[Footnote 3: A paper read before the Engineers' Society of Western
Pennsylvania, Dec. 10, 1884.]
By JOHN A. BRASHEAR.
In our study of the exact methods of measurement in use to-day, in the
various branches of scientific investigation, we should not forget that it
has been a plant of very slow growth, and it is interesting indeed to
glance along the pathway of the past to see how step by step our micron of
to-day has been evolved from the cubit, the hand's breadth, the span, and,
if you please, 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 Cambridge, use a modification of the Rosse method which in their hands
is productive of the very highest results. The device is very simple,
consisting of a telescope (_a_, Fig. 1) in which aberrations have been
well corrected, so that the focal plane of the objective is as sharp as
possible. This telescope is first directed to a distant object, preferably
a celestial one, and focused for parallel rays. The surface, _b_, to be
tested is now placed so that the reflected image of the same object,
whatever it may be, can be observed by the same telescope. It is evident
that if the surface be a true plane, its action upon the beam of light
that comes from the object will be simply to change its direction, but not
disturb or change it any other way, hence the reflected image of the
object should be seen by the telescope, _a_, without in any way changing
the original focus. If, however, the supposed plane surface proves to be
_convex_, the image will not be sharply defined in the telescope until the
eyepiece is moved _away_ from the object glass; while if the converse is
the case, and the supposed plane is concave, the eyepiece must now be
moved _toward_ the objective in order to obtain a sharp image, and the
amount of convexity or concavity may be known by the change in the focal
plane. If the surface has periodic or irregular errors, no sharp image can
be obtained, no matter how much the eyepiece may be moved in or out.
[Illustration: FIG. 4]
This test may be made still more delicate by using the observing
telescope, _a_, at as low an angle as possible, thereby bringing out with
still greater effect any error that may exist in the surface under
examination, and is the plan generally used by Alvan Clark & Sons. Another
and very excellent method is that illustrated in Fig. 2, in which a second
telescope, _b_, is introduced. In place of the eyepiece of this second
telescope, a diaphragm is introduced in which a number of small holes are
drilled, as in Fig. 2, _x_, or a slit is cut similar to the slit used in a
spectroscope as shown at _y_, same figure. The telescope, _a_, is now
focused very accurately on a celestial or other very distant object, and
the focus marked. The object glass of the telescope, _b_, is now placed
against and "square" with the object glass of telescope _a_, and on
looking through telescope a an image of the diaphragm with its holes or
the slit is seen. This diaphragm must now be moved until a sharp image is
seen in telescope _a_. The two telescopes are now mounted as in Fig. 2,
and the plate to be tested placed in front of the two telescopes as at
_c_. It is evident, as in the former case, that if the surface is a true
plane, the reflected image of the holes or slit thrown upon it by the
telescope, _b_, will be seen sharply defined in the telescope, _a_.
[Illustration: FIG. 5.]
If any error of convexity exists in the plate, the focal plane is
disturbed, and the eyepiece must be moved _out_. If the plate is concave,
it must be moved _in_ to obtain a sharp image. Irregular errors in the
plate or surface will produce a blurred or indistinct image, and, as in
the first instance, no amount of focusing will help matters. These methods
are both good, but are not satisfactory in the highest degree, and two or
three important factors bar the way to the very best results. One is that
the aberrations of the telescopes must be perfectly corrected, a very
difficult matter of itself, and requiring the highest skill of the
optician. Another, the fact that the human eye will accommodate itself to
small distances when setting the focus of the observing telescope. I have
frequently made experiments to find out how much this accommodation was in
my own case, and found it to amount to as much as 1/40 of an inch. This is
no doubt partly the fault of the telescopes themselves, but unless the eye
is rigorously educated in this work, it is apt to accommodate itself to a
small amount, and will invariably do so if there is a preconceived notion
or bias _in the direction of the accommodation_.
[Illustration: FIG. 6.]
Talking with Prof. C.A. Young a few months since on this subject, he
remarked that he noticed that the eye grew more exact in its demands as it
grew older, in regard to the focal point. A third and very serious
objection to the second method is caused by diffraction from the edges of
the holes or the slit. Let me explain this briefly. When light falls upon
a slit, such as we have here, it is turned out of its course; as the slit
has two edges, and the light that falls on either side is deflected both
right and left, the rays that cross from the right side of the slit toward
the left, and from the left side of the slit toward the right, produce
interference of the wave lengths, and when perfect interference occurs,
dark lines are seen. You can have a very pretty illustration of this by
cutting a fine slit in a card and holding it several inches from the eye,
when the dark lines caused by a total extinction of the light by
interference may be seen.
[Illustration: FIG. 7.]
