~  —— 
ON THE 
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ABSOLUTE MEASUREMMNT OF HARDNESS. 209 
hardness of each substance is expressed, irrespective of other substances 
and without reference to a normal body, in terms of the fundamental 
units of physics. 
The method of rating hardness by seratching is best known and 
most generally applied. One body is harder than another, if,a point 
or sharp edge of the former is capable of scratching a plane over face 
of the latter. Of the two conditions which make an arbitrary scale 
possible in this case, the first is approximately given, to the extent 
only that the differences of hardness to be rated are in any two bodies 
marked. If this differences is small, it is usually found that a sharp 
edge of either will scratch a plane surface of the other. It is custo- 
mary to refer this discrepancy to the sensitiveness of the method. 
The two bodies are flatly pronounced equally hard, and since the see- 
ond of the conditions above given is also borne out by all the cases 
hitherto tested, a rough scale of hardness is thus feasible. The first 
investigator who made use of such a scale, Hauy, confined his work 
to four steps. They were limited by calcite, glass, and quartz. Mohs 
increased the number of steps to ten, and although later mineralogists, 
believing some of the steps disproportionately large, have inserted 
intermediate degrees, the Mohs scale has in general been retained to the 
present day. Indeed the justice of this is apparent, for in view of 
the absence of any means of even approximately defining the relative 
values of the successive degrees, all attempts to reduce them in size 
would, in the long run, rather be productive of error than of increased 
accuracy. 
The first attempt at measurement was made by Frankenheim,* who 
estimated the hand pressure under which a given hard point or stylus 
leaves ascratch on the surface to be tested. Butinstruments by which 
this pressure or the depth of penetration of the stylus is actually regis- 
tered were not invented till much later. They are due, respectively, to 
Seebeck,t Franz,i Grailich and Pekarek,§ F. Exner,|| Pfaff,{] Turner,** 
and others, and have been called “‘sklerometers.” The results obtained 
by these forms of apparatus, as Exner himself admits, are not of the 
nature of measurements, for all trae measurements of an unknown 
quantity determine the latter by inclosing it between well-defined 
limits, and it is by the distance apart of these limits that the accuracy 
of the method is conditioned. Sklerometers however are capable of 
furnishing only an upper limit. The lower limit is left to conjecture. 
*Franukenheim: De cohwsione, etc., Inaug. Diss., Breslau, 1829. 
tSeebeck: Progr. Céln. Real-Gymn., 1883. 
tPranz: De lapidarum duritate Inaug. Diss., Bonn, 1850; Pogg. Ann., vol. LXXxx, 
1850, p. 37. 
§ Grailich u. Pakarek: Wien. Ber., vol. xii, 1854, p. 410. 
|| F. Exner: Unters iiber d. Hirte an Krystallfldchen, Wien, 1873. 
q Pfaff: Minch Ber., 1883, pp.55, 372. Pfatf’s invariable use of the term ‘absolute 
hardness” is quite unjustifiable. His data are relative at best.” 
**Turner: Proc. Birm. Phil Soc., 1887, vol. v (2). 
H. Mis, 334, pt. 1——14 
