inferred from page 15, to set the opaque screen exactly in the proper
position. The best method for ascertaining its location is, having
received the image into the eye, placed purposely too near the mirror,
to cause the screen to move across the cone of rays from the right
towards the left side. A jet black shadow begins to advance at the same
time, and in the same direction across the mirror. If the eye is then
moved from the mirror sufficiently, this black shadow can be made to
originate by the same motion of the screen as before, from the left or
opposite side of the mirror. Midway between these extremes there is a
point where the advance is from neither side. This is the true position
for the screen when it is desired to see the imperfections of the
surface in highly exaggerated relief, as in Fig. 20, which represents
the appearance of Fig. 12.[2]
[2] In order to examine Fig. 20, the book should be held with the
left side of the page toward a window or lamp. The eye should also be
at least two feet distant. The centre will then be seen to protrude,
and the surface present the apparent section engraved below it.
The interpretation of the lights and shadows upon the face of a mirror
in this test is always easy, and the observer is not likely to mistake
an elevation for a depression, if he bears in mind the fact that the
surface under examination must always be regarded as illuminated by an
oblique light coming from a source on the side opposite to that from
which the screen advances, coming for instance from the left hand side,
in the above description.
In practice, the diaphragms commonly used for a 15-1/2 inch mirror have
been as small as the light from the unsilvered surface would allow. A
six inch aperture at the centre, a ring an inch wide round the edge,
and a two inch zone midway between the two.
e. _Machines._
In the beginning of this section the difficulties into which I fell
with Lord Rosse’s machine were stated. These caused it at the time
to be abandoned. A machine based on the same idea as Mr. Lassell’s
beautiful apparatus was next constructed. It varied, however, in this,
that the hypocycloidal curve was described partly by the rotation of
the mirror, and partly by the motions of the polisher--the axes of
the spindles carrying the two being capable either of coincidence or
lateral separation to a moderate extent. A great deal of time and labor
was expended in grinding and polishing numerous mirrors with it, but
still the difficulty that had been so annoying in the former machine
persisted. Frequently, in fact generally, from six to eight zones of
unequal focal length were visible, although on some occasions when the
mirror was hyperbolic, the number was reduced to two. At first it was
supposed that the fault lay with the polishing, the pitch accumulating
irregularly from being of improper softness, for it was found to be
particularly prone to heap up at the centre. But after I had introduced
a method of fine grinding with elutriated hone powder, which enabled
the glass to reject light before the pitch polishing, it became evident
that the zones were connected with the mode of motion of the mechanism.
Many changes were made in the speed of its various elements, and a
contrivance to control the irregular motion of the polisher introduced,
but a really fine and uniform parabolic surface was never obtained,
the very best showing when finished zones of different focal lengths.
Although it cannot be said that I have tried this machine thoroughly,
for Mr. Lassell has produced specula of exquisite defining power with
it, and must have avoided these imperfections to a great extent, yet
the evident necessity of complicating the movement[3] considerably, to
avoid the polishing in rings, led me to adopt an entirely different
construction, which was used until quite recently. Although it has now
been replaced by another machine, which is still better in principle,
and gives fine results much more quickly, yet as it produced one
parabolic surface that bore a power of more than 1000, and as it serves
to introduce the process of grinding, it is worthy of description.
The action of machines for grinding and polishing has been thoroughly
examined in my workshop, no less than seven different ones having been
made at various times.
[3] Messrs. De La Rue and Nasmyth, who used one of Mr. Lassell’s
machines, as I have since learned, met with the same trouble, and
were led to make two additions to the mechanism: 1, to control
the rotation of the polisher rigorously; and 2, to give the whole
speculum a lateral motion, by which the intersecting points of the
curves described by the polisher were regularly changed in distance
from the centre of the mirror. Mr. Lassell had previously, however,
introduced a contrivance for this latter purpose himself.
The machine, which is a simplification of Lord Rosse’s, was intended
to give spiral strokes. It differed from the original, however, in
demanding a changeable stroke, and in the absence of the lateral
motion. In another most essential feature it varied from both that
and Mr. Lassell’s, _the mirror was always uppermost while polishing_,
and being uncounterpoised escaped to as great an extent as possible
from the effects of irregular pressure. To any one who has studied the
deformations of a reflecting surface, and knows how troublesome it is
to support a mirror properly, the advantage is apparent.
