eat fea thhs: ay ad x J idcera wat ete ieee Z 
ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 217 
_ sharply marked by the occurrence of either permanent set or of rup- 
ture at the area of contact, it is merely necessary to measure the total 
pressure P and the diameter of the impressed area D for the time 
in question. The first of the equations (4) then leads at once to the 
value of theoretical hardness. In the interest of accurate work, how- 
ever, it is unfortunate that the two quantities P and D can be meas- 
ured but once. It is therefore desirable to introduce some variation of 
method at least for D, for P does not admit of a second expression. 
For this purpose the other two equations given under (4) are available. 
One of them (the second in order) premises a knowledge of both FH! 
and p, as wellas of P. Now, although p may be considered sufficiently 
given by the radius of the spherical stylus, #', on the other hand, 
would have te be taken from tabulated data of H and yu, or be prelim- 
inarily measured by aid of a special piece of the given body. Neither 
of these alternatives is acceptable, while ;< is known to vary even with 
insignificant structural differences of the given substance, and can not 
even be considered constant for different parts of it. On the other 
hand, the third in order of the equations (4) is useful in every particu- 
lar. Based as it is on the values of P and g=p/d’ only, its availability 
is enhanced by the fact that the q is constant, and can therefore be taken 
from a whole series of measurements of increasing p. Far from being 
dependent on a single measurement, therefore, the observer is at liberty 
to reject the limiting value Q altogether; for if it should differ from 
the other values q, an explanation is readily found in the fact that @ 
is measured when * set” has already occurred. The additional labor 
involved in a step-for-step increase of P is of no moment, seeing that 
such procedure is under all circumstances necessary. For the limits 
of elasticity must be gradually approached and not overstepped. 
I have already stated that brittle bodies present a case of easy obser. 
vation, for here set is accompanied by rupture. Only in rare instances 
is this criterion preceded by a visible indentation without break of con- 
tinuity, and a puncture of this kind can usually be referred to a lack 
of homogeneity in the material or to anomalies of brittleness. Hence 
I found it advantageous to begin my work with brittle bodies, and the 
general method was devised with special reference to the fact that 
nearly all such bodies, in particular the glasses and the greater number 
of crystals, are more or less transparent. 
The spheres in these experiments are suitably ground in the form of 
a plano-convex lense, with a radii of curvature of 1 to 30 millimeters. 
The plane surface is preferably a plate, about 11.6 millimeters in diam- 
eter and 8 millimeters thick. The thickness is purposely chosen of 
the same order of magnitude as the diameter,in order that any dis- 
crepancy of the nature of flexure may be excluded from the start. The 
plate is fixed in position while the lense is free to move up and down, 
aud pressure is suitably transmitted by a lever actuated by a set of 
weights. The area of contact and the occurrence of the indentation are 
