This paper presents two techniques for the comparison of Adams formulas and methods based on natural splines. A rigorous foundation to the claim that a pth order natural spline formula produces better results than a pth order Adams method, but not quite as good as a
(
p
+
1
)
(p + 1)
st order Adams formula is given for
p
=
2
,
3
,
4
p = 2,3,4
, which suggests the general case.