ON THE ABSOLUTE 
MEASUREMENT OF HARDNESS. 
| p— > D 10 15 
|- ——s 
:D?—= | 81.7 _ | 67.0 | 56.6 | 49.8 
es 1. 64 0.96 | 0.50 0). 32 
pp 0.142 | 0.119 | 0.094 0.080 
All of which relations, instead of being constant, appreciably decrease. 
This may be expressed as follows: The pressure per unit of area 
which just produces a line of rupture in the surface of a given plate of 
a given body, is not always the same; the said pressure increases in 
proportion as the test lens is more convex or the area of contact smaller. 
A further statement to the same effect may be made by indicating that 
the total pressure just sufficient to produce a line of rupture is not pro- 
portional to the square of the lens curvature; or again that the diam- 
eter of the impressed area when rupture just occurs is not directly pro- 
portional to the radius of the lens, seeing that both quantities increase 
at a retarded rate. Mere inspection of the above table shows, how- 
ever, that the values of the second row (P:p*) decrease at the rate in 
which thevalues pincrease, and the sameobservation applies to the other 
rows. Hence it follows that the relations theoretically deduced above 
are to be replaced by empirical relations such that (1) P is not propor- 
tional to D*, but to D*”’, (2) P is not proportional to p*, but to p; (3) not 
D, but D** is proportional to p. 
In how far these inferences are actually borne out by experiment is 
shown by the following summary: 
— 3. 5. 10. 15. Mean values. 
| as PES ae ch? J ‘eee sah*3 
Pz D 32 53.4 52. 0 34. 8 54.5 53.7 +04 
Pap — 4. 93 4.78 5. 04 4. 80 4.89 +0. 04 
De: — 0.092} 0.092 | 0.092) 0.088 0. 091 +0. 001 
The probable errors are throughout only about 1 per cent. 
For the other plates these relations were also applicable. In these 
cases, however, only two values of p (4 and 12 millimeters) were availa- 
ble, so that the test is not very cogent. I therefore had a new plate and 
lens made out of each of the samples of soft glass I and of quartz, 
selecting the radius in such a way that the impressions of the stylus 
approach the effect produced by a point or needle. A small radius 
also seemed preferable from the following ulterior considerations: If the 
value of the pressure per unit of area which just produces rupture 
is a function of the radius of the lens, then the value p=1 (milli- 
meter) as compared with the above radii, must possess the particular 
importance of a unit. Experiments made with these small and highly 
convex lenses, cannot of course lead to as great a regularity of data as 
were obtained in many of the above cases; but the mean result is none 
