VI
177
ON HARDNESS
tions, divide the major axes by the function μ belonging to
the inclination used and the minor axes by the corresponding
function v, the quotient of all these divisions must be one and
the same constant, namely, the quantity 2(3p9/8p)*. The
following table gives in the first column the inclination w in
degrees, in the next two the values of 2 a and 2 b as measured
in parts of the scale of the micrometer eye-piece, of which
96 equal one millimetre, and in the last two the quotients 2a/μ
and 2b/v-
3
2 a
26
2 a
26
μ
90
40.6
40.6
40.6
40.6
80
45.4
36.6
40.2
41.0
70
52.8
31.0
41.3
38.7
60
59.6
27.6
40.0
38.5
50
72.2
26.4
41.2
41.2
40
90.4
23.8
42.2
42.0
30
110.0
21.0
40.3
42.6
20
156.2
18.4
41.3
45.3
10
274.6
15.0
41.6
47.0
The quotients are fairly constant, excepting those for the
minor axes at small inclinations. But at such an inclination
it is extremely difficult to bring the cylinders together so as
to make the common tangent plane exactly horizontal; and in
any other position a slight slipping of one cylinder on the
other occurs, which unduly magnifies the minor axis. In all
these measurements the pressure was 12 kg. weight. Taking
for the value 0005790 already used, we get from the given
values the value of the constant to be 40.80, which agrees
almost exactly with 40.97, the mean resulting from the values
for a; whilst it differs slightly, for the reasons explained, from
41.88, the mean resulting from the value for b.
Lastly, I have attempted to examine the effect of the
moduli of elasticity by pressing a steel lens against planes of
different metals. But here I encountered difficulties in the
observation. In the first place, it is not so easy to obtain
quite plane and smooth surfaces as for glass; secondly, the
metallic surfaces cannot so easily be covered with lamp-black;
thirdly, we have to confine ourselves to very small pressures
M. P.
N