ula, before being combined with the adjacent section. Where
the width sampled is narrower than the necessary stoping width,
and where the waste cannot be broken separately, the sample value
must be diluted to a stoping width. To dilute narrow samples to
a stoping width, a blank value over the extra width which it is
necessary to include must be averaged with the sample from the
ore on the above formula. Cases arise where, although a certain
width of waste must be broken with the ore, it subsequently can
be partially sorted out. Practically nothing but experience on
the deposit itself will determine how far this will restore the
value of the ore to the average of the payable seam. In any event,
no sorting can eliminate all such waste; and it is necessary to
calculate the value on the breaking width, and then deduct from
the gross tonnage to be broken a percentage from sorting. There
is always an allowance to be made in sorting for a loss of good
ore with the discards.

PERCENTAGE OF ERROR IN ESTIMATES FROM SAMPLING.--It must be remembered
that the whole theory of estimation by sampling is founded upon
certain assumptions as to evenness of continuity and transition
in value and volume. It is but a basis for an estimate, and an
estimate is not a statement of fact. It cannot therefore be too
forcibly repeated that an estimate is inherently but an approximation,
take what care one may in its founding. While it is possible to
refine mathematical calculation of averages to almost any nicety,
beyond certain essentials it adds nothing to accuracy and is often
misleading.

It is desirable to consider where errors are most likely to creep
in, assuming that all fundamental data are both accurately taken
and considered. Sampling of ore _in situ_ in general has a tendency
to give higher average value than the actual reduction of the ore
will show. On three West Australian gold mines, in records covering
a period of over two years, where sampling was most exhaustive as
a daily regime of the mines, the values indicated by sampling were
12% higher than the mill yield plus the contents of the residues.
On the Witwatersrand gold mines, the actual extractable value is
generally considered to be about 78 to 80% of the average shown
by sampling, while the mill extractions are on average about 90
to 92% of the head value coming to the mill. In other words, there
is a constant discrepancy of about 10 to 12% between the estimated
value as i