28 Kip — Determination of the U<ti'<l m** of Minerals. 



to reach the same depth in gypsum.* The number of abrading 

 movements is no true test of hardness unless the effective force 

 of the average movement is the same in all cases. 



6. While bringing in one factor which has hitherto been 

 generally disregarded, I attach, on the other hand, much less 

 importance to another variable which Pfaff, Jaggar and others 

 have been careful to maintain constant or to submit to careful 

 measurement, namely, depth. It is not too much to say that 

 instead of keeping depth constant it ought to be left to shift 

 for itself. Imagine two minerals the dimensions of whose 

 molecular unit spaces stand in the ratio of 1:3 but which are alike 

 in respect to intermolecular attraction and molecular form and 

 arrangement. Evidently the resistance to abrasion will be the 

 same in both. If, however, we should make depth a constant, 

 the hardness of the mineral with the lesser molecular volume 

 would appear three times as great as that of the other. Pfaff's 

 substitution of equal volumes of abraded substance for equal 

 depth of abrasion is, of course, merely a device for measuring 

 depth, the length and breadth of the abraded surface being 

 kept constant. In determining hardness we are concerned with 

 a molecular phenomenon. Therefore depth and volume, as 

 used by the authors quoted (as well as by Rosiwal, M tiller, 

 Bottone and others), involving as they do arbitrary spacial units 

 of measurement, have here as little significance as the size of 

 crystal faces in crystallographic determinations. A further 

 objection to the method in which weight and rate are kept 

 constant and hardness determined by the number of abrading 

 movements necessary to reach a given depth is the fact that a 

 point weighted sufficiently to procure molecular dislocation 

 when drawn over or revolved upon a given mineral will almost 

 certainly produce mass dislocation when applied to any mineral 

 softer than the first. Hence by this method the actual differ- 

 ences between the harder and the softer minerals will be inva- 

 riably exaggerated. The weight, therefore, in all cases should 

 be great enough when put in motion to produce molecular 

 displacement, but no greater. 



T. It follows from the above that hardness must be deter- 

 mined either : 



(1.) By observing the least force (whose components for a 

 given mineral may be designated as the critical pressure and 

 the critical pull for that mineral) sufficient to produce abrasion, 

 or 



(2.) By noting the total force required to produce a given 

 amount of molecular dislocation. 



* In justice to Professor Jaggar it should be stated that he attaches himself 

 no great value to the numerical results obtained in the series of experiments 

 described in his article ; a fact which those who quote him would do well 

 to mention. 