[Illustration: Fig. 21. Polishing Machine.]
[Illustration: Fig. 22. The Foot Power.]
The construction is as follows: A stout vertical shaft, _a_, Fig. 21,
carries at its top a circular table _b_, upon which the polisher _c_
is screwed. Below a band-wheel _d_ is fixed. Above the table, at a
distance of four inches, a horizontal bar _e_ is arranged, so as to
move back and forward in the direction of its length, and to carry
with it by means of a screw _l_, the mirror _m_, and its iron back or
chuck _n_. The bar is moved by a connecting rod _f_, attached to it
at one end, and at the other to a pin _g_ moving a slot. This slot is
in a crank _h_, carried by a vertical shaft _i_, near the former one
_a_. The band-wheel _k_ is connected with the foot power, Fig. 22. The
machine, except those parts liable to wear by friction, is made of
wood. The ends _o o′_ of the horizontal bar _e_, are defended by brass
tubes working in mahogany, and have even now but little shake, though
many hundred thousands of reciprocations have been made.
The foot power consists of an endless band with wooden treads _a a′_,
passing at one end of the apparatus over iron wheels _b b′_, which
carry the band-wheel c upon their axle. At the other end it goes over
the rollers _d d′_. Two pairs of intermediate wheels _e e′_, serve
to sustain the weight of the man or animal working in it. The treads
are so arranged that they interlock, and form a platform, which will
not yield downwards. Owing to its inclination when a weight is put on
the platform _a′_, it immediately moves from _b_ toward _d_ and the
band-wheel turns. By a moderate exertion, equivalent to walking up a
slight incline at a slow rate, a power more than sufficient to polish
a 15-1/2 inch mirror is obtained. This machine, in which very little
force is lost in overcoming friction, is frequently employed for dairy
use, and is moved commonly in the State of New York by a sheep. I have
generally myself walked in the one used by me, and have travelled some
days, during five hours, more than ten miles.
In order to give an idea of the method of using a grinding and
polishing machine, the following extract from the workshop note-book is
introduced:--
“A disk of plate glass 15-1/2 inches in diameter, and 1-1/4 inch
thick was procured. It had been polished flat on both sides, so that
its internal constitution might be seen.[4] It was fastened upon the
table _b_ of the machine, by four blocks of wood as at _c_, Fig. 21.
Underneath the glass were three thick folds of blanket, 15 inches in
diameter, to prevent scratching of the lower face, and avoid risk of
fracture. A convex disk of lead weighing 40 pounds having been cast,
was laid upon the upper surface of the glass, and then the screw _l_
was depressed so as to catch in a perforated iron plate _n_, at the
back of the lead _m_, and press downward strongly.
[4] The glass that I have used has generally been such as was
intended for dead-lights and sky-lights in ships.
“Emery as coarse as the head of a pin having been introduced, through
a hole in the lead, motion was commenced and continued for half an
hour, an occasional supply of emery being given. The machine made 150
eight-inch cross strokes, and the mirror 50 revolutions per minute. The
grinder _m_ was occasionally restrained from turning by the hand. At
the end of the time the detritus was washed away, and an examination
with the gauge made. A spot 11 inches in diameter, and 1/60 of an
inch deep, was found to have been ground out. The same process was
continued at intervals for ten hours, measurements with the gauge being
frequently made. The concave was then sufficiently deep. The leaden
grinder was kept of the right convexity by beating it on the back when
necessary. A finer variety of coarse emery, and after that flour emery
were next put on, each for an hour. These left the surface moderately
smooth, and nearly of the right focal length. The leaden grinder was
then dismissed, and the iron one, Fig. 6, put in its stead. The mirror
was removed from its place, and ground upon a large piece of flat glass
for ten minutes, to produce a circular outline to the concavity. It
was cemented with soft pitch to the concave iron disk, the counterpart
of Fig. 6, and again recentred on the blanketed table _b_. Emeries
of 3 and 20 seconds, and 1, 3, 10, 30, 60 minutes’ elutriation were
worked on it, an hour each. The rate of cross motion was reduced to
25 per minute to avoid heating, the mirror still revolving once for
every three cross strokes. The screw pressure of _l_ was stopped. This
produced a surface exquisitely fine, semi-transparent, and appearing as
if covered with a thin film of dried milk. It could reflect the light
from objects outside the window until an incidence of 45 degrees was
reached, and at night was found to be bright enough for a preliminary
examination at the centre of curvature.
