234 ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 
quartz 7), They further show a highly satisfactory degree of accord- 
ance (remembering always that this is the first attempt made to define 
hardness rigorously); for the errors lie within 1 per cent. In case of 
the individual values for glass even the extreme data lie far enough 
apart to indicate the difference of material. Nor is it remarkable that 
the value for quartz is not larger relatively to glass, seeing that all 
these bodies are closely related to each other. Indeed, I shall show 
elsewhere that quartz plates cut parallel to the axis are not harder 
than glass of average hardness. 
Inasmuch as hardness thus appears as a particular kind of tenacity, 
it is interesting to compare the results obtained with tenacities 
obtained by other and more common methods. This can at once be done 
for glass, thanks to the elaborate reserches of v. Kowalski.* I will 
therefore compare his data for Thuringian glass with the mean of my. 
values for hardness 
Tenacity of glass in kg/mm? 
"TENSION Ss eee Poe Cle wee ee eS SEE ee ee 8.8 
1 eR) 2 -<] LN ed See A ee eR ee oe Ee Re ee ees aT Soe ee 8.8 
TROT SUOMI es see em eA Lok a te 5 Se ly A ype Pen ote a 10.1 
Comipresstomee -astes a. eee See eee a ee eee eee ee eee 37.7 
Fat MES Sipe ese ey = merase ee ee eee a ee 
Hence longitudinal and flexural tenacity are about equally large, 
torsional tenacity is somewhat larger, compressional tenacity four times, 
and hardness twenty-six times as large as the first quantity. 
I shall now attempt to avail myself of equation (5) and thus obtain 
the elastic constant K' and possibly the modulus E'. 
The following values obtain for E'. 
Material. Glass I. | Glass I. |Glass III. Quartz. | 
HEPES 2edeeec ean! | 5592 | 6960 | 7764; 10 164 
i\Probable error = --| +15 | +24 445 | +18 
Now #' contains both # and jy, and these can be individually meas: 
ured only by a combination of methods; for instance, from data for 
flexure and torsion, or for longitudinal extension and radial contrac- 
tion. In view of the peculiar signification of #',it is possible to obtain 
approximate results at least, without special experiments; for /. occurs 
in #' in the form of (1— ;/), a function which does not markedly change 
even if the extreme values for ju be inserted. 
According to Cornu,t Everett, Voigt,§ Cantone, 
*V. Kowalski: ‘‘Tenacity of glass.” Wied. dnn., 1889, vol. xxxvi, p. 307. The 
older results of Wertheim are much smaller. 
tCornu: Compt. Rend., 1869, vol. LXIx, p. 333. 
¢ Everett: Phil. Trans., 1867, p. 139. 
§ Voigt: Wied. Ann., 1882, vol. xv, p. 497. 
|| Cantone: Acc. Linc., 1888, vol. Iv, pp. 220, 292. 
q Kowalski, l. ¢., p. 15. 
and v. Kowalski §[ 
