proceedings

126
these solutions. It turns out that if you try to make a rough
check on results by identical relation between the integrals,
the check is not nearly accurate enough unless you have
added in these extra terms to the sums. I had hoped that
I would not have to do this for the originally assumed
values of y, but it turns out that to get a good check one
must.
vVell, then, these solutions were made originally for
n = 0, for a wide set of values of y. Gamma equals 1, 2,
3, 4, 5, 6-1 think that is as far as it went. For each of
these we computed the corresponding value of Z. Actually,
that was computed as we went along, and we found that
this covered the whole of the periodic table. We then took
the part which included the whole of the periodic table and
took even intervals among these values of y = 2.1, 2.2,
and so on, up to 5.9. And with the integrations of the differential
equations at this distance apart in y, we found
the values of Z. That gave a table in which inverse interpolations
gave us new values of y which would lead to
assigned values of Z accurate to five decimals. So that
as it turns out, without too much work, it was possible
to get for any values of nand Z-and we have done this
SCIENTIFIC COMPUTATION
also for n = 1 and 2-by an inverse interpolation, the
corresponding value of y, to put that in as a starting value,
and to compute the whole field for that particular case.
To compute the field by integration, once the sequence
is set up, is a good deal easier than to get the whole field
at each point by interpolation among the solutions that
have been made, although that would be perfectly possible.
I think actually we shall probably tabulate and publish just
certain selected solutions. However, we hope to be able to
do enough so that anyone could interpolate to find any
solution that they might want.
It should again be realized that the statistical fields only
give a rather rough order of approximation to the properties
of the atomic ion. You really want to use these as a
starting field to start after the real approximations in any
particular case in which you are interested. I think it is
clear that it would be too much work to work out complete
sets of Hartree approximations for every possible atom.
I f you have once got a statistical field., that is a good start
toward obtaining the Hartree field. You could probably get
the Hartree field with at most two successive approximations
of the Hartree type. '