ASTRONOMY- 



Ixxiii 



is the solar day, beginning at noon, and divided to hours numbered continuously 

 from o* to 24''. This is called astronomical time ; and such a day is called the 

 astronomical day. It begins, therefore, 12 hours later than the civil day. 



b. Relation of apparent and mean time. 



A = apparent time = hour angle of real sun, 

 J/= mean time = hour angle of mean sun, 

 E = equation of time. 



In the use of this relation, E may be most conveniently derived (by interpola- 

 tion for the place of observation) from an ephemeris. 



c. Relation of sidereal and mean solar intervals of time. 



/=: interval of mean solar time, 

 /' = corresponding interval in sidereal time, 

 r = the ratio of the tropical year expressed in sidereal days to the tropical 

 year expressed in mean solar days 



^ 366.2422 ^^^^^^^^3^ 

 365.2422 



/' = r/= /+ (r - i) /= /+ 0.002738 7 

 /= r-' 7' = 7' — (i — r-') /' = /' — 0.002730 7'. 



Tables for making such calculations are usually given in ephemerides (see, for 

 example, the American Ephemeris). Short tables for this purpose are Tables 

 34 and 35 of this volume. 



Frequent reference is made to the relations 



24'' sidereal time = 23'' 56'" o4.'o9i solar time, 

 24^ mean time = 24'' 03'" 56.'555 sidereal time. 



d. Interconversion of sidereal and mean solar time. 



Tn = mean time at any place, 

 Ts = corresponding sidereal time, 



= right ascension of meridian of the place, 

 , A = right ascension of mean sun for place and date, 

 = sidereal time of mean noon for place and date. 



T,= A -{- T„ expressed in sidereal time. 



T^=z (T, — A) expressed in mean time. 



The quantity^ is given in the ephemerides for particular meridians, and can 

 be found by interpolation for any meridian whose longitude with respect to the 

 meridian of the ephemeris is known. The formulas assume that A is taken out 

 of the ephemeris for the next preceding mean noon. 



