determining the Hardness of Minerals. 401 



objection has been made to the results obtained on the ground 

 of the interference of tenacity and plasticity. Dana has stated 

 concisely the generally accepted definition of the mineralogists : 

 " Hardness is the resistance offered by a smooth surface to 

 abrasion." 



For practical purposes it has been demonstrated that when 

 softer substances are abraded by a very hard substance, other 

 conditions being constant, the amount of abrasion suffered 

 varies with the hardness of the abraded substance. For obtain- 

 ing values relative to an empirically selected abrader, it is 

 obvious that any one of the numerous variable conditions in 

 the process may be selected for functional purposes, provided 

 all the other conditions are maintained constant. What is 

 required, then, is an absolutely defined abrading agent, a 

 method, one condition, variable with the resistance to abrasion, 

 selected as functional, and devices for maintaining the others 

 absolutely constant. The values obtained would be relative to 

 the hardness of the abrader : this is a point that seems to have 

 been frequently overlooked. Attention has been called, in the 

 text-books,* to the fact that the results of sclerometry show 

 the hardness differences between the lower members of the 

 Mohs scale to be much less than between the harcL:' m rubers, 

 where the differences are said to be enormous, as shown by the 

 great length of time requisite for polishing »]- harder .^ems, 

 etc. It must be remembered, however, that when the diamond 

 scratches quartz there is interaction, the phenomenon of the 

 scratch is a relative one ; if sufficient force is applied the dia- 

 mond may be perceptibly abraded as well as the quartz. On 

 the basis of the definition that hardness is the resistance to 

 abrasion by diamond, diamond is almost infinitely harder ; but 

 assuming hardness to be the molecular or atomic tenacity, we 

 must have a means for measuring that tenacity in absolute 

 terms of energy expended before we may be sure of the actual 

 differences between different substances. 



The hardness of a substance as expressed in resistance to 

 scratching, is, in the case of fine-granular aggregates, dependent 

 on the fineness of the particles, the interlocking or loose struc- 

 ture, and the strength of the cement. If such an aggregate as, 

 for instance, chalk is scraped with a tool, we overcome the 

 tenacity of the particles and produce a scratch : if the sub- 

 stance were an aggregate of diamond particles the scratch 

 would still be produced. If the particles are so rigidly inter- 

 locked that the tool does not overcome their tenacity, a scratch 

 will not be produced by reason of a separation of the frag- 

 mental particles : yet we know that the soft carbonate will be 

 scratched, and the hard carbon will resist. The first case was 

 * Tschermak, p. 139. 



