¢ 7 
228 ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 
Quartz, values of q. 
| il ae 
p=1 + p=4 p—12 + p=12 = 
we -— nb hs Raps 
SO3e Vil eee es. DiGi ere We etO sone |= see Til, Oak eee 
S48) Flee sen PAU Tey | ease Gono Lea 70.9 Peas. 
ehary eee Bb lee, ae (eet oi ees ee eet |, ee 
ln GD > veil leeee pce Pa al Raaee eas WG Tva0 gale et (OBO Wiese ater 
ECOG Beeree ae P10 Wena Vcc Oed alll ans est 72.0 Cee 
|e | ail BEE) SES | 
846 4 212.2 | 1.2 | Mean value = ROGAS i OS9, 
| | 
(2) The following data are sufficient to verify equation (2), viz, pg—const. 
| (| p= ie 2! 12 
Glass T2--4| og || 488 9) 118.5) 89,1202. | : no eased 
| pq= 463 | 466 469 ase Serepe 
y= 3 5 10 1D 
GlassII..4/ q= | 195.4] 1149] 583) 38.3 /$ pg= | 58022 
| p= | 586 575 583 575 
(| ae 4 12 BOS terciericcies 
| Glass TII.4| g= KBE | SGBEO) || SPaRE SI ee ee |S pg= 647 44 
area 650 | 636 654. | Sagara: 
(| p 1 4 [Dic ti eee ae 
Quartz.) g—= .| 846° |) gio! “Wea  pg= | 84741 
| p= 846...) 6849) 9) 45 ol arcs | | 
(5) It is now only necessary to prove the equations (3), The data for 
P vary between 4 and 140 kilograms, an interval which in comparison 
with the small areas of contact encountered is strikingly large. In the 
vase of different experiments made under the same conditions, 7. é., for 
values all corresponding to the same material and the same lens curva- 
ture, P varies pronouncedly, as the following example shows. The series 
is again chosen at random and represents an unfavorable case, for the 
probable error of the mean result is fully 34 per cent. 
Glass IIL 
p—4 
18. 2 
0. 48 
19: 2 
0.48 
Mean value, P=20.3 +-0.7. 
Now, it is to be observed (1) that at large value of P is usually ecor- 
related with a large value of D), and therefore also corresponds to a 
smaller q, thus the fluctuations are in part rectified; (2) thatin the final 
equation (4) the cube root of P only enters, so that all errors are reduced 
as 1 to 3. 
Quite an unexpected result is reached, however, when the data for dif- 
ferent lens curvatures are compared. The equations (3) are not corrob- 
vrated, not even approximately, though it would not be difficult to find 
acorrectedterm. Thus, for instance, in case of the glass II the data are: 
