ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 2393 
is distributed radially until a line of rupture is the visible result. Hence 
it is not remarkable that constant results can only be reached if P is 
divided by a low power of D. 
VIIl. DATA FOR HARDNESS AND ELASTICITY. 
The remarks of the preceding paragraph have shown that though the 
theoretical questions encountered in the present paper are in need of 
further elucidation, the considerations involved do not inuch affect the 
practical side of the issue. I have already pointed out that irrespective 
of the shortcomings of the theory, the relative scale of hardness is 
vouched for. Again there is one particular case in which the data are 
virtually absolute. This occurs when the curvature of the lens, p=1. 
Finally the absolute value of the data obtained will necessarily be gen- 
eral, since the facts show that by multiplying Hertz’s expression by 
* Vp, the results for a given substance are constant throughout. This 
datum may sately be taken as the absolute hardness of the body, 
although its mechanical interpretation is not quite apparent nor quite 
certain. Furthermore even these strictures will disappear, if the 
occurrence of a particularized surface hardness can be inferred from 
other and independent experiments, or if the dependence of tenacity 
and of hardness on lens curvature can be similarly computed in all 
zases. With these conditions premised the quantity P; yp may be 
termed the absolute hardness of the body, and hence 
6 ; 
H=— VP py 
To give an example of the fluctuations here in question, the following 
two series of individual values of hardness may be adduced : 
rlass 99) 99 299 110 
Gibssl 57s Ure alle all hee) eee oy Raney o 
’ . . 227 +2 
| p=10 ...... | 5 U1 934 236 Bap) = 2310) | 
Quartz. ---.- 298 281 PAD Ne |e ead 
|¢ a. a | Yogoxo 
| P=1 ------- 5 Y 298 285 PD) ee ae ae | ¢ 29242. 
} | | | 
It was my habit to compute all the values of H individually. From 
these the following mean values of hardness were derived: 
Mean | 
) 
p i ] 4 5 10 12 i 30 aalaese 
Glass I ..... PAA | ee ee LD) Nore ete eerste PAM ey se ene eee 214+1 
Glass epee a DY) | ee ae 222 Oil eee: DSN tee g ere | 2264-2 
| OWES G7 Ol Gees ale a ee ZAE? NS oro asl sta eet PSH (eH Seine 236 | 239+2 
Quartz. - -- ? 550i i coe! 198 193 995 +2 
| to axis . 5 
These data show a sequence of values which in the first place is 
qualitatively in accord with the usual scale of hardness (glass 4 to 6, 
