226 ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 
the circles of rupture are so large that for a given plate relatively few 
tests can be made. 
My first measurements, made with the sole object of verifying Hertz’s 
theory, bear directly on the truth or the degree of approximation of the 
equations (1) (2) (3) of section 2. Not until this was done was it war- 
rantable to proceed with equations (4) and (5) for the measurement of 
P, and E', (1) To test the equation, (1), ¢=const., or p/d’—const., 
many measurements were made for each of the four samples enumer- 
ated, and for increasing values of pressure. Here a few results selecte¢ 
at random from my notebook may be exhibited. 
| Glass II, p=10. | Quartz p=12. | Glass ITI, p=4. 
Aue be tie Aad a a io |b DAS 2 a 
[p]. [d]. | 1,000 [a]. [p]. [d}. | 1,000 [a]. |) [p]. [d]. | 1,000 [q]. 
: = Varo Sree le 
227| 8.9 321 754 | 12.4 396 || 854 | 10.0 854 | 
354| 10.5 306 || 1,254] 15.0 ST || 115d] 9 a0 866 
554 | 12.1 313 || 1,677 | 17.0 | 341 || 1,754| 12.6 877 
754 | 18.5 307 || 2,677| 19.6 | 356 || 2,454] 14.3 | 876 
954] 14.6 306 || 3,177] 20.5 369 || 2,479| 14.4 866 
1,354| 16.4 307 || 3,677] 21.6 368 || 
1,554 | 17.1 311 | 4,390] 23.0 359 || 
1,677| 18.0 288 || 4,800] 23.7 361 || 
1,925 | 18.7 294 || 4,887] 28.9 357 || 
3,177 | 22.1 294 || 
3,995 | 99.2 296 | | 
3,725 | 23.4 291 | | 
4,547 | 24.6 306 |) | | 
! i) 
It appears at a glance that in the third series q is constant and that 
the same is true as a first approximation in the first and second series. 
Closer scrutiny of the data reveals a gradual but slight decrease of ¢ 
in the latter cases, arbitrary fluctuations being allowed for. Thus in 
the first series the average q for the first seven observations is 310, and 
for the last six 295; in the second series similarly the mean q for the 
first five and the last four observations is 367 and 361, repectively. 
This discrepancy is accounted for by equation (5), and indicates a cor- 
responding decrease of H', that is either a gradual diminution of the 
modules H, or of Poisson’s ratio. Both conditions may plausibly be 
assumed. But since the observed march is insignificant or even quite 
absent in some of my series, it may justifiably be neglected. I shall 
therefore take g=const. throughout my work. With this understand- 
ing the probable errors of @ in the above table may be computed and 
appear as follows: 
[q] = 0.3028 + 0.0016; [q] = 0.3643 + 0.0031; [q] = 0.868 + 0.003, 
so that the mean value of q for the experiments is correct to about 
one-half per cent and the error of the quartz series does not exceed 1 
per cent. By repeating the above work a number of times the attain- 
