##### Abstract

When fitting a curve to. a given set of data , it is
usual , having chosen the curve-type which will best
suit the data, to take as abscissae for the plotted
points of the curve the observations themselves ,..
and then 'smooth' the frequencies or weights of
these observations.to the correct ordinates , as if
considering these frequencies to be subject to 'error'
but the points at which the observations were made
to be exact .

In the present method , however , we intend to make
use of the inverse process. That is , we work as if
considering the frequencies to be exact , but the
observations to be in error . Thus we make no
alteration in the frequencies as they are presented.
to us, but combine two processes for 'smoothing'
the observations as follows ,

(i) We take , as our abscissae , not the given.
observations , but a certain set of points calculated
from the frequencies and the chosen curve -type
which have been called 'Ekke's Best Values',. after
some work done by A.Ekke in connection with them in.
a Kiel dissertation, 1934.
(ii) We now further smooth these abscissae to as
close an approximation to the given observations as
is required)by combining the given observations in
a set of polynomials with coefficients to be
determined , (a process suggested by R.Schmidt in an.
article appearing in the Annals of Mathematical
Statistics , Vol.v , P.30 ).