THOSE who have had occ.asion to sample a mine not infrequently find that it is impossible to take their sample cuts at regular distances apart, owing to the ground being close timbered, a stope having been taken out, or some other cause. When such is the case a tedious calculation becomes necessary in order to obtain an accurate result. A conscientious man will make the tedious calculation, but one who is inclined to be lazy, or who does not recognize the importance of accuracy, or has not the time, may be satisfied with either the arithmetical or weighted arithmetical mean result.There are two main systems of taking samples when the cuts are taken-(l) at equal distances, (2) at unequal distances. When the samples are out at equal distances apart there are three methods of computing the assay value :-1 (a) By Arithmetical Mean. The sum of the values and sum of the widths are each divided by the total number of samples, in order to obtain the value and width respectively, no allowance being made for the relative widths arid values. The result isabsolutely inaccurate, and should never be used under any circumstances.1 (b) By Geometrical Mean. The assay widths ie, feet %, feet oz, inch dwt, &c, are added together and the sum of these is divided by the sum of the widths.