Januaet 5, 1906.] 



SCIENCE. 



25 



tallized out with the other bases from the 

 molten magma, we are yet confronted with 

 the fact that their very presence and de- 

 tection in the rock show that they have 

 escaped leaching even though they occur 

 in a district where underground circula- 

 tions have been especially active. From 

 the results which we have in hand, it is 

 quite as justifiable to argue that the metals 

 in the rocks are proof against the leaching 

 action of underground circulations as that 

 they fall victims to it. These considera- 

 tions tend Ifo restrict the activities of the 

 meteoric waters to the vadose region as 

 Posepny calls it, i. e., that belt of the 

 rocks Avhich stands between the permanent 

 water-level and the surface. Within it is 

 an active area of solution, as we have all 

 recognized for many years, but, as pre- 

 viously stated, experience shows that the 

 metals which go into solution in it strongly 

 tend to reprecipitate 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 neces- 

 sary 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 prob- 

 able natural compound or mineral in each 

 ease. I have next calculated the volume 

 of a cube corresponding 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 value, and 

 allow it 11 to 12 ci^bic 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 enclosing 

 rock, will give us an idea of the chance that 

 a crack , large enough to form a solution- 

 water-way will have of intersecting that 

 amount of contained metallic mineral. Of 

 course in endeavoring to establish this 

 quantitative 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 assume 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 min- 

 erals is not cubical. I am convinced from 

 microscopic study of rocks and the small 

 size of the metallic particles that their sub- 

 division certainly keeps pace with any con- 

 ceivable 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, there- 

 fore, multiply the ratio of probability that 

 any single set will intersect it by three in 

 order to have the correct expression. The 

 chance, therefore, that a crack, of • the 

 width of the cubic edge of the enclosed 

 mineral, will strike that cube is given by 

 the ratios in the last column, which ratios 

 I assume hold good with increasing fine- 

 ness of subdivision both of metallic min- 

 erals and of cracks. 



From the table it is evident that the 

 chances vary from a maximum in the case 

 of copper of one in six through various 

 intermediate values to a minimum for gold 

 of one in» over one hundred. This is 

 equivalent to saying that with cracks 



