of using such otherwise valueless mirrors put in practice as above
stated, chance brought a letter of Maskelyne to my notice. He says,
“I hit upon an extraordinary experiment which greatly improved the
performance of the six-feet reflector”.... It was one made by Short.
“As a like management may improve many other telescopes, I shall here
relate it: I removed the great speculum from the position it ought to
hold perpendicular to the axis of the tube when the telescope is said
to be rightly adjusted, to one a little inclined to the same and found
a certain inclination of about 2-1/2° (as I found by the alteration of
objects in the finer one of Dollond’s best night glasses with a field
of 6°), which caused the telescope to show the object (a printed paper)
incomparably better than before; insomuch that I could read many of
the words which before I could make nothing at all of. It is plain,
therefore, that this telescope shows best with a certain oblique
pencil of rays. Probably it will be found that this circumstance is by
no means peculiar to this telescope.” This very valuable observation
has lain buried for eighty-two years, and ignorance of it has led to
the destruction of many a valuable surface.
As regards the method of combating this tendency, it is as a general
rule best to re-grind or rather re-fine the surface, for though pitch
polishing has occasionally corrected it in a few minutes, it will
not always do so. I have polished a surface for thirteen and a half
hours, examining it frequently, without changing the obliquity in the
slightest degree.
Glass, then, is a substance prone to change by heat and compression,
and requiring to be handled with the utmost caution.
b. _Emery and Rouge._
In order to excavate the concave depression in a piece of glass, emery
as coarse as the head of a pin has been commonly used. This cuts
rapidly, and is succeeded by finer grained varieties, till flour emery
is reached. After that only washed emeries should be permitted. They
are made by an elutriating process invented by Dr. Green.
Five pounds of the finest sifted flour emery are mixed with an ounce
of pulverized gum arabic. Enough water to make the mass like treacle
is then added, and the ingredients are thoroughly incorporated by the
hand. They are put into a deep jar containing a gallon of water. After
being stirred the fluid is allowed to come to rest, and the surface be
skimmed. At the end of an hour the liquid containing extremely fine
emery in suspension is decanted or drawn off with a siphon, nearly down
to the level of the precipitated emery at the bottom, and set aside to
subside in a tall vessel. When this has occurred, which will be in the
lapse of a few hours, the fluid is to be carefully poured back into the
first vessel, and the fine deposit in the second put into a stoppered
bottle. In the same way by stirring up the precipitate again, emery
that has been suspended 30, 10, 3, 1 minutes, and 20, 3, seconds is to
be secured and preserved in wide-mouthed vessels.
The quantity of the finer emeries consumed in smoothing a 15-1/2 inch
surface is very trifling--a mass of each as large as two peas sufficing.
Rouge, or peroxide of iron, is better bought than prepared by the
amateur. It is made by calcining sulphate of iron and washing the
product in water. Three kinds are usually found in commerce: a very
coarse variety containing the largest percentage of the cutting black
oxide of iron, which will scratch glass like quartz; a very fine
variety which can hardly polish glass, but is suitable for silver
films; and one intermediate. Trial of several boxes is the best method
of procuring that which is desired.
c. _Tools of Iron, Lead, and Pitch._
In making a mirror, one of the first steps is to describe upon two
stout sheets of brass or iron, arcs of a circle with a radius equal to
twice the desired focal length, and to secure, by filing and grinding
them together, a concave and convex gauge. When the radius bar is very
long, it may be hung against the side of a house. By the assistance
of these templets, the convex tools of lead and iron and the concave
surface of the mirror are made parts of a sphere of proper diameter.
The excavation of a large flat disc of glass to a concave is best
accomplished by means of a thick plate of lead, cast considerably more
convex than the gauge. The central parts wear away very quickly, and
when they become too flat must be made convex again by striking the
lead on the back with a hammer. The glass is thus caused gradually
to approach the right concavity. Ten or twelve hours usually suffice
to complete this stage. The progress of the excavating is tested
sufficiently well by setting the convex gauge on a diameter of the
mirror, and observing how many slips of paper of a definite thickness
will pass under the centre or edge, as the case may be. This avoids the
necessity of a spherometer. The thickness of paper is found correctly
enough by measuring a half ream, and dividing by the number of sheets.
