position of eyepiece when used the
with the plane. When the plane is not in the way, the converging beam goes
back to the eyepiece, _c_. When the plane, _d_, is introduced, the beam is
turned at a right angle, and if it is a perfect surface, not only does the
focal plane remain exactly of the same length, but the expanded star
disks, are similar on either side of the focal plane.

[Illustration: FIG. 9.]

I might go on to elaborate this method, to show how it may be made still
more exact, but as it will come under the discussion of spherical
surfaces, I will leave it for the present. Unfortunately for this process,
it demands a large truly spherical surface, which is just as difficult of
attainment as any form of regular surface. We come now to an instrument
that does not depend upon optical means for detecting errors of surface,
namely, the spherometer, which as the name would indicate means sphere
measure, but it is about as well adapted for plane as it is for spherical
work, and Prof. Harkness has been, using one for some time past in
determining the errors of the plane mirrors used in the transit of Venus
photographic instruments. At the meeting of the American Association of
Science in Philadelphia, there was quite a discussion as to the relative
merits of the spherometer test and another form which I shall
presently mention, Prof. Harkness claiming that he could, by the
use of the spherometer, detect errors bordering closely on one
five-hundred-thousandth of an inch. Some physicists express doubt on this,
but Prof. Harkness has no doubt worked with very sensitive instruments,
and over very small areas at one time.

I have not had occasion to use this instrument in my own work, as a more
simple, delicate, and efficient method was at my command, but for one
measurement of convex surfaces I know of nothing that can take its place.
I will briefly describe the method of using it.

[Illustration: FIG. 10.]

The usual form of the instrument is shown in Fig. 4; _a_ is a steel screw
working in the nut of the stout tripod frame, _b_; _c c c_ are three legs
with carefully prepared points; _d_ is a divided standard to read the
whole number of revolutions of the screw, _a_, the edge of which also
serves the purpose of a pointer to read off the division on the top of the
milled head, _e_. Still further refinement may be had by placing a vernier
here. To measure a plane or curved surface with this instrument, a perfect
pla