moid.*
_V WLD_/C_ = total metal contents.

[Footnote *: Strictly, the prismoidal formula should be used, but
it complicates the study unduly, and for practical purposes the
above may be taken as the volume.]

The average value of a number of samples is the total metal contents
of their respective prismoids, divided by the total tonnage of
these prismoids. If we let _W_, _W_1, _V_, _V_1 etc., represent
different samples, we have:--

_V(_WLD_/_C_) + _V_1 (_W_1 _L_1 _D_1/_C_) + _V_2 (_W_2 _L_2 _D_2/_C_)
---------------------------------------------------------------------
_WLD_/_C_ + _W_1 _L_1 _D_1/_C_ + _W_2 _L_2 _D_2/_C_
= average value.

This may be reduced to:--

(_VWLD_) + (_V_1 _W_1 _L_1 _D_1) + (_V_2 _W_2 _L_2 _D_2,), etc.
---------------------------------------------------------------
(_WLD_) + (_W_1 _L_1 _D_1) + (_W_2 _L_2 _D_2), etc.

As a matter of fact, samples actually represent the value of
the outer shell of the block of ore only, and the continuity of
the same values through the block is a geological assumption.
From the outer shell, all the values can be taken to penetrate
equal distances into the block, and therefore _D_, _D_1, _D_2
may be considered as equal and the equation becomes:--

(_VWL_) + (_V_1 _W_1 _L_1) + (_V_2 _W_2 _L_2), etc.
---------------------------------------------------
(_WL_) + (_W_1 _L_1) + (_W_2 _L_2), etc.

The length of the prismoid base _L_ for any given sample will be
a distance equal to one-half the sum of the distances to the two
adjacent samples. As a matter of practice, samples are usually taken
at regular intervals, and the lengths _L_, _L_1, _L_2 becoming thus
equal can in such case be eliminated, and the equation becomes:--

(_VW_) + (_V_1 _W_1) + (_V_2 _W_2), etc.
----------------------------------------
_W_ + _W_1 + _W_2 , etc.

The name "assay foot" or "foot value" has been given to the relation
_VW_, that is, the assay value multiplied by the width sampled.[*]
It is by this method that all samples must be averaged. The same
relation obviously can be evolved by using an inch instead of a
foot, and in narrow veins the assay inch is generally used.

[Footnote *: An error will be found in this method unless the two
end samples be halved, but in a long run of samples this may be
disregarded.]

Where the payable cross-section is divided into more than one sample,
the different samples in the section must be averaged by the above
form