In this manner differences in the versed sine of a thousandth of an
inch may be appreciated, and a close enough approximation to the
desired focal length reached--the precision required in achromatics not
being needed. The preparation of the iron tools on which the grinding
is to be finished is very laborious where personal exertion is used.
They require to be cast thin in order that they may be easily handled,
and hence cannot be turned with very great exactness.
The pair for my large mirrors are 15-1/2 inches in diameter, and were
cast 3/8 of an inch thick, being strengthened however on the back by
eight ribs 3/4 of an inch high, radiating from a solid centre two
inches in diameter (_a_, Fig. 6). They weighed 25 pounds apiece. Four
ears, with a tapped hole in each, project at equal distances round the
edge, and serve either as a means of attachment for a counterpoise
lever, or as handles.
[Illustration: Fig. 6. The Iron Grinder.]
After these were turned and taken off the lathe chuck, they were found
to be somewhat sprung, and had to be scraped and ground in the machine
for a week before fitting properly. The slowness in grinding results
from the emery becoming imbedded in the iron, and forming a surface as
hard as adamant.
Once acquired, such grinders are very valuable, as they keep their
focal length and figure apparently without change if carefully used,
and only worked on glass of nearly similar curvature. At first no
grooves were cut upon the face, for in the lead previously employed
for fining they were found to be a fruitful source of scratches, on
account of grains of emery imbedding in them, and gradually breaking
loose as the lead wore away. Subsequently it appeared, that unless
there was some means of spreading water and the grinding powders
evenly, rings were likely to be produced on the mirror, and the iron
was consequently treated as follows:--
A number of pieces of wax, such as is used in making artificial
flowers, were procured. The convex iron was laid out in squares of 3/4
of an inch on the side, and each alternate one being touched with a
thick alcoholic solution of Canada balsam, a piece of wax of that size
was put over it. This was found after many trials to be the best method
of protecting some squares, and yet leaving others in the most suitable
condition to be attacked. A rim of wax, melted with Canada balsam, was
raised around the edge of the iron, and a pint of aqua regia poured in.
In a short time this corroded out the uncovered parts to a sufficient
depth, leaving an appearance like a chess-board, except that the
projecting squares did not touch at the adjoining angles (_b_, Fig. 6).
I should have chipped the cavities out, instead of dissolving them
away, but for fear of changing the radius of curvature and breaking the
thin plate. However as soon as the iron was cleaned, it proved to have
become flatter, the radius of curvature having increased 7-3/4 inches.
This shows what a state of tension and compression there must be in
such a mass, when the removal of a film of metal 1/50 of an inch thick,
here and there, from one surface, causes so great a change.
When the glass has been brought to the finest possible grain on such
a grinder, a polishing tool has to be prepared by covering the convex
iron with either pitch or rosin. These substances have very similar
properties, but the rosin by being clear affords an opportunity of
seeing whether there are impurities, and therefore has been frequently
used, straining being unnecessary. It is, however, too hard as it
occurs in commerce, and requires to be softened with turpentine.
A mass sufficiently large to cover the iron 1/8 of an inch thick
is melted in a porcelain or metal capsule by a spirit lamp. When
thoroughly liquid the lamp is blown out, and spirits of turpentine
added, a drachm or two at a time. After each addition a chisel or
some similar piece of metal is dipped into the fluid rosin, and then
immersed in water at the temperature of the room. After a minute or two
it is taken out, and tried with the thumb-nail. When the proper degree
of softness is obtained, an indentation can be made by a moderate
pressure.
The iron having been heated in hot water is then painted in stripes
1/8 of an inch deep with this resinous composition. The glass concave
to be polished being smeared with rouge, is pressed upon it to secure
a fit, and the iron is then put in cold water. With a narrow chisel
straight grooves are made, dividing the surface into squares of one
inch, separated by intervals of one-quarter of an inch (Fig. 7). Under
certain circumstances it is also desirable to take off every other
square, or perhaps reduce the polishing surface irregularly here and
there, to get an excess of action on some particular portion of the
mirror.
[Illustration: Fig. 7. The Polishing Tool.]
