VIII 



INTERPOLATION TABLES. 



EXAMPLES OF INTERPOLATION. 



1. Given the value of Si for D = 0, 1, 2, 3 . . . . as stated below, to obtain 

 from them the value of 2 t for D = 1.107, 2.107, 3.107, .... 



(From computation of Ephemeris of the Moon for 1923 from the new Tables of the Moon published by the Yale 

 University Press.) 



Here 



n = + .107, -2= 87. Since |A" < -, we use Case 2 where v = A' . 



Tfr /t 



2. Given the values of A(u) for u = 560, 565, 570, to derive by interpolation 

 the value of A(u) for u = 562.7. (From Handbook of Problems in Direct Fire, by 

 Col. James M. Ingalls, example 4, page 13). 

 The form of computation is as follows : 



In the above computation, 



h = u - U A = 565 - 560 = 5, 



u - w n 562.7 - 565 - 2.3 



n = 



h 



Aii/2 + A; 



1/2 



5 5 



- 104.3 - 99.8 



= - 0.46, 

 - 204.1 



- 5, 



A" 

 n^ = 



- o.46 



- - 0.46 X + 2.2 = - - 1.0, 



v = A'o + n - : - 102.0 - 1.0 = - - 103.0, 



no = - 0.46 X - - 103.0 = + 47.4, 



4(562.7) = 4(565) + nv = 2620.0 + 47.4 = 2667.4, 



using Case 3, since the numerical value of Ajj, in units of the last place, is greater 

 than 1/n 2 ; i.e. 45 > 5. 



