150 PRACTICAL ASTRONOMY 



at eastern or western elongation. The line of sight will then 

 be directed along the true meridian, and by marking another 

 point 400 or 500 ft. from that occupied by the instrument, 

 the direction of the true meridian will be established. 



This is the most accurate method of determining the true 

 meridian, and, where possible, should be used in preference 

 to others. 



DETERMINATION BY SOLAR OBSERVATION 



One of the most convenient methods of determining the 

 meridian is to measure the altitude of the sun at any hour angle 

 with a transit. At the same time that the altitude is meas- 

 ured, determine also the horizontal angle between the sun and 

 a fixed object, or reference mark. Then, the azimuth of the 

 sun is calculated by the formula that follows. The azimuth 

 of the reference mark is then equal to the algebraic sum of the 

 azimuth of the sun and the measured angle between the sun 

 and the mark. Finally, the true north-and-south line may 

 be located from the azimuth of the reference mark. 



Formula for Azimuth of the Sun. Let a represent the 

 required azimuth counted from north toward east; 3, the zenith 

 distance of the sun, which is equal to 90 minus the altitude; 

 &, declination of the sun; and <f> , the latitude of the observer. 

 Then. 



,a 



sin = 

 2 



a . a 



Two values of will correspond to the computed sin -; one 



angle will be acute and the other obtuse. The acute angle 

 should be used for morning observations and the obtuse for 

 afternoon observations. 



Values of 5 and </>. The method just described requires 

 that the declination of the sun at the time of observation, and 

 the latitude of the place be known. The declination of the sun 

 for every day of the year at the instant of Washington noon, 

 together with the hourly change, is given in the Ephemeris, 

 and has to be reduced to the time of observation as follows: 



Rule. Change the local time to Washington lime by adding 

 algebraically to the former the longitude of the place counted from 