If now you look toward the edge of a gas or lamp flame; you will see a
series of colored bands, that bring out the phenomenon of partial
interference. This experiment shows the difficulty in obtaining a perfect
focus of the holes or the slit in the diaphragm, as the interference
fringes are always more or less annoying. Notwithstanding these defects of
the two systems I have mentioned, in the hands of the practical workman
they are productive of very good results, and very many excellent surfaces
have been made by their use, and we are not justified in ignoring them,
because they are the stepping stones to lead us on to better ones. In my
early work Dr. Draper suggested a very excellent plan for testing a flat
surface, which I briefly describe. It is a well known truth that, if an
artificial star is placed in the exact center of curvature of a truly
spherical mirror, and an eyepiece be used to examine the image close
beside the source of light, the star will be sharply defined, and will
bear very high magnification. If the eyepiece is now drawn toward the
observer, the star disk begins to expand; and if the mirror be a truly
spherical one, the expanded disk will be equally illuminated, except the
outer edge, which usually shows two or more light and dark rings, due to
diffraction, as already explained.
[Illustration: FIG. 8.]
Now if we push the eyepiece toward the mirror the same distance on the
opposite side of the true focal plane, precisely the same appearance will
be noted in the expanded star disk. If we now place our plane surface any
where in the path of the rays from the great mirror, we should have
identically the same phenomena repeated. Of course it is presumed, and is
necessary, that the plane mirror shall be much less in area than the
spherical mirror, else the beam of light from the artificial star will be
shut off, yet I may here say that any one part of a truly spherical mirror
will act just as well as the whole surface, there being of course a loss
of light according to the area of the mirror shut off.
This principle is illustrated in Fig. 3, where _a_ is the spherical
mirror, _b_ the source of light, _c_ the eyepiece as used when the plane
is not interposed, _d_ the plane introduced into the path at an angle of
45° to the central beam, and _e_ the 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
plane or perfect spherical surface of known radius must be used to
determine the zero point of the division. Taking for granted that we have
this standard plate, the spherometer is placed upon it, and the readings
of the divided head and indicator, _d_, noted when the point of the screw,
_a_, just touches the surface, _f_. Herein, however, lies the great
difficulty in using this instrument, _i.e._, to know the exact instant of
contact of the point of screw, _a_, on the surface, _f_. Many devices have
been added to the spherometer to make it as sensitive as possible, such as
the contact level, the electric contact, and the compound lever contact.
The latter is probably the best, and is made essentially as in Fig. 5.
[Illustration: FIG. 11.]
I am indebted for this plan to Dr. Alfred Mayer. As in the previous
figure, _a_ is the screw; this screw is bored out, and a central steel pin
turned to fit resting on a shoulder at _c_. The end of _d_ projects below
the screw, _a_, and the end, _e_, projects above the milled head, and the
knife edge or pivot point rests against the lever, _f_, which in turn
rests against the long lever, _g_, the point, _h_, of which moves along
the division at _j_. It is evident that if the point of the pin just
touches the plate, no movement of the index lever, _g_, will be seen; but
if any pressure be applied, the lever will move through a multiplied arc,
owing to the short fulcri of the two levers. Notwithstanding all these
precautions, we must also take into account the flexure of the material,
the elasticity of the points of contact, and other idiosyncrasies, and you
can readily see that practice alone in an instrument so delicate will
bring about the very best results. Dr. Alfred Mayer's method of getting
over the great difficulty of knowing when all four points are in contact
is quite simple. The standard plate is set on the box, _g_, Fig. 4, which
acts as a resonater. The screw, _a_, is brought down until it touches the
plate. When the pressure of the screw is enough to lift off either or all
of the legs, and the plate is gently tapped with the finger, a _rattle_ is
heard, which is the tell-tale of imperfect contact of all the points. The
screw is now reversed gently and slowly until the _moment_ the rattle
ceases, and then the reading is taken. Here the sense of hearing is
brought into play. This is also the case when the electric contact is
used. This is so arranged that the instant of touching of the point of
screw, _a_, completes the electric circuit, in which an electromagnet of
short thick wire is placed. At the moment of contact, or perhaps a little
before contact, the bell rings, and the turning of the screw must be
instantly stopped. Here are several elements that must be remembered.