It is well, on commencing to polish with a tool made in this way, to
warm the glass as well as the tool in water (page 4) before bringing
the two in contact. If this is not done the polishing will not go on
kindly, a good adaptation not being secured for a length of time, and
the glass surface being injured at the outset. The rosin on a polisher
put away for a day or two suffers an internal change, a species of
irregular swelling, and does not retain its original form. Heating,
too, has a good effect in preventing disturbance by local variations of
temperature in the glass.
The description of “Local Polishers” will be given under _Machines_.
d. _Methods of Examining Surfaces._
I have been in the habit of testing mirrors exclusively at the centre
of curvature, not putting them in the telescope tube until nearly
parabolic or finished. The means of trial are so excellent, the
indications obtained so precise, and the freedom from atmospheric
disturbances so complete, that the greatest facilities are offered
for ascertaining the nature of a surface. In addition the observer
is entirely independent of day or night, and of the weather. I do
not think that anything more is learned of the telescope, even under
favorable circumstances, than in the workshop. For the improvement
of these methods of observation, Science is largely indebted to M.
Foucault, whose third test--the second in the next paragraph--is
sufficient to afford by itself a large part of the information required
in correcting a concave surface.
There are two distinct modes of examination: 1st, observing with an
eye-piece the image of an illuminated pin-hole at the focus, and the
cone of rays inside and outside that plane; 2d, receiving the entire
pencil of light coming from the mirror through the pupil on the retina,
and noticing the distribution of light and shade, and the appearances
in relief on the face of the mirror.
[Illustration: Fig. 8. Testing a Concave at the Centre of Curvature.]
The arrangements for these tests are as follows: Around the flame of a
lamp (_a_, Fig. 8) a sheet of tin is bent so as to form a cylindrical
screen. Through it at the height of the brightest part of the flame,
as at _b_, two holes are bored, a quarter of an inch apart, one 1/32
of an inch in diameter, the other as small as the point of the finest
needle will make--perhaps 1/200 of an inch. This apparatus is to be set
at the centre of curvature of the mirror _c_--the optical axis of the
latter being horizontal--and so adjusted that the light which diverges
from the illuminated hole in use, may, after impinging on the concave
surface of the glass, return to form an image close by the side of
the tin screen. In the case of the first test, the returning rays are
received into an eye-piece or microscope, _d_, magnifying 20 times, and
moving upon a divided scale to and from the mirror. In the second test
the eye-piece is removed away from before the eye, and a straight-edged
opaque screen, _e_, is put in its place. The mirror is supported in
these trials by an arc of wood _f_, lined with thick woollen stuff, and
above two wooden latches, _g_, _g_, prevent it from falling forward,
but do not compress it. It is, of course, unsilvered. In the figure the
table is represented very much closer to the mirror than it should be.
In trials on the 15-1/2 inch it has to be 25 feet distant.
The appearance that a truly spherical concave surface presents with
the first test is: the image of the hole is sharply defined without
any areola of aberration around it, and is surrounded by interference
rings. Inside and outside the focus the cone of rays is exactly
similar, and circular in section. It presents no trace of irregular
illumination, nor any bright or dark circles. With the second test,
when the eye is brought into such a position that it receives the whole
pencil of reflected rays, and the opaque screen is gradually drawn
across in front of the pupil, the brightness of the surface slowly
diminishes, until just as the screen is cutting off the last relic of
the cone of rays (Fig. 9), the mirror presents an uniform grayish tint,
followed by total darkness, and gives to the eye the sensation of a
plane.
[Illustration: Fig. 9. Action of the Opaque Screen.]
[Illustration: Fig. 10. Caustic of Oblate Spheroidal Mirror.]
