EXAMPLES OF INTERPOLATION. 



IX 



3. Given the latitude of the Moon for every half day to find, by interpolation, 

 the latitude for 1919 August 25 d 3 h 37 m l, the date of New Moon. 



Taking the latitude of the moon from the American Ephemeris and differencing 

 it we have: 



whence 



a - 



n = 



3 h 62 



h 



= + 0.302, Jj = 109, ^ = 131. 



3 12 



Therefore |A 1U < - and |A 1V < -5; so we use Case 4 where 



Aiii Aii 



AO t\o 



v = AQ -^- + n ~n~ 



The compution is then as follows : 



r- 116.8 + 128.3 _, 7.2 

 n v = .302 - + -^- + . 



^ o 



= .302 [ + 5.8 + 1.2 + .302 (122.6)] 



= .302 ( + 44.0) 



= + 13T3 



Latitude Aug. 25.0 5 0' 28.3 



Latitude Aug. 25 d 3 h 37 m l 5 0' 15?0 



This problem may also be treated by Case 7, although n is slightly outside 

 the desirable limits. From the above data we derive 



v = 2n - - 1 = - 0.396 



/(a ) = Latitude Aug. 25 d O 5 00' 28! 3 



Aj/2 + 128.3 

 2 2 



3A\ V , 2 - 240.6 -0.6 



_ 



8 128 



8 



64.15 

 30.15 



a 4- = Latitude Aug. 25 d 25 = - 4 59' 54T3 



vy = - .396[64.2 - .396(30.1)] 20.7 



Latitude Aug. 25 d 3 h 37 m l 



= - 5 00' 15.0 



HENRY B. HEDRICK. 



YALE UNIVERSITY, 



March, 1918. 



