Kip — Determination of the Hardness of Minerals. 29 



The two methods are, of course, the same in principle and 

 one may be used to control and verify the other. 



Given any two minerals, to determine the relative amounts 

 by weight that must be abraded from each to produce equal 

 molecular dislocation, the following method is suggested : 



Multiply the specific gravity of the first over the specific grav- 

 ity of the second by the density of the second over the density 

 of the first. The result will be the weight of n molecules of 

 the first over the weight of n molecules of the second. Thus 

 if the specific gravity of fluorite be 3 - 183 and its density '123, 

 and the specific gravity of quartz be 2 - 65 and its density -132,* 

 then 



3-183 -132 -420156 



X = 



2-65 -123 -32595 



that is, a mass of fluorite that contains as many molecules as a 

 given mass of quartz will weigh 1*3 of the weight of the 

 quartz. 



Omitting the conception of mass or volume, we can arrive 

 at the same result more simply by making the weight of the 

 material abraded from each mineral proportional to the molec- 

 ular weight of each. It is evident that if the molecular weight 

 of fluorite be 78 and of quartz 60 the weight of n molecules of 

 each will stand in the same ratio. If, now, we determine the 

 total amount of force required to abrade 1 mg. of quartz and 

 then .the total force required for 1-3 mg. of fluorite, we shall 

 have the respective hardness of the two minerals. These 

 values should be exactly proportionate to those obtained 

 by Method 1, provided both are carried out with sufficient 

 accuracy. 



This plan, however, is open to some objection in practice. 

 It would necessitate constant weighing of the fluorite lest the 

 amount abraded should exceed 1*3 of the weight of the quartz. 

 Furthermore in view of the unequal density of the two miner- 

 als we evidently could not multiply the force employed by the 

 distance traversed in determining the total force, nor yet by 

 the time during which the force operated, except on the assump- 

 tion that the time of passage of the point over the surface was 

 determined by molecular resistance alone. This assumption is 

 generally made, but it evidently only approximates the truth. 



8. A more feasible plan for amorphous and isometric 

 minerals, and one which could be adapted to minerals of lesser 

 symmetry as our knowledge of molecular structure increases, 

 is the following : It is clear that if we would dislocate the 

 same number of molecules in two minerals, A and B, of which' 

 B is the denser, we must cause the abrading agent to traverse a 

 greater distance on A than on B. In general the distance to 

 * These values according to Schroeder van der Kolk, loc. cit. 