If, however, the mirror is not spherical, but instead gradually
_decreases_ in focal length toward the edge, the following changes
result: The image at the best focus is surrounded by a nebulosity,
stronger as the deviation from the sphere is greater, and neither can
a sharp focus be obtained nor interference fringes seen. In order to
include this nebulosity in the image, it will be necessary to push the
eye-piece toward the mirror. Before the cone of rays has completed its
convergence, the mass of light will be seen to have accumulated at the
periphery, and after the focus is past and divergence has commenced,
the accumulation will be around the axis. That is, a caustic (Fig. 10)
is formed with its summit from the mirror. By the second test, in
gradually eclipsing the light coming from the mirror, just before all
the rays are obstructed, a part of those which have constituted the
nebulosity will escape past the screen (Fig. 11) into the eye, and
cause there an extremely exaggerated appearance in relief of the solid
superposed upon the true surface beneath. The glass will no longer
seem to be a plane, but to have a section as in Fig. 12. Let us examine
by the aid of M. Foucault’s diagrams why it is that the surface seems
thus curved. If the dotted line, Fig. 13, represents the section of
the mirror, and the solid line a section of a spherical mirror of the
same mean focal length, it will be seen that the curves touch at two
points, but are separated by an interval elsewhere. If this interval be
projected by means of the differences of the ordinates, the resulting
curve will be found to be the same as that which the mirror apparently
has.
[Illustration: Fig. 12. Apparent Section of Oblate Spheroidal Mirror.]
If the opaque screen be drawn a short distance from the mirror, the
appearance of the section curve will seem to change, the bottom of the
groove (Fig. 12) between the centre and edge advancing inwards, and the
mound in the middle growing smaller. If the screen be pushed toward the
mirror the reverse takes place, the central mound becoming larger, but
the edge decreasing. The reason for these variations becomes apparent
by considering the three diagrams, Fig. 14. The dotted curve in each
instance represents the real curve of the mirror described in the
last paragraph, while the solid lines are circles drawn with radii
progressionally shorter in _a_, _b_ and _c_, and represent sections of
three spherical mirrors whose focal lengths also progressively shorten.
[Illustration: Fig. 11. Action of the Opaque Screen.]
[Illustration: Fig. 13. Section of Spherical and Spheroidal Mirrors.]
[Illustration: Fig. 14. Relation of Spheres to Oblate Spheroid.]
When the opaque screen is at a given distance from the mirror under
examination, the only parts of the mirror which can officiate well are
those which have a curvature corresponding to a radius equal to the
same distance. All the other parts seem as if they were covered by
projecting circular masses. In looking at Fig. 14, it is plain, then,
if the opaque screen is at a maximum distance from the mirror, that the
central parts alone will seem to operate, because the two curves (_a_)
only touch there. If the screen is moved toward the mirror the curves
(_b_) will coincide at some point between the centre and edge, while if
carried still farther in only the edges touch and the appearance will
be as if a large mound were fixed upon the centre. I have been careful
in explaining how a surface may thus seem to present entirely different
characteristics if examined from points of view which vary slightly
in distance, because a knowledge of these facts is of the utmost
importance in correcting such an erroneous figure. It is now obvious
that the correction will be equally effectual if the mirror be polished
with a small rubber on the edge, or on the centre, or partly on each.
The only difference in the result will be, that the mean focal length
will be increased in the first instance, and decreased in the second,
while it will remain unchanged in the third.
[Illustration: Fig. 15. Caustic of Hyperbolic Mirror.]
[Illustration: Fig. 16. Apparent Section of Hyperbolic Mirror.]
If the mirror, instead of having a section like that of an oblate
spheroid, should have either an ellipse, parabola, or hyperbola, as
its section curve, the appearances seen above are reversed. Whilst by
the first test there is still an aberration round the image at the
best focus, the eye-piece must now be drawn from the mirror to include
it. The cone of rays is most dense round the axis inside, and at the
periphery outside the focus, and the summit of the caustic (Fig. 15)
is turned towards the mirror. The second test shows a section as in
Fig. 16, a depression at the centre, and the edges turned backwards.
The nature of the movement necessary to reduce the surface to a sphere
is very plainly indicated, action on a zone _a_ between the centre and
edge. If, however, a parabolic section is required, the zone _a_ must
not be entirely removed, and the surface rendered apparently flat, but
as much of it must be left as experience shows to be desirable.
[Illustration: Fig. 17. Action of the Opaque Screen.]
[Illustration: Fig. 18. Apparent Section of Mirror with Rings.]
If, in still a fourth instance, the mirror is not formed by the
revolution of any regular curve upon its axis, but has upon its surface
zones of longer and shorter radius intermixed irregularly, a very
common case, the two tests still indicate with precision the parts in
fault, and the correction demanded. Thus the mirror seen in section in
Fig. 17, when the principal mass of light was obstructed by the opaque
screen, would still permit that coming from certain parts to find its
way into the eye.
