16 Jjl l T PRACTICAL ASTRONOMY. n (n 1 (42) In this formula, J^ n is the value of the function to be deter- mined ; F, the ephemeris value from which we set out ; d 1 , d^ , d 3 , etc., are the terms of the successive orders of differences, deter- mined as explained below; n is the fractional value of the time interval, in terms of the constant interval taken as unity corre- sponding to which the values of the function F are computed and recorded in the tables. To use this formula, draw a horizontal line below the value of F from which we set out, and one above the next consecutive value taken from the ephemeris. These lines are to enclose the values of the odd differences d l ,d a ,d si , etc. The values of the even differences d y , d^ , d 6 , etc., being each the mean of two numbers, one above and one below in their respective col- umns, are then inserted in their proper places. The following ex- ample is given to illustrate the application of Bessel's formula. Find the distance of the moon's center from Eegulus at 9 P.M. West Point mean time March 24th, 1891. The longitude of West Point is 4.93 hrs. west of Greenwich; hence the Greenwich time corresponding to 9 P.M. West Point mean time is 13.93 hrs. Referring to pages 54 and 55 American Ephemeris we take out the following data, namely : A March 24. F $ <*, d z
6 h 27 01' 24" 1 28' 9" 9 h 28 29' 33" + 11" 1 28' 20" + 1" 12 h 29 57' 53" + 12" -2" 13' .93 30 54' 47".31 1 28' 32<' (+11".5) -1". -1" 15 h 31 26' 25" + 11"
1 28' 43" -1" 18 h 32 55' 8" + W! 1 28' 53" 21 h 34 24' 1"
)JL
