- 7 m7. hi sig Wr tq me 
4 —— sy 
a ee 
216 -ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 
tities inclosed are not expressed in the absolute units given, but in 
some convenient relative measure. Hence, the following formule are 
under consideration : 
for the same p and H!: 
d 
a? 
——-=const., and —=const.,alsoqg=const., . . (2). 
p 
By Vp 
This constant quantity must also be identical with Q. Hence, for 
the same p and E', p:/*Vp»=const. For a different value of p, but a 
given value of LH’, 
d/> Vp» p=const.,and pq=const. . . . . . (2). 
For different values of both p and EH’, 
> Zp p ‘HOP p 
d= | = “a Pond D= Sar 
For different values of p and a given value of EH’, 
P 
Em 
eae ery aay 2 
P= const., or J p=ooust., 
v 
D =CONSL.; ) . 
. — 
three equations which are merely different expression of a common 
inherent relation. Finally for given values of p and 2H’, the theoretical 
hardness has the form 
SOUP EA ie pepe, 
ane ; 
and the elastic constant 4’, the form 
Hi! =12 0.9. «4s ed =: 
Ill. METHOD. 
[t appears from the foregoing equations that to compute hardness 
by aid of the phenomenon of contact between a sphere and a plane of 
a given body the total pressure under which contact takes place is to 
be increased up to the elastic limits. The time of yielding being 
