sun by adding the value of the sun's parallax = 

 8".9 cos v, opposite in effect to refraction. 



"C." 



Zeta: True zenith distance of the sun'scenter. 



Phi: Latitude of the station of observation. 



"A." 

 Lambda: Longitude of the station of observation. 



"d." 



Delta: Declination of the sun or Polaris; to be taken from the Ephemeris for the 

 date of observation; the declination of the sun is to be corrected in hourly difference 

 to the longitude of the station and to the time of observation: north declinations are 

 treated as positive and south declinations as negative; a northerly hourly motion Is 

 treated as positive and a southerly hourly motion is treated as negative; in the use of 

 the solar attachment the declination of the sun is to becorrected for refraction in polar 

 distance, always north. 



"A." 



Azimuth angle from the true meridian to Polaris, or to the sun's center; in the 

 following analytical solutions "A" is referred to the north point unless otherwise 

 modified, and the reductions are symmetrical either east or west of the meridian; all 

 determinations for azimuth imply the recording of horizontal angles from a fixed 

 reference point to Polaris or to the sun, or a point marked on the ground to define 

 the direction of observation, the mean horizontal angle, or the mean point in direc- 

 tion, being used in the determination; in single observations on the sun, the reduc- 

 tion to the sun'scenter in azimuth -jj{j^'> a refinement in thevalueof the sun's semi- 

 diameter Is had by referring to the Ephemeris for the date of observation. 



