. The sampling and estimation of ore in a mine . by what many call thefoot-ounce method, which, applied to the foregoingexample, works out thus : Width. Assay. Foot-ounces feet oz. per ton .45 oz. .62 oz. .85 oz. OZ. OZ. OZ. .8 oz. oz. oz. 35-0 Tlie assay f>€i5==f©^^if^^dth-is oz. per ton, insteadof 2)^2 oz. In matters of this kind mathematical reasoningconfirms the conclusions of rough common sense. Themethod just described is based upon the higher mat
. The sampling and estimation of ore in a mine . by what many call thefoot-ounce method, which, applied to the foregoingexample, works out thus : Width. Assay. Foot-ounces feet oz. per ton .45 oz. .62 oz. .85 oz. OZ. OZ. OZ. .8 oz. oz. oz. 35-0 Tlie assay f>€i5==f©^^if^^dth-is oz. per ton, insteadof 2)^2 oz. In matters of this kind mathematical reasoningconfirms the conclusions of rough common sense. Themethod just described is based upon the higher mathe-matics, as the following integrations, kindly suggested byMr. Ross Hoffman, will demonstrate: Problem i.—To determine the average value of the sec-tion of vein A between tine samples whose widths are w,and w^, and values v. and v^, respectively, under the as-sumption that the values vary gradually over the area « -35— SAMPLING AND KSTIM A IION OK ORE IN A MINE from V, to V, in the direction d, then at any distance x fromw, the vahie. v= — (v. — V,) + d [I) also d —X X (Wij — Wi) or y — i-Wj (2) w,—W2 y—w^ A = (Wj + w.) d (3) X = d -x = o -^ y dx -f- A = average value for the section A. P>om 1 and 2 v y = (wj v, + w,, V2) + d^ .X X^ . 2X (W2 Vj + w, V,)+( I )Wi Vi Vd d2/ ? d^ ^d Wi V, + W2 V2J V y dx = 5^ — 1- d d 2 (w, +W2)do Wl+W2 W2 V, + Wi V, Wr Vi + Wj v. (Wi—W2) (V2—VJ^ = -\.y, W1 + W2 Wi+Wa W1+W2 The last term = O when w^ = Wj or v^ = v^ Under normal conditions, where ordinary sani])!ingcan be depended on to give fairly approximate averages,this last term will be small enough to neglect. (See bysubstitutions.) Hence w, Vi + W2 V2 can be taken as the average value Wi+W2 for section A. -36- SAMPLING AND ESTIMATION OF ORE IN A MINK ProWcm 2.—To find the average value from a numberof samples taken as above, where vv equals width of
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