176
VI
ON HARDNESS
I first examined whether the dimensions of the surface of
pressure increased as the cube root of the pressure. To this
end a glass lens of 280 mm. radius was fastened to the lever;
the small arm of the lever measured 1140 mm., the large one
930 mm. The basis of support was a plane glass plate; the
Young's modulus was determined for a bar of the same glass
and found to be 6201 kg/mm². According to Wertheim,
Poisson's ratio for glass is 0.32, whence,K= 2349kg/mm,2
and 90005790 mm²/kg. Hence our formula gives for the
diameter of the circle of pressure in mm., d=0.3650p*, where
p is measured in kilogrammes weight. In the following
table the first row gives in kilogrammes the weight suspended
from the long arm of the lever, the second the measured
diameter of the surface of pressure in turns of the micrometer
screw of pitch 0.2737 mm. Lastly, the third row gives the
quotient d: ✔p, which should, according to the preceding, be
a constant.
8
0.4 0.6
680-81-0
p
0.2
d 1.56 2:03 2.19
3
1.5 2.0 25 30 3
3.5
2.59 2.68 3.13 3.52 3.69 3.97 4.02
d: vp 2.67 2.75 2.60 2.79 2.68 2.73 2.79 2.71 2.70 2.65
The ratio in question does indeed remain constant, apart
from irregularities, though the weights vary up to fifteen times
their initial value. To get the theoretical value of the ratio
we must divide the factor 3650 calculated above by the pitch
in millimetres of the screw, and multiply by the cube root of
the ratio of the long to the short arm of the lever; we thus
obtain 2.685, a number almost exactly coincident with 2-707,
the mean of the experimental numbers.
Secondly, I have tested the laws relating to the form of
the curve of pressure by pressing together two glass cylinders,
of equal diameter 7.37 mm., with their axes inclined at dif-
ferent angles to each other. If this angle be called w, using
former equations we get P₁ = P12 P, P21 - P220, A+B = p,
A - B -p cos w, and therefore the auxiliary angle = w
Hence if we determine the large and small axes of the ellipse
of pressure for one and the same pressure but different inclina-
=
=