If you are just wanting to interpolate, you should get good results from
fitting
y = (a+b*x)/(1+c*x)
to the nearest 3 points (multiply both sides by (1+c*x) and you have 3
equations that are linear in the 3 unknowns). This rational linear form
allows some curvature from linear, while preserving monotonicity.

If you want to extrapolate beyond the upper end of your data, good luck!
The last point suggests a change in the relationship, but you have precious
little data describing what happens there. Is there a theoretical form for
this relationship?

Jerry

"andy duncan" wrote:

I think I can reach my goal but with many complicated steps - all probably
summarised in a simple function !

I have two columns of data :
Soundings, Mass :
0.000 0.000
0.772 65.750
1.335 129.640
1.897 198.700
2.460 271.350
3.022 346.640
3.585 424.020
4.147 503.130
4.710 591.880
5.272 695.640
5.835 800.290
6.397 905.730
6.960 1011.760
7.522 1118.300
8.085 1133.090


the iterations of my known column of data, (the soundings), is first 0.7 and
therafter 0.3.

I need to examine the data to increments of 0.1, and hence spread it out
over far more iterations.

Any good ways of doing this that you know of ?

Cheers Andy