Kip — Determination of the Hardness of Minerals. 27 



the lesser pull required in the direction BA being offset by the 

 greater pressure required to overcome the tendency of the 

 molecules to " shed" the pressure, and conversely in the direc- 

 tion AB. It is evident at once what untrustworthy values will 

 be obtained if either component alone be taken as the measure 

 of hardness. It also becomes clear how futile it is to compare 

 results obtained from abrasion tests with those obtained from 

 static pressure tests, since the two forces required to produce 

 abrasion are in no sense a function of the force required to 

 produce penetration. It should be remarked in passing that 

 the force EC in fig. 1 is not necessarily the same in value as 

 the corresponding force in a static pressure test on the same 

 specimen. EC in itself may produce no appreciable effect 

 , upon the surface, molecular dislocation taking place only when 

 it acts in union with the force CF. 



5. A fallacy into which some investigators seem to have 

 fallen is the substitution of rate for pull, in cases where the 

 abrading instrument passes over the same portion of the sur- 

 face repeatedly, in a single direction or with a rotary movement. 

 Thus Jaggar speaks of four variables : rate, weight, depth and 

 duration, and states that any one of them may be made a meas- 

 ure of hardness provided the other three be kept constant. 

 The value of the lateral component in the abrading force is not 

 taken into account, although care is taken to specify that it 

 must operate at a known rate. Thus, it is argued, if with a 

 given weight and a given rate 50 revolutions of the diamond 

 point be required to attain a given depth in the case of calcite 

 and 113 revolutions be required to reach the same depth in 

 fluorite, then 50 and 143 represent the respective hardness of 

 these minerals in relation to the abrading agent. This state- 

 ment, however, would be true only on the theory that the work 

 done by the 50 revolutions was exactly 50/143 of the work 

 done by the 143 revolutions, or in other words, that the resist- 

 ance overcome by the average revolution on the specimen of 

 calcite was exactly the same as that accomplished by the average 

 revolution in the case of fluorite. The mere fact that the rate 

 was maintained constant in both cases is, of course, no proof 

 that this assumption is correct. The discrepancy involved 

 becomes still more apparent when we consider the results 

 obtained by this method for No. 2 and No. 9 of the Mohs's 

 scale, the hardest and least hard of the minerals tested. Doubt- 

 less scores of the 188,808 revolutions required to reach a depth 

 of 10/x in the case of corundum were entirely or practically 

 ineffective in producing abrasion, and probably no one of them 

 represents as great an expenditure of abrasive force as is 

 represented by the average of the 8.3 revolutions that sufficed 



