the previous yield recourse must be had to actual
treatment runs on every block of ore separately.

After reduction of erratic assays, a preliminary study of the runs of
value or shapes of the ore-bodies is necessary before any calculation
of averages. A preliminary delineation of the boundaries of the
payable areas on the assay plan will indicate the sections of the
mine which are unpayable, and from which therefore samples can
be rightly excluded in arriving at an average of the payable ore
(Fig. 1). In a general way, only the ore which must be mined need
be included in averaging.

The calculation of the average assay value of standing ore from
samples is one which seems to require some statement of elementals.
Although it may seem primitive, it can do no harm to recall that if
a dump of two tons of ore assaying twenty ounces per ton be added
to a dump of five tons averaging one ounce per ton, the result has
not an average assay of twenty-one ounces divided by the number of
dumps. Likewise one sample over a width of two feet, assaying twenty
ounces per ton, if averaged with another sample over a width of five
feet, assaying one ounce, is no more twenty-one ounces divided by
two samples than in the case of the two dumps. If common sense were
not sufficient demonstration of this, it can be shown algebraically.
Were samples equidistant from each other, and were they of equal
width, the average value would be the simple arithmetical mean of
the assays. But this is seldom the case. The number of instances,
not only in practice but also in technical literature, where the
fundamental distinction between an arithmetical and a geometrical
mean is lost sight of is amazing.

To arrive at the average value of samples, it is necessary, in
effect, to reduce them to the actual quantity of the metal and volume
of ore represented by each. The method of calculation therefore
is one which gives every sample an importance depending upon the
metal content of the volume of ore it represents.

The volume of ore appertaining to any given sample can be considered
as a prismoid, the dimensions of which may be stated as follows:--

_W_ = Width in feet of ore sampled.
_L_ = Length in feet of ore represented by the sample.
_D_ = Depth into the block to which values are assumed to penetrate.

We may also let:--

_C_ = The number of cubic feet per ton of ore.
_V_ = Assay value of the sample.

Then _WLD_/C_ = tonnage of the pris