First, it takes time to set the bell ringing, time for the sound to pass
to the ear, time for the sensation to be carried to the brain, time for
the brain to send word to the hand to cease turning the screw, and, if you
please, it takes time for the hand to stop. You may say, of what use are
such refinements? I may reply, what use is there in trying to do anything
the very best it can be done? If our investigation of nature's profound
mysteries can be partially solved with good instrumental means, what is
the result if we have better ones placed in our hands, and what, we ask,
if the _best_ are given to the physicist? We have only to compare the
telescope of Galileo, the prism of Newton, the pile of Volta, and what was
done with them, to the marvelous work of the telescope, spectroscope, and
dynamo of to-day. But I must proceed. It will be recognized that in
working with the spherometer, only the points in actual contact can be
measured at one time, for you may see by Fig. 6 that the four points, _a a
a a_, may all be normal to a true plane, and yet errors of depression, as
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
beautiful diffraction gratings now so well known over the scientific
world, as also other plane surfaces for heliostats, etc., etc. I am now
approaching the border land of what may be called the abstruse in science,
in which I humbly acknowledge it would take a vast volume to contain all I
don't know; yet I hope to make plain to you this most beautiful and
accurate method, and for fear I may forget to give due credit, I will say
that I am indebted to Dr. Hastings for it, with whom it was an original
discovery, though he told me he afterward found it had been in use by
Steinheil, the celebrated optician of Munich. The principle was discovered
by the immortal Newton, and it shows how much can be made of the ordinary
phenomena seen in our every-day life when placed in the hands of the
investigator. We have all seen the beautiful play of colors on the soap
bubble, or when the drop of oil spreads over the surface of the water.
Place a lens of long curvature on a piece of plane polished glass, and,
looking at it obliquely, a black central spot is seen with rings of
various width and color surrounding it. If the lens is a true curve, and
the glass beneath it a true plane, these rings of color will be perfectly
concentric and arranged in regular decreasing intervals. This apparatus is
known as Newton's color glass, because he not only measured the phenomena,
but established the laws of the appearances presented. I will now endeavor
to explain the general principle by which this phenomenon is utilized in
the testing of plane surfaces. Suppose that we place on the lower plate,
lenses of constantly increasing curvature until that curvature becomes
nil, or in other words a true plane. The rings of color will constantly
increase in width as the curvature of the lens increases, until at last
one color alone is seen over the whole surface, provided, however, the
same angle of observation be maintained, and provided further that the
film of air between the glasses is of absolutely the same relative
thickness throughout. I say the film of air, for I presume that it would
be utterly impossible to exclude particles of dust so that absolute
contact could take place. Early physicists maintained that absolute
molecular contact was impossible, and that the central separation of the
glasses in Newton's experiment was 1/250,000 of an inch, but Sir Wm.
Thomson has shown that the separation is caused by shreds or particles of
dust. However, if this separation is equal throughout, we have the
phenomena as described; but if the dust particles are thicker under one
side than the other, our phenomena will change to broad parallel bands as
in Fig. 8, the broader the bands the nearer the absolute parallelism of
the plates. In Fig. 7 let _a_ and _b_ represent the two plates we are
testing. Rays of white light, _c_, falling upon the upper surface of plate
_a_, are partially reflected off in the direction of rays _d_, but as
these rays do not concern us now, I have not sketched them. Part of the
light passes on through the upper plate, where it is bent out of its
course somewhat, and, falling upon the _lower_ surface of the upper plate,
some of this light is again reflected toward the eye at _d_. As some of
the light passes through the upper plate, and, passing through the film of
air between the plates, falling on the upper surface of the _lower_ one,
this in turn is reflected; but as the light that falls on this surface has
had to traverse the film of air _twice_, it is retarded by a certain
number of half or whole wave-lengths, and the beautiful phenomena of
interference take place, some of the colors of white light being
obliterated, while others come to the eye. When the position of the eye
changes, the color is seen to change. I have not time to dwell further on
this part of my subject, which is discussed in most advanced works on
physics, and especially well described in Dr. Eugene Lommel's work on "The
Nature of Light." I remarked that if the two surfaces were perfectly
_plane_, there would be one color seen, or else colors of the first or
second order would arrange themselves in broad parallel bands, but this
would also take place in plates of slight curvature, for the requirement
is, as I said, a film of air of equal thickness throughout. You can see at
once that this condition could be obtained in a perfect convex surface
fitting a perfect concave of the same radius. Fortunately we have a check
to guard against this error. To produce a perfect plane, _three surfaces
must_ be worked together, unless we have a true plane to commence with;
but to make this true plane by this method we _must_ work three together,
and if each one comes up to the demands of this most rigorous test, we may
rest assured that we have attained a degree of accuracy almost beyond
human conception. Let me illustrate. Suppose we have plates 1, 2, and 3,
Fig. 11. Suppose 1 and 2 to be accurately convex and 3 accurately concave,
of the same radius. Now it is evident that 3 will exactly fit 1 and 2, and
that 1 and 2 will separately fit No. 3, _but_ when 1 and 2 are placed
together, they will only touch in the center, and there is no possible
way to make three plates coincide when they are alternately tested upon
one another than to make _perfect planes_ out of them. As it is difficult
to see the colors well on metal surfaces, a one-colored light is used,
such as the sodium flame, which gives to the eye in our test, dark and
bright bands instead of colored ones. When these plates are worked and
tested upon one another until they all present the same appearance, one
may be reserved for a test plate for future use. Here is a small test
plate made by the celebrated Steinheil, and here two made by myself, and I
may be pardoned in saying that I was much gratified to find the
coincidence so nearly perfect that the limiting error is much less than
0.00001 of an inch. My assistant, with but a few months' experience, has
made quite as accurate plates. It is necessary of course to have a glass
plate to test the metal plates, as the upper plate _must_ be transparent.
