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ON THE ABSOLUTE MEASUREMENT OF HARDNESS. 223 
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the observed load at the end of the lever (including of course the weight 
both of the stirrup & and the pan) is to be multiplied by 9.8. Thus 
the values of spot diameter and total pressure are reduced to absolute 
units. 
The third elass of constants are the lens curvatures, purposely 
varied in different experiments. I did not attempt to find them, how- 
ever, for I was able to avail myself of the values of the mechanician in 
charge, who, in addition to the chief datum, also supplied me with 
the errors probably made in their manufacture. These errors never 
exceeded 0.1", and were even smaller than this for smaller curvatures, 
Another important question may be alluded to here. It does not 
follow at once that the diameter of the black spot measured in the field 
of the telescope actually coincides with the area of contact. The ques- 
tion relative to the correction to be applied is to be looked at from four 
points of view: (1) It is known that in case of Newton’s rings, light is 
not only extinguished throughout the area of contact, but throughout 
a somewhat wider margin to a point at which the vertical distance 
between plate and lens is about + wave length (say), depending on 
the intensity ofthe illumination. The spot is therefore to this extent 
lerger than the area of contact. Now, it would be possible to compute 
this correction from the data theoretically given for the curvature of 
the area of contact in a way sufficient for all possible cases; and this 
has been done. It is much simpler, however, and more free from 
assumptions which need not be detailed here, to refer such measure- 
ments to the first of the rings surrounding the black spot. For the 
position of the ring is such that the vertical distance between plate 
and lens is necessarily § wave length. Now, since the area of contact 
is always very small, the curvature of contiguous parts may be neg- 
lected. Hence the correction to be applied [deducted] is 4 of the 
distance of the first ring from the edge of the spot, meaning, of course, 
the true edge. In other words, the correction is one-half the distance, 
é, between the first ring and the apparent edge of the spot; and since 
this correction (§ €) is to be deducted from both ends of the diameter 
d, the full correction is ¢, or the true diameter of the area of contact is 
d-e. It isadvisable, therefore (other considerations willappear below), 
to construct a table in which for any given substance the correction 
may be taken at once as a function of the pressure applied and the 
curvature of the lens used. For practical purposes, moreover, an 
approxunate table, in which the correction is mapped out as a function 
of spot-diameter and lens-curvature, p;, will in most cases be sufficient, 
no matter what the substance may be. Such a table may here be 
inserted, spot-diameters, d, being given in scale parts, and the cor- 
rection in ;\; seale parts of the ocular micrometer. 
