THE PROBLEM OF THE METALLIFEROUS VEINS. 201 



tions tend to restrict the activities of the meteoric waters to the vadose 

 region, as Posepny calls it, i. e., that belt of the rocks which stands 

 between the permanent water level and the surface. Within it is an 

 active area of solution, as we have all recognized for many j'^ears, 

 but, as previously stated, experience shows that the metals which 

 go into solution in it strongly tend to precipitate at or not far below 

 the water level itself. 



It is of interest, however, to seek some quantitative expression of 

 the problem, and the assays given above furnish the necessary data. 



I have taken the values of the several metals which have been 

 found by the assays of what were in most cases believed to be normal 

 wall rocks, selecting those of igneous nature, because experience 

 shows them to be the richest. The percentages have been turned into 

 pounds of the metal per ton of rock. This latter value has then been 

 recast into pounds of the most probable natural compound or mineral 

 in each case. I have next calculated the volume of a cube corre- 

 sponding to the last weight, and by extracting its cube root have 

 found the length of the edge of such cube. If now we assume a rock 

 of a specific gravity of 2.70, which is a fair average A^alue, and allow 

 it 11 to 12 cubic feet to the ton, or, say, 20,000 cubic inches, the edge 

 of the cube-ton will be 27.14 inches. The ratio of the edge of the 

 cube of metallic mineral to the edge of the cube-ton of inclosing rock 

 will give us an idea of the chance that a crack large enough to form a 

 solution waterway will have of intersecting that amount of contained 

 metallic mineral. Of course in endeavoring to establish this quanti- 

 tative conception I realize that the metallic mineral is not in one 

 cube, and that through a cube-ton of rock more than one crack passes, 

 but I assvime that the fineness of division of the metallic mineral 

 practically keeps pace with the lessening width and close spacing of 

 the crevices. It is also realized that the shape of the minerals is not 

 cubical. I am convinced from microscopic study of rocks and the 

 small size of the metallic particles that their subdivision certainly 

 keeps pace with any conceivable solution-cracks, and that no great 

 error is involved in the first assumption made. The sides of a cube 

 represent three planes which intersect at right angles and which are 

 mathematically equivalent to any series of planes intersecting at 

 oblique angles. Hence, if we consider as cubes the subdivisions 

 formed in our rock mass by any series of intersecting cracks, there 

 are three sets of planes, any one of which might intersect the cube of 

 ore. We must therefore multiply the ratio of probability that any 

 single set will intersect it by three in order to have the correct expres- 

 sion. The chance that a crack of the width of the cubic edge of the 

 inclosed mineral will strike that cube is given by the ratios in the last 

 column, which ratios I assume hold good with increasing fineness of 

 subdivision both of metallic minerals and of cracks. 



