. , 77 



c. Directions. For finding the Sun's apparent declination. Look in the table 

 of Washington Solar Ephemeris against the date of the observation, and take out 

 the following quantities. First, the sun's apparent declination, with its sign, + 

 when N., when S., from its column. Second, the hourly change, with its sign, 

 from its column. Find from a map or otherwise, the difference in longitude 

 between the place of observation and Washington, as near as one-half hour, or 

 seven and one-half degrees. This is + when W. and when E. of Washington. 

 Add to this difference of longitude the time of the observation from noon, this time 

 being + when the sun is W. and when E. of the meridian. Multiply the hourly 

 change by this result, in hours, noting all the signs. Apply this product, regarding 

 its sign, to the sun's apparent declination as taken, from the table, for the sun's 

 apparent declination at the time of the observation. 



d. Example. Date, 1881 6 14. Haur, 9h 26m 24s, A.M. Longitude 

 about 40 minutes East of Washington, considered in time. 



Q's apparent declination. 1881 6 14. 

 Washington mean noon, + 23 18' 15" 

 Hourly motion, 1" 



Time of observation from noon, 2 hours 30 minutes, about. 



Longitude East of Washington, - 40 minutes. 



Total time of correction, 3 hours 10 minutes, =3 l /e hours. 



Amount of correction = 3*4 X 1" = 22 l /6 /f 



Q's apparent declination from table, + 23 18' 15" 



Q's apparent decimation at time of observation^ + 23 17' 53" nearly. 



12. Reducing 1 Observations. 



a. Conditions. Let h' = the sun's altitude, as observed. 



Let (j> = the latitude of the place of observation. 

 Let 6 = the sun's apparent decimation at the time of obser- 

 vation, found as above directed. 



Let z' the sun's observed zenith distance. 

 Let z = the sun's true zenith distance, always +. 

 Let k and kf be two auxiliary angles used in the reductions. 

 Let A = the azimuth of the line of sight of the instrument at the instant of the 

 observation, reckoned from the N. point of the horizon, either E. or W. as the sun 

 is E. or W. of the meridian. 



Let t = the sun's apparent hour angle at the time of the observation, that is the 

 local apparent time from apparent noon plus the change in the sun's right ascension 

 between apparent noon and the time of the observation. This is + when W. and 

 when E. of the meridian, or + for P.M , and for A.M. times. The mean or 

 watch time is sufficient for use in 2. 



Let^> == an auxiliary angle used in some of the reductions. 

 Let all signs be faithfully regarded. Let logarithms be used. 



b. Directions. For 'finding z from z' '. Use the following equations. 



z= z' + 55" tan z' (2) 



c. Directions. For finding A when 0, d and z are given. 



Find tan y z (kk') = cot % O + d) tan ^ O d) cot y z . (3) 



When <j> < d and of the same name find k = y z + ^ (k k'} . . (4) 



When ^ > d and of the same name find k' = ^ z y 2 ( k AT) . . (5) 



When <f> and d have different names find kf = ^ z % (k jf) . . (6) 



Then find A from Cos A = tan k tan q> or tan kf tan o .... (7) 



Checks. 



When (4) is used Sin * cos * 



kJIH v \^V/O /V 



Qin A Ctn A 



. . . . . (9) 



