26 Kip — Determination of the Hardness of Minerals. 



Thus Jaggar, while accepting Dana's definition in theory and 

 repudiating static pressure tests, reverses this in practice and 

 actually employs a method which, as Auerbach has pointed 

 out. is fundamentally only a modification of the method he 

 condemns. Pfaff likewise passes from abrasion tests, or what 

 are certainly intended as such, to the boring method, apparently 

 without realizing that he is implying thereby a very considerable 

 modification of his definition of hardness. 



4. Abrasion being a mechanical process, the question at 

 once arises what force or forces produce it and how are these 

 forces to be measured and combined. In fig. 1 let CD rep- 

 resent a tool producing abrasion upon the surface AB, and let 

 it represent by its length the least force adequate for this 

 purpose. The value of CD is evidently ^EC 2 a. (jp 2 . Or, 



expressed in words, the force that produces abrasion is resolv- 

 able into two forces, one perpendicular to and the other in the 

 l plane of the surface. Calling the 



^ tj former the pressure and the latter 



/\ the pull, the force producing abra- 



/ i sion is equal to the square root of 



/ \ the square of the pressure plus the 



A ^- — : ~ B square of the pull. In practice the 



two components are generally ap- 

 plied as separate forces. It should be noted further that the 

 lateral component may also be a complex force, though not 

 necessarily so. Thus in a mineral with striations running at an 

 angle between 0° and 90° to the direction of CF, this force will 

 again be resolvable into two forces acting at right angles in the 

 plane of the surface, and its value will have to be determined 

 before it can be combined with EC. 



Investigators have hitherto assumed that a sufficient measure 

 for abrasion could be found in pressure alone or in pull alone. 

 This assumption would be true only when the one force was a 

 direct function of the other, a condition which may obtain 

 among amorphous substances but which nowhere else can be 

 assumed as true, or even probable, without proof. Imagine a 

 mineral with the molecular structure suggested in fig. 2. A 

 tool passing in the direction AB will produce abrasion, let us 

 say, with a pressure of x grams and a pull of 2x grams. Pro- 

 ceeding in the direction BA 

 it is quite conceivable that a 



A- * ^ ^ ^ ^ ^ -B ll 1 j^Xt ™!url 



of 2x grams would be re- 

 quired. In both directions the resistance to abrasion would 

 be the same, though the factors that combine to produce this 

 resistance might differ accordine to the direction of the test. 



