"(ti+h)": The sum of tho hour angles from ap]nirent noon, or the total watdi time 

 from the a. m. to I he p. in. ob.serval ion, ex pressed in angular measure. 



The symmetry of the equal altitude observation is preserved by observing opposite 

 limbs in azimuth in the a. in. and p. m. observations, in connection with the same limb 

 in vertical angle in both observations. 



With "M d d" and " '.1 (/i-Hz)" calculated, the computation can be concluded by 

 applying to "^ dS" the declination coefficient obtained by entering the table of 

 coefficient^ for computing errors in azimuth due to small errors in declination, argu- 

 ments: "4>" and "J-$(i+fc)." 



Azimuth of Polaris at elongation. 



A table of azimuths of Polaris at elongation, for latitudes from 25 to 70 N., appears 

 in the Ephemcris, arguments: " 3" and "<." 



Azimuth of Polaris at any hour angle. ""=sidereal hour angle in angular measure; 

 in hour angles exceeding 90 the function "sin <j> cos t" becomes positive by virtue 

 of the cosine of an angle between 90 and 270 being treated as negative in analyti- 

 cal reductions: 



___ _ sin / 



cos tan d sln^ cos t 



A table of azimuths of Polaris at all hour angles, for latitudes from 30 to 50 N., 

 appears in the Ephemeris, arguments: "8," mean time hour angle, and "<f>." 



For other than the above latitudes the surveyor will be required to perform the 

 above analytical solution, accomplished by the following process: convert the usual 

 mean time hour angle into sidereal hour angle, and convert the sidereal hour angle 

 into angular measure to obtain l -t" for the above equation. 



Polaris at sunset or sunrise. Polaris is conveniently observed for azimuth by the 

 hour angle method at sunset or sunrise without artificial illumination; the prepara- 

 tion for the observation consists in computing in advance the approximate settings in 

 azimuth and altitude in order to find Polaris, and the plan contemplates an approxi- 

 mate reference meridian: with the time of sunset or sunrise assumed as the time of 

 observation, the hour angle "t" and azimuth "A" are determined in order to find the 

 position of Polaris in azimuth; the position in altitude is found by the following 

 approximation, the positive sign being used for hour angles less than G hours, and the 

 negative sign for hour angles exceeding 6 hours: 



CONVERGENCY OF MERIDIANS. 



": Measurement along the parallel. 



/': Measurement along the meridian. 



: Equatorial radius of the earth= 3063.3 miles=80X39C3.3 chains. 



: Factor of eccentricity, log c- 8.915 2515. 



^ ": Linear amount of the convergency on the parallel, of two meridians dis- 

 tance apart "m^," and distance "m^" along the meridian: "d7W^,""7n > i,""77i^"and 

 "a" to be expressed in the same unit: 



dm^ - -~~ tan Vl-**sin*tf 



O 



224 



