236 ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 
For quartz the value has no immediate meaning, but the factor 
with which H' is to be multiplied to obtain the modulus E, in the direc- 
tion of the axis is certainly nearer 1 than in the case of glass, seeing that 
both hardness and elasticity are more pronounced in the former case. 
Hence, the error made by putting M,=H' or H)=10164 will not be 
larger than 2 percent. Indeed, this value when compared with Voigt’s 
value, L,=10304, agrees with it to about 1 per cent. In consideration 
of the totally different methods by which the two results are reached, 
the agreement is very satisfactory. Moreover, since the two data cor- 
respond to different intensities of strain, complete co-incidence is not to 
be looked for. 
I will close with a short comparison of the values of hardness and 
elasticity. It appears at once that the harder of two bodies is the 
more elastic, but hardness increases less rapidly than elasticity. If H 
be expressed in per cents of H, the following values obtain: Glass I, 
3.9; glass II, 3.3; glass III, 3.2; quartz, 2.9. This state of things is 
strikingly manifest in the experiments themselves. One would natur- 
ally expect that greater pressures are to be brought to bear in the cases 
of the harder and more elastic bodies. As a rule the reverse of this is 
the fact. For in the case of the softer material the surface of contact 
rapidly increases, and hence greater pressures must be exerted to pro- 
duce the same stress per unit of area. 
