8 PROCEEDINGS OF THE AMERICAN ACADEMY 



-A+B A+B B'-C B+C 



m. B. m. s. s. e. 



—6 18.3465 6 19.8119 0.1522 0.2156 



—6 21.8330 6 24.4922 0.2910 0.3748 



"With these values (6) gives 



R.A. 



{ 



h. m. B. m. 8. B. 



.614 .000 #_4 21 34 25.25 12 36.09 

 .307 .391 F_. 21 47 1.34 12 37.30 1.21 

 .623 .138 Fo 21 59 38.64 12 38.76 1.46 

 .248 .000) F2 22 12 17.40 12 40.49 1.73 

 .668 .000 1 F, 22 24 57.89 12 42.50 2.01 

 .334 .836 F_2 22 37 40.39 12 44.83 2.33 

 .984 .501 Fo 22 50 25.22 12 47.48 2.65 

 .969 .000 F2 23 3 12.70 12 50.49 3.01 

 Ft 23 16 3.19 



The following very convenient method of interpolation was published 

 several years ago in an imperfect form in the Mathematical Monthly. 

 The expressions for the constants have been here obtained in a quite 

 different manner, and are given in a different function of the differ- 

 ences, which are more exact, and the whole matter is given in an 

 improved form. 



If we put in (1) 



(8.) F^ = Fo-\-B,x-j-B,x'-\- Bs x\ 



and determine Bi, B2, and Bg, so as to make the expression coincide 

 with (1) when x = ^, a: = |, and a; == 1, we obtain very nearly, re- 

 instating A^ — ^ A^ for A/, A^ — ^ A^ for A/, &c., 



^3=6^3^A^-AA^ \ 



The greatest possible error, E, in using (8) with these constants 

 instead of (1), is only 



(9.) E=± (t^W A^ + ttVtt ^' + ttVcf A« ) 



