se, the barleycorn of our schoolboy days. It would also be a
pleasant task to investigate the properties of the gnomon of the Chinese,
Egyptians, and Peruvians, the scarphie of Eratosthenes, the astrolabe of
Hipparchus, the parallactic rules of Ptolemy, Regimontanus Purbach, and
Walther, the sextants and quadrants of Tycho Brahe, and the modifications
of these various instruments, the invention and use of which, from century
to century, bringing us at last to the telescopic age, or the days of
Lippershay, Jannsen, and Galileo.

[Illustration: FIG. 1.]

It would also be a most pleasant task to follow the evolution of our
subject in the new era of investigation ushered in by the invention of
that marvelous instrument, the telescope, followed closely by the work of
Kepler, Scheiner, Cassini, Huyghens, Newton, Digges, Nonius, Vernier,
Hall, Dollond, Herschel, Short, Bird, Ramsden, Troughton, Smeaton,
Fraunhofer, and a host of others, each of whom has contributed a noble
share in the elimination of sources of error, until to-day we are
satisfied only with units of measurement of the most exact and refined
nature. Although it would be pleasant to review the work of these past
masters, it is beyond the scope of the present paper, and even now I can
only hope to call your attention to one phase of this important subject.
For a number of years I have been practically interested in the subject of
the production of plane and curved surfaces particularly for optical
purposes, _i.e._, in the production of such surfaces free if possible from
all traces of error, and it will be pleasant to me if I shall be able to
add to the interest of this association by giving you some of my own
practical experience; and may I trust that it will be an incentive to all
engaged in kindred work _to do that work well?_

[Illustration: FIG. 2.]

In the production of a perfectly plane surface, there are many
difficulties to contend with, and it will not be possible in the limits of
this paper to discuss the methods of eliminating errors when found; but I
must content myself with giving a description of various methods of
detecting existing errors in the surfaces that are being worked, whether,
for instance, it be an error of concavity, convexity, periodic or local
error.

[Illustration: FIG. 3]

A very excellent method was devised by the celebrated Rosse, which is
frequently used at the present time; and those eminent workers, the Clarks
of Cambri