Figure 18 represents an irregular mirror, that was produced in the
process of correction of a hyperbolic surface, which had an apparent
section like Fig. 16 previously. The zone _a_ had been acted upon with
a small local polisher, and the mirror was finished by subsequently
softening down _b_ and _c_ with a larger tool.
After having gained from the preceding paragraphs a general idea of
the value and nature of these tests at the centre of curvature, a more
particular description of their use is desirable. M. Foucault in his
methods first brings the mirror to a spherical surface, and then by
moving the luminous pin-hole toward the mirror, and correspondingly
retracting the eye-piece or opaque screen, carries it, avoiding
aberration continually by polishing, through a series of ellipsoidal
curvatures, advancing step by step toward the paraboloid of revolution.
The length of the apartment, however, soon puts a termination to this
gradual system of correction, and he is forced to perform the last
steps of the conversion by an empirical process, and eventually to
resort to trial in the telescope.
With my mirrors of 150 inches focal length, demanding from the outset
a room more than 25 feet long, this successive system had to be
abandoned. It was not found feasible to place the lamp in the distant
focus of the ellipse--the workshop being less than 30 feet long--and
putting the luminous source on stands outside, introduced several
injurious complications, not the least of which was currents in the
layers of variously refracting air in the apartment. In a still room
the density and hygrometric variations in its various parts only give
rise to slight embarrassment. The moment, however, that currents are
produced, satisfactory examination of a mirror becomes difficult.
The air is seen only too easily to move in great spiral convolutions
between the mirror and the eye, areolæ of aberration appear around
a previously excellent image, and were it not for the second test,
any determination of surface would be impossible. By that test the
real deviations from truth of figure can be distinguished from the
atmospheric, and to a practised eye sufficient indications of necessary
changes given. Such a movement as that caused by placing the hand in
or under the line of the converging rays, will completely destroy the
beauty of an image, and by the second test give origin in the first
case to the appearance Fig. 19. In order to be completely exempt at
all times from aërial difficulties, it is desirable to have control
of a long underground apartment, the openings of which can be tightly
closed. As no artificial warmth is needed, there is the minimum of
movement in the inclosed air, and conclusions respecting a surface may
be arrived at in a very short time. The mirror may also be supported
from the ground, so that tremulous vibrations which weary the eye, and
interfere with the accuracy of criticism, may be avoided.
[Illustration: Fig. 19. Atmospheric Motions.]
Driven then from observing an image kept continually free from
aberration, through advancing ellipsoidal changes, it became necessary
to study the gradual increase of deformation, produced by the greater
and greater departures from a spherical surface, as the parabola was
approached. It was found that a sufficient guide is still provided in
these tests, by modifying them properly. The longitudinal aberration
of a mirror of small angular opening is easily calculated--being
equal to the square of half the aperture, divided by eight times
the principal focal length. That is, if a 15-1/2 inch mirror of
150 inches focal length were spherical, and were used to converge
parallel rays, those from its edge would reach a focus 5/100 of an
inch nearer the mirror than those from its central parts. If now the
converse experiment be tried, and a mirror of the same size and focal
length which can converge parallel rays, falling on all its parts, to
one focus, be examined at the centre of curvature, it gives there an
amount of longitudinal aberration 10/100 of an inch, equal to twice
the preceding. This latter, then, is the condition at the centre of
curvature, to which such mirror must be brought in order to converge
parallel rays with exactness. In addition, strict watch must be kept
upon the zones intermediate between the centre and edge, both by
measurement with diaphragms of their aberration, and better yet, by
observation of the regularity of the curve of that apparent solid,
Fig. 16, seen by the second test.
This modification of the first test is literally a method of
parabolizing by measure, and is capable of great precision when the
eye learns to estimate where the exact focus of a zone is. The little
irregularities found round the edges of the holes through the tin
screen, Fig. 8, are in this respect of material assistance. They show,
too, the increased optical or penetrating power that is gained by
increase of aperture. Minute peculiarities, not visible under very high
powers with a 10 inch diaphragm, become immediately perceptible even
with less magnifying when the whole aperture is used, provided the
mirror is spherical.
[Illustration: Fig. 20. Adjusting the Opaque Screen.]