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