So far we have been dealing with perfect surfaces. Let us now see what
shall occur in surfaces that are not plane. Suppose we now have our
perfect test plate, and it is laid on a plate that has a compound error,
say depressed at center and edge and high between these points. If this
error is regular, the central bands arrange themselves as in Fig. 9. You
may now ask, how are we to know what sort of surface we have? A ready
solution is at hand. The bands _always travel in the direction of the
thickest film of air_, hence on lowering the eye, if the convex edge of
the bands travel in the direction of the arrow, we are absolutely certain
that that part of the surface being tested is convex, while if, as in the
central part of the bands, the concave edges advance, we know that part is
hollow or too low. Furthermore, any small error will be rigorously
detected, with astonishing clearness, and one of the grandest qualities of
this test is the absence of "personal equation;" for, given a perfect test
plate, _it won't lie_, neither will it exaggerate. I say, won't lie, but I
must guard this by saying that the plates must coincide absolutely in
temperature, and the touch of the finger, the heat of the hand, or any
disturbance whatever will vitiate the results of this lovely process; but
more of that at a future time. If our surface is plane to within a short
distance of the edge, and is there overcorrected, or convex, the test
shows it, as in Fig. 10. If the whole surface is regularly convex, then
concentric rings of a breadth determined by the approach to a perfect
plane are seen. If concave, a similar phenomenon is exhibited, except in
the case of the convex, the broader rings are near the center, while in
the concave they are nearer the edge. In lowering the eye while observing
the plates, the rings of the convex plate will advance outward, those of
the concave inward. It may be asked by the mechanician, Can this method be
used for testing our surface plates? I answer that I have found the
scraped surface of iron bright enough to test by sodium light. My
assistant in the machine work scraped three 8 inch plates that were tested
by this method and found to be very excellent, though it must be evident
that a single cut of the scraper would change the spot over which it
passed so much as to entirely change the appearance there, but I found I
could use the test to get the general outline of the surface under process
of correction. These iron plates, I would say, are simply used for
preliminary formation of polishers. I may have something to say on the
question of surface plates in the future, as I have made some interesting
studies on the subject. I must now bring this paper to a close, although I
had intended including some interesting studies of curved surfaces. There
is, however, matter enough in that subject of itself, especially when we
connect it with the idiosyncrasies of the material we have to deal with, a
vital part of the subject that I have not touched upon in the present
paper. You may now inquire, How critical is this "color test"? To answer
this I fear I shall trench upon forbidden grounds, but I call to my help
the words of one of our best American physicists, and I quote from a
letter in which he says by combined calculation and experiment I have
found the limiting error for white light to be 1/50000000 of an inch, and
for Na or sodium light about fifty times greater, or less than 1/800000 of
an inch. Dr. Alfred Mayer estimated and demonstrated by actual experiment
that the smallest black spot on a white ground visible to the naked eye is
about 1/800 of an inch at the distance of normal vision, namely, 10
inches, and that a line, which of course has the element of extension,
1/5000 of an inch in thickness could be seen. In our delicate "color test"
we may decrease the diameter of our black spot a thousand times and still
its perception is possible by the aid of our monochromatic light, and we
may diminish our line ten thousand times, yet find it just perceivable on
the border land of our test by white light. Do not presume I am so foolish
as to even think that the human hand, directed by the human brain, can
ever work the material at his command to such a high standard of
exactness. No; from the very nature of the material we have to work with,
we are forbidden even to hope for such an achievement; and could it be
possible that, through some stroke of good fortune, we could attain this
high ideal, it would be but for a moment, as from the very nature of our
environment it would be but an ignis fatuus. There is, however, to the
earnest mind a delight in having a high model of excellence, for as our
model is so will our work approximate; and although we may go on
approximating _our_ ideal forever, we can never hope to reach that which
has been set for us by the great Master Workman.
* * * * *
[JOURNAL OF GAS LIGHTING.]