ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 235 
the values of jy for glass lie between 0.208 and 0.264, and for these 
extremes the values of (1— 2) are 0.957 and 0.930, respectively. Fur- 
thermore, the mean value and probable error of j« will, in consideration 
of the weights of the individual measurements, be “~=0.225-+ 0.008, and 
therefore, 
(1 — 2) = 0.949 + 0.003. 
Hence the error would be no larger than one-third per cent, but for the 
fact that j is only given for very small strains. In case of marked 
deformation j, according to Réntgen* and others, is smaller; and when 
} b4 = 5 7 y] 
the body is incompressible (where ;.= 0.5), the decrease in question is 
y } ’ 1 
pronounced. These extreme conditions are without relevancy in the 
present case, and, proceeding from analogy, I shall put 
(1— 2) = 0.97 + 0.01, 
so that the probable error is 1 per cent. Hence to compute FH it is 
merely necessary to deduct 5 per cent from #', whence 
| Material. | Glass, I. \etasas IL,| Glass, IIT.| 
The elasticity of different glasses is therefore subject to large varia- 
tions, and it is scarcely possible to make a detailed comparison with 
the results of other observers, as long as the character of the glass in 
question is not definitely specified. In how far my results are in keep- 
ing with such value may be gathered, in a general way, from the follow- 
ing interesting table: 
Substance. | Observer. 10 all Substance. | Observer. E. 
ee = aes 
DOL PIASS == ones. | Auerbach. ---- Sone 5424 || Plate glass.....-..-.| Wertheim .......- | 7015 
Crystal, contain- Wertheim! ....... 5477 || Plate glass, Rhen- | Voigt-.-.......--- | 7358 
ing Pb. | ish. | 
Greenish glass..----- WO Gar ebcnadeansao 6480 Glass of Furth... --- Ps cheidlsase= see 7427 
Thuringian glass .-.-..| v. Kowalski3-.-.-- 6702 || Belgian glass ..--... iPscheidl= assesses 7493 
Half hard glass. ----- | Auerbach......--- G751)||\PHardicliss=.-.-2--< Amerbach...--..-.. 7531 
[Oss \ CRS Se oe ee Wertheim .....--. | 6890 || Bohemian glass...-.) Pscheidl.......--- | 7550 
Plate slass.-.......-. | Pscheidl* =. <---..- 6920 || Window glass ......| Wertheim ......-.. | 7917 
‘Wertheim and Chevandier: Compt. Rend., 1845, vol. xx, p. 1637. 
“Voigt: Wied. Ann., 1882, vol. xv, p. 497. 
3v. Kowalski: l. ¢., p. 10. 
4Pscheidl: Wiln. Ber., 1877, vol. lxxix, p. 114; 1882, vol. lxxxvi, p. 115. 
It is my purpose to carry out a comparison of this kind systematic. 
ally, by testing both the modulus of elasticity and the hardness of a great 
variety of glasses. 
Roéntgen: Poge. Ann., 1876, vol. CLIX. p. 601, 
