212 ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 
tually ruptured at the point of observation. At the time and place of 
measurement the body necessarily differs from the original body. Thus 
it appears that the results of such methods are not available. 
With the object of corroborating the above rewarks I will exhibit two 
typical series of data from the papers of Franz and of Pfaff (the latter 
obtained by means of the meso-sklerometer already referred to), choos- 
ing such substances as are sufficiently definite for comparison. In the 
first table the numbers for gypsum are made identical; in the second 
the same is done for corundum, the respective ratios being retained in 
both cases. 
Gypsum identically hard. Corundum identically hard. 
Body. | Franz.| Pfaff. | Ratio. | Body. Franz.| Pfatf. | Ratio. 
Cry P SUT eset | 6 | 6 1 Corundimisss--eee-eee ee 340 | 340 120 
Caleiten sched Nace he Soe 36 8 NEG) |i) ANOHEA Ge Sector cn2 oaasc- 298 240 nL 2) 
MUMOrite 27 22s eee ee 144 | 20 7 Quantiveesess. ose ee 228 | 160 1.4 
WMontifewn se ao-sece poset Goo 38) 15 Reldsparts: s25205 ee | -184-| © q05y| eae 
INGIGI Ie Googe soe caaes 1, 040 TNs |/t) APabIter = v2. = =see Ea ee | 84 38 2.2 
Queries mee ae IA77O' une 160n| Molin wee ete bas tates ee | fis 20.9 
AUG NAG Ge Gr Gann eceaae oe 2, 230 240 9 Calcitess eee aries 5 8 0.6 
Cormndum qo ese sae =o 2, 650 340 8 Gy PSUMyjs2=~ 2 Se 32 see 1 6 0.2 
Mere inspection of the table shows that the ratios of hardness* 
run as high as 15 in the first table, and fluctuate between 2.2 and 0.2 
in the second. 
It has already been stated that Hertzt investigated a definition of 
hardness which is mathematically exact, and which does not conflict 
with the prevailing notions of the quality. He replaces the indefinite 
point by a definite spherical surface; or, to state this more correctly, 
since the point is after all a spherical surface of very small radius, 
Hertz uses a stylus with a radius of curvature large enough to be 
measurable. Moreover, the material out of which the stylus (now a 
ball) is to be made, virtually does not at all enter into the problem. A 
body may therefore be tested for hardness by aid of a probe made of 
its own substance and the result is in no way dependent on vague 
properties of a foreign body. Finally, the body to be examined is not 
subjected to any permanent strain (set), but all operations are con- 
ducted within the limits of elasticity. The definition of hardness 
thus obtained takes the following general form: Hardness is the limit- 
ing elastic resistance (tenacity) of a body, in case of contact of one of 
its plane surfaces with the spherical surface of another body, thus 
all vagueness of conception has been removed, and hardness is tersely 
* Similarly enormous variations of the ratios for metals may be obtained from the 
series of Bottone and Hugueny (Cu—100, Ni—104 to 58, Pt—81 to 150, Pb—42 to 
9, etc). 
tHertz: Verh, Berl. phys. Ges., 1882, p. 67; Verh. d. Ver. z. F. d., Gewerbefl,, 1882, 
p. 441. 
