112 



equations 



Periodic Law of the Chemical Elements. 



A=c x spec, heat (Dulong and Petit's law), 

 A=c (m + \/v), 



the atomic weight A is not exactly but only approximately 

 equal to the expressions on the right-hand side, since the 

 latter are a function of the temperature, whereas the atomic 

 weight, so far as we know, is constant. 



According to Bettone the hardness of an element is 

 inversely proportional to its specific volume. If this be so, 

 then hardness may be represented in terms of the specific 

 gravity and the expression 6' 6 (m+ y/v), thus 



Hardness = 



SP- gr.__ sp. gr. 



spec. vol. at. wt. 6'6(m+ y/v) 



The following Table gives the hardness of a number of 

 elements as found experimentally by Bettone, and as calcu- 

 lated by the above equation : — 





Specific 

 gravity. 



Hardness. 



Calculated. 



sp. gr. 

 6-6(>+ Vv)l 



Pound 



(Bettone). 



Carbon (diamond) ... 



33 



8-0 

 8-8 

 715 

 10-5 

 19-3 

 2-56 

 8-65 

 1-74 

 7-29 

 11-38 

 11-86 

 1-57 

 •97 

 •86 



•250 



•158 



•140 



•109 



•0964 



•096 



•092 



•077 



•071 



•063 



•055 



•057 



•037 



•042 



•022 



•301 

 •146 

 •136 

 •108 

 ■099 

 •098 

 •082 

 •076 

 •073 

 •065 

 •057 

 •056 

 •041 

 •040 

 •023 





Zinc 



Silver 



Gold... 



Aluminium 



Cadmium 





Tin 







Calcium 







It should be noted, however, that Bettone's values, on 

 which he founds his law of hardness, do not agree in several 

 cases with those found by other observers, i. e. Calvert and 

 Johnson. 



In the expression A = C(m+ y/v) it has been stated that 

 m is the member of an arithmetical progression. For even 