“The polisher was constructed in the usual way (page 12), and being
smeared with rouge was fastened to the table _b_, where the mirror
had been. The latter warmed in water to 120° F., was then put face
downwards upon the former, and the screw _l_ so lowered as to cause no
pressure. The machine was allowed to make 20 four-inch cross strokes
per minute, and the polisher to revolve once for every three strokes.
The mirror being unconstrainedly supported on the polisher, was
irregularly rotated by hand, or rather prevented from rotating with the
polisher. The tendency of this method is to produce an almost spherical
surface. To change it to a paraboloid, it was only necessary when the
glass was polished all over to increase the length of the stroke to 8
inches, and continue working fifteen minutes at a time, examining in
the intervals by the tests at the centre of curvature. The production
of a polish all over occupied about two hours, but the correction of
figure took more time, on account of the frequent examinations, and
the absolute necessity of allowing the mirror to come back to a state
of equilibrium from which it had been disturbed when worked on the
machine.” I have seen a mirror which was parabolic when just off the
machine, by cooling over night become spherical. And these heat changes
are often succeeded by other slower molecular movements, which continue
to modify a surface for many days after.
This correction, where time and not length of stroke is the governing
agent, has once or twice been accomplished in fifteen minutes, but
sometimes has cost several hours. If the figure should have become a
hyperboloid of revolution, that is, have its edge zones too long in
comparison with the centre, it is only necessary to shorten the stroke
to bring it back to the sphere, or even to overpass that and produce
a surface in which at the centre of curvature the edge zones have too
short a focal length (Fig. 12).
Very much less trouble from zones of unequal focal length was
experienced after this machine and system of working were adopted.
This was owing probably partly to the element of irregularity in the
rotation of the mirror, and partly to the fact that the surface is
kept spherical until polished, and is then rapidly changed to the
paraboloid. Where the adjustments of an apparatus are made so as to
attempt to keep a surface parabolic for some hours, there is a strong
tendency for zones to appear, and of a width bearing a fixed relation
to the stroke.
The method of producing reflecting surfaces next to be spoken of, is
however that which has finally been adopted as the best of all, being
capable of forming mirrors which are as perfect as can be, and yet
only requiring a short time. It is the correction of a surface by local
retouches. In the account published by M. Foucault, it appears that he
is in France the inventor of this improvement.
The mode of practising the retouches is as follows: Several disks
of wood, as _a_, Fig. 23, varying from 8 inches to 1/2 an inch in
diameter, are to be provided, and covered with pitch or rosin of the
usual hardness, in squares as at _c_, on one side.[5] On the other a
low cylindrical handle _b_, is to be fixed. The mirror _a_, Fig. 24,
having been fined with the succession of emeries before described, is
laid face upward on several folds of blanket, arranged upon a circular
table, screwed to an isolated post in the centre of the apartment,
which permits the operator to move completely round it. An ordinary
barrel has generally supplied the place of the post, the head _c_,
Fig. 24, serving for the circular table, and the rim _b_ preventing
the mirror sliding off. The other end is fastened to the floor by four
cleets _d d´_.
[5] M. Foucault used plano-convex lenses of glass, of a radius of
curvature slightly less than that of the mirror, and covered with
paper on the convex face.
[Illustration: Fig. 23. Local Polisher.]
[Illustration: Fig. 24. Section of Optician’s Post.]
