utes, and observing simultaneously the sun's upper and east limbs; the settings for 

 the approximate altitudes of the sun's lower and upj>er limli.s, n-.sj^-tivcly, are: 



Altitude observation of Polaris at upper culmination for latitude. 



Altitude observation of Polaris at lower culmination for latitude. The mean timehour 

 angle of Polaris at lower culmination is 11 hours 5H minutes 2 seconds: 



The settings for the approximate altitude of Polaris at upper and lower culmina- 

 tions, respectively, are: 



AZIMUTH. 



Altitude observation of the sun for azimuth. Reverse the signs of "d" for south 

 declinations: . 



Tan H A~y cos ^ (C _^_j) s i n ^ (C _ 



The spherical angles "C," "tf," and "J" appear in this equation combined as in 

 the formula for the reduction of an altitude observation of the sun for apparent time, 

 and when it is desired to reduce for both time and azimuth, the above equation for 

 azimuth is to be preferred to any that follow. 



Altitude observation of the sun for azimuth. For south declinations the function 

 "sin i" becomes negative by virtue of the sine of a negative angle being treated as 

 negative in analytical reductions: If the algebraic sign of the result is positive the 

 azimuth "A" is referred to the north point, but if negative, the azimuth "A" is 

 referred to the south point: 



The above equat'on is very convenient in reducing for azimuth only. 



Altitude observationofthesunfor azimuth. To many surveyors the following equa- 

 tion is familiarly expressed directly in terms of the spherical triangle" pole-zenith- 

 sun": reverse the sign of "i" for south declinations: 



Tole to zenith-90-^-colat.; 

 Pole to sun 90 * coded.; 

 Zenith to sun -90'-*- < 

 8- H sum of the three sides: 



II S vein (S ro.lerl.) 



/sin 8 sin (8 -codec 

 Ji A-'Y sin ootet. sin omit 



Equal altitude observations of the tun for meridian. The sun's center at equal alti- 

 tudes occupies symmetrical positions In azimuth cast ami west of the meridian in the 

 morning and in the afternoon except for the . ossary to be applied due 



to the change in the sun'9 declination In the Interval between the a. m. and p.m. 

 observations: 



"d \ 3 ": Correction in azimuth in minutes of angular measure to be applied to the 

 mean position in azimuth to obtain the tme south point; the correction is to be 

 applied to the east with a northerly hourly change in declination, or to the west with 

 a southerly hourly change. 



"d d": Change in declination of the sun from the a. m. to the p. m. observation, 

 expressed in minutes of angular measure. 



