440 ON CERTAIN FORMS OF INTERPOLATION. 
Formula (19) is sufficient to do the whole interpolation, using (20”) and (9"). 
But it is often better (especially when, in interpolating to sixths or twelfths, it is 
desirable not to write down the inserted values of the function themselves, till the 
whole is finished, but only their differences) to use (8”) and (21”), as follows: — 
(26) eee i : $4 = ð, 
9i — 9, = 0 + a. 
INTERPOLATION TO FOURTHS. 
(207) Ot = ddr — ee Feit do fis AË eel 
(15°) Y -—i[4—d4e4-o3.w4...] 
(9) Y = a vk 4^ - dp ...]; 
Gs) | Q4 = hlt- hst. Jl, 
Sinton of interpolating twice to halves, 9, ER 9, may be got by (19), using 
(20") and (97), and 9, and 9, by 
en ae ee 
9; — 9 = 2. 
Either the second or third member of the first equation may be used; and 82 
may be got by interpolating ð to halves, using for this purpose (11") if necessary. 
INTERPOLATION TO Firrus, 
(207) 044, = Edy — fs lt H S54, +e], 
(8") ò = d[4— ABLA ME ...], 
(9) P = hlt htt AL, 
go oo H. = hlt de d- We «Ld, 
(117) Y cux [A dE 
If, besides getting 9, — ô from (8"), we use ( 20") and e in (19) to get 9, and 
93, " will remain only 2, and 9, to be filled in. 
