In contemplating the manner in which high values occur throughout the ore, we may recognize what might be called the "texture" of the variations in grade. In a "fine-textured" distribution, the high assays which some of the samples yield are attributable to small spots of rich material. Recutting the sample or taking additional samples on both sides of it will in general fail to duplicate the high assay but will not disprove the existence of rich spots. Increasing the bulk of each sample, however, tends to reduce the range of sample values and to give results which are more nearly representative.

In a "coarse-textured" distribution the high assays actually represent sizable rich portions within the deposit. Here recutting the sample serves the useful purpose of confirming the presence of rich material; the new samples on each side indicate its size and consistency. The rich portions may prove to be distributed at random and conform to Swan-son's criteria based on calculation of probable error, or they may be arranged according to some pattern. If it is possible to recognize distinctly localized rich and lean areas within the orebody, the samples from each should be averaged separately. Geological observation is the best guide to such localization, and no juggling with mathematical formulas is a substitute for it.

Resumé.    An arithmetical average is proper:
(a)     if the high-grade spots occur in random arrangement.
(b)      if the high values occur in. the form of an elongated oreshoot traversing the ore-block under consideration.     (But in this case it is preferable to treat the shoot separately in calculation.)

An arithmetical average is incorrect:

If the high values constitute a roughly equidimensional oreshoot or form the core of an oreshoot. In this case either the Watermeyer or the Truscott method may give a more accurate result.

Pragmatic Methods. Contemplation of statistical and frequency-weighting methods gives an insight into the nature of high assays and the manner in which they influence the average grade. But although they find application in special cases, frequency methods are not widely used, partly because they involve laborious calculations and partly be¬cause they are applicable only where a large fund of assay data is avail-able.

Instead, most engineers use one of a variety of simpler but more arbitrary methods depending on the manner of distribution of the high values:

1.    Taking auxiliary" samples on each side of the high one and substituting for the high the average of the three. An alternative method is to include in the average the next two samples on each side, thereby combining the results of five samples.

2.     Calculating the mean of the whole series of samples, reducing all the highs to this mean and then calculating the "cut" average.    This usually gives too drastic a reduction. Consequently, highs are cut to one and a half or two times the mean.

3.      Cutting all high samples to an arbitrary value, say $25 or $50.

4.      Applying a percentage correction to the arithmetical average.

Any one of these may give satisfactory results in a particular case, but it would be unsafe to place final reliance on any one method without confirming its applicability to the orebody in question. The final check is the value that the ore yields on mining and milling or smelting. In an operating property such a check is readily available through test mill-runs or trial smelter shipments. In an inactive property one may need to mine out material for bulk shipments from areas that have been sampled. If costs or transportation difficulties prohibit shipping, an alternative is to take systematic bulk samples and crush them down to the proper size for quartering or splitting.

In examination work, however, it is often necessary to make a preliminary estimate before bulk sampling can be undertaken or indeed be-fore its expense can be justified. In this case the examiner has no alternative but to select the method which, in the light of his experience, seems best adapted to the particular orebody.