6 PROCEEDINGS OP THE AMERICAN ACADEMY 



put a) = 12 and use i'+.j, which comprises only the two constants A 

 and B, and hence is very simple. 



As an example of the application of the preceding formula, let it be 

 required to interpolate the moon's Right Ascension to twelfths, that is, 

 to every second hour, having the Right Ascension and the differences 

 given for each day at noon, as follows : — 



1867. R.A. A 1 A 2 A 3 A 4 A 5 A 6 



d. h. m. s. m. s. s. s. s. 8. 6. 



Ap. 1 21 59 38.G4 +50 46.58 -f 23.84 +18.97 +6.09 —2.22 —1.62 



2 22 50 25.22 51 29.39 42.81 22.84 3.87 3.75 1.53 



3 23 41 54.61 52 35.04 65.65 22.96 0.12 5.68 1.93 



With these differences we get from (7), putting a> = 12, 

 -A+B A+B B'-C - B'+C -±C+D +±C+D 



m. s. m. s. 



-4 12.3637 +4 13.0129 +0719 +.0907 —.0043 +.0051 

 -4 14.8104 4 15.9910 .1354 .1604 .0059 .0065 



With these values (6) gives the following, in which the first column 

 contains the multiples of a few of the last places of — A + B and 

 A + B, or of their complements, when the multiples are negative, the 

 second, the multiples of B' — G and B + C, or of their complements 

 when the multiples are negative ; and so on. 



