308 Dr. T. Carnelley on the 



to drive the molecules apart, and therefore the less will it ex- 

 pand on being heated ; and consequently the greater the coeffi- 

 cient of expansion the lower the melting-point. The two 

 phenomena of fusion and expansion by heat thus admit of a 

 common explanation, viz. the attraction between the molecules. 

 Again, the greater the attraction between the molecules of a 

 body the greater the external force required to separate them 

 mechanically, and therefore the harder the body. If this be 

 true, then the hardness of a body ought to bear some relation 

 to its melting-point. We actually find that, as a general rule, 

 the harder a body the higher its melting-point : thus diamond, 

 steel, &c. have a very high melting-point and great hardness, 

 whilst lead, potassium, sodium, wax, &c, have a low melting- 

 point and are soft. This relation, however, is not so regular 

 and easily traced as in the case of the melting-point and co- 

 efficient of expansion, the reason being that the separating 

 force (viz. heat) in the case of fusion and expansion is exerted 

 internally, and therefore more uniformly than in the case of 

 determining the hardness of a body, for in the latter the sepa- 

 rating force is exerted externally* . 



Quincke ('Watts's Diet.' vii. p. 241) has shown that the 

 order of capillarity of metals in the solid state is the same as 

 their order of hardness ; and this is what we might expect. 

 Bettone (Pogg. Ann. cl. p. 644) has determined the hardness 

 of the elements by finding the time required for a steel drill 

 to penetrate to a certain depth, and has by this means shown 



that the hardness of an element = ~~ *v = r, the fol- 



at. wt. sp. vol. 



lowing being a few examples out of a large number given in the 



original memoir : — 



Hardness. 1- 



spec. vol. 



Diamond .... 0*301 '292 



Iron 0-137 -137 



Copper .... 0-136 -136 



Platinum .... 0-109 -111 



Zinc 0-108 -108 



Silver 0-099 -096 



Tin 0-065 -062 



Lead 0-057 -055 



Potassium . . . 0"023 '022 



* The first part of the present paper was written in the summer of 1878, 

 and read before the Owens-College Chemical Society, January 1879, since 

 when an article by F. Mohr, "On Cohesion," has appeared in Liebig's An- 

 nale/i, exevi. p. 104 (1879), in which he points out that the metals form a 

 " scale of hardness agreeing- closely with the order of their melting-points."' 



