son Wigs Sy 
224 ON THE ABSOLUTE MEASUREMENT OF HARDNESS. Bi 
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(2) The astigmatic aberration of the image observed through the plate 
is next to be considered. In view of the small angular deviation of the 
lines of sight, the error in question will never exceed one-tenth per cent 
of the observed value, unless, indeed, the observations are made near 
the circumference of the field of view. This is quite unnecessary and 
should not be done. 
(3) Another negligible error is introduced by the fact that the ob- 
served spot is a horizontal projection of the curved area ot contact. 
Even in the case of my most convex lenses and the highest pressure 
admissible, the effect of the difference of area of the actual surface and 
its projection will not exceed 2 in 1,000. 
(4) Finally the flexure of the test plate p, which under the cireum- 
stances is converted into a concave lens, may be adduced. <A correction 
of this kind would be appreciable, if the object to be observed were 
situated at an appreciable distance below thelens. This state of things 
can not be at once dismissed, for the locus of the circumference of the 
spot is at a place where the plate and the lens no longer touch each 
other, as has just been indicated. In other words, the question contein- 
plates the actual position of the locus or seat of interference. Divers 
experiments which I made with special reference to this discrepancy 
proved however that the present source of error is not of greater - 
moment than the preceding. 
VII. THE THEORY TESTED. 
The materials to which I confined my present experiments were glass 
and quartz. The glass was obtained from the well-known house of 
Schott & Gen, and the three samples furnished were marked I (rather 
soft), II (of mean hardness), and III (rather hard). The mere fact that 
I was thus able to avail myself of three degrees of hardness of one and 
the same substance lent a peculiar interest to the tests, for the differ- 
ences of hardness in question could not in any case be very marked, 
and the tests would therefore contain an immediate indication of the 
sensitiveness of my method. In addition to these substances I also 
worked with a plate of quartz (IV) eut at right angles to the crystallo- 
graphic axis. Here, as well as in the case of the glass (1, LH, III), the 
lens and plate were cut from one and the same substance in each case. 
