at _e_, or elevation, as at _b_, exist between them, so that the
instrument must be used over every available part of the surface if it is
to be tested rigorously. As to how exact this method is I cannot say from
actual experience, as in my work I have had recourse to other methods that
I shall describe. I have already quoted you the words of Prof. Harkness.
Dr. Hastings, whose practical as well as theoretical knowledge is of the
most critical character, tells me that he considers it quite easy to
measure to 1/80000 of an inch with the ordinary form of instrument. Here
is a very fine spherometer that Dr. Hastings works with from time to time,
and which he calls his standard spherometer. It is delicately made, its
screw being 50 to the inch, or more exactly 0.01998 inch, or within
2/100000 of being 1/50 of an inch pitch. The principal screw has a point
which is itself an independent screw, that was put in to investigate the
errors of the main screw, but it was found that the error of this screw
was not as much as the 0.00001 of an inch. The head is divided into two
hundred parts, and by estimation can be read to 1/100000 of an inch. Its
constants are known, and it may be understood that it would not do to
handle it very roughly. I could dwell here longer on this fascinating
subject, but must haste. I may add that if this spherometer is placed on a
plate of glass and exact contact obtained, and then removed, and the hand
held over the plate without touching it, the difference in the temperature
of the glass and that of the hand would be sufficient to distort the
surface enough to be readily recognized by the spherometer when replaced.
Any one desiring to investigate this subject further will find it fully
discussed in that splendid series of papers by Dr. Alfred Mayer on the
minute measurements of modern science published in SCIENTIFIC AMERICAN
SUPPLEMENTS, to which I was indebted years ago for most valuable
information, as well as to most encouraging words from Prof. Thurston,
whom you all so well and favorably know. I now invite your attention to
the method for testing the flat surfaces on which Prof. Rowland rules the