74 POPULAR LECTURES AND ADDRESSES. 



matter may be. I may illustrate by a case in 

 which this first step has not been taken. The 

 hardness of different solids, as precious stones and 

 metals, is reckoned by a merely comparative test. 

 Diamond cuts ruby, ruby cuts quartz, quartz, I 

 believe, cuts glass-hard steel, and glass-hard steel 

 cuts glass ; hence diamond is reckoned harder than 

 ruby ; ruby, than quartz ; quartz, than glass-hard- 

 steel ; and glass-hard steel, than glass : but we have 

 no numerical measure of the hardness of these, or 

 of any other solids. We have, indeed, no know- 

 ledge of the moduluses of rigidity, or of the tensile 

 strength, of almost any of the gems or minerals, of 

 which the hardness is reckoned by mineralogists in 

 their comparative scale, beginning with diamond, 

 the hardest of known solids. We have even no 

 reason to believe that the modulus of rigidity of 

 diamond is greater than that of other solids ; and 

 we have no exact understanding of what this 

 property of hardness is, nor of how it is related to 

 moduluses of elasticity, or to tensile or shearing 

 strength, or to the quality of the substance in 

 respect to its bearing stresses exceeding the limit 



