NEW YORK ACADEMY OF SCIENCES 



651 



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 enclosed 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. 













4-1 

 O 



a 







I 









bo . 

 -O.J4 



>> 





s 



a 



>> B 



ft M 





°fiJ 



2 





< 

 >> 

 .a 



a 



<D 







U 







e 



u 



a 



B 

 3 



unds Chalco 

 lume Cubic 



9) 



s 

 O 







M 



ta B 

 bo 



s 



Pm 



O 



.2 

 '■+3 





<D 



O 



s> 



T3 



ni 



oJ 





Ph 



Oh 



PL, > 



m 



rt 



P4 



Copper. 



.OO9 



.18 



•52 3-42 

 Galena. 



i-5 



1/18 



1/6 



Lead. 



.OOII 



. 022 



.025 .092 



•45 



1/60 



1/20 





.OOS 



.16 



.186 .700 



.89 



1/3 1 



1/10 





.004 



.08 



.002 -340 

 Zincblende. 



.70 



i/39 



i/i3 



Zinc. 



.OO48 



.096 



.128 .90 



•97 



i/35 



1/12 





.OO9 



.180 



.240 1.60 

 Argentite. 



1. 17 



1/2 1 



i/7 



Silver. 



.00007 



.OOI4 



.0016 .006 



.18 



1/148 



i/49 





.OOOl6 



.OO32 



.0037 .014 

 Gold. 



.24 



V 1 ^ 



1/38 



Gold. 



.00002 



.0004 



.0004 .00065 



.086 



1/3 13 



1/104 





.OO0O4 



. OO08 



.0008 .00130 



. 109 



1/249 



1/83 



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 whose 

 total width bears the same relation to the width of the rock 

 mass as is borne by the diameter of the particle of ore, the 

 chance of crossing a particle varies from one in six to one in 

 one hundred. Or we may say that with cracks of this spacing 