The large polisher is first moved over the surface in straight strokes
upon every chord, and a moderate pressure is exerted. As soon as the
mirror is at all brightened, perhaps in five minutes, the operation
is to be suspended, and an examination at the centre of curvature
made. By carefully turning round, the best diameter for support is to
be found, and marked with a rat-tail file on the edge, and then the
curve of the mirror ascertained. If it is nearly spherical, as will be
the case if the grinding has been conducted with care and irregular
heating avoided, it is to be replaced on the blanketed support, and
the previous action kept up until a fine polish, free from dots
like stippling, is attained. This stage should occupy three or four
hours. Another examination should reveal the same appearances as the
preceding. It is next necessary to lengthen the radius of curvature of
the edge zones, or what is much better shorten that of the centre, so
as to convert the section curve into a parabola. This is accomplished
by straight strokes across every diameter of the face, at first with
a 4 inch, then with a 6 inch, and finally with the 8 inch polisher.
Examinations must, however, be made every five or ten minutes, to
determine how much lateral departure from a direct diametrical stroke
is necessary, to render the curve uniform out to the edge. Care must be
taken always to warm the polisher, either in front of a fire or over a
spirit lamp, before using it.
Perhaps the most striking feature in this operation is that the mirror
presents continually a curve of revolution, and is not diversified with
undulations like a ruffle. By walking steadily round the support, on
the top of which the mirror is placed, there seems to be no tendency
for such irregularities to arise.
If the correction for spherical aberration should have proceeded too
far, and the mirror become hyperbolic, the sphere can be recovered
by working a succession of polishers of increasing size on the zone
_a_, Fig. 16, intermediate between the centre and edge, causing their
centres to pass along every chord that can be described tangent to the
zone.
A most perfect and rapid control can thus be exercised over a surface,
and an uniform result very quickly attained. It becomes a pleasant
and interesting occupation to produce a mirror. But two effects have
presented themselves in this operation, which unfortunately bar the
way to the very best results. In the first place the edge parts of
such mirrors, for more than half an inch all around, bend backwards
and become of too great focal length, and the rays from these parts
cannot be united with the rest forming the image. In the second place,
the surface, when critically examined by the second test, is found
to have a delicate wavy or fleecy appearance, not seen in machine
polishing.[6] Although the variations from the true curve implied by
these latter greatly exaggerated imperfections are exceedingly small,
and do not prevent a thermometer bulb in the sunshine appearing like
a disk surrounded by rings of interference, yet they must divert some
undulations from their proper direction, or else they would not be
visible. All kinds of strokes have been tried, straight, sweeping
circular, hypocycloidal, &c. without effecting their removal. M.
Foucault, who used a paper polisher, also encountered them. Eventually
they were imputed to the unequal pressure of the hand, and in
consequence a machine to overcome the two above mentioned faults of
manual correction was constructed.
[6] By this it is not meant that there is a rippled polish, like that
produced by buckskin.
[Illustration: Fig. 25. Machine for Local Corrections.]
The mirror _a_, is carried by an iron chuck or table _b_, covered with
a triple fold of blanket, and is prevented from slipping off by four
cleets _c c′_. The vertical shaft _d_ passes through a worm-wheel
_e_, the endless screw of which _f_, is driven by a band _g_, from
the primary shaft _h_. At _i_ is the band-wheel for connection to
the foot-power. At one end of the primary shaft is firmly fixed the
cogwheel _k_, which drives the crank-shaft _l_. Attached to the
horizontal part of _l_, is the crank-pin _m_. The two bolts _n n′_
move in a slot, so that the crank-pin may be set at any distance from
0 to 2 inches, out of line with _l_. Above, the crank-pin carries
one end of the bar _o_, the other end passing through an elliptical
hole in the oak-block _p_. Down the middle of the bar runs a long
slot, through which the screw-pin _q_ passes, and which permits _q_
to be brought over any zone from the centre to the edge of the mirror
_a_. It is retained by the bolts _r r′_, which are tapped into _s_.
The local polisher is seen at _t_. The curve which the centre of the
local polisher describes upon the face of the mirror, varies with the
adjustments. Fig. 26 is a reduction from one traced by the machine,
the overlapping being seen on the left side. The mirror is not tightly
confined by the cleets _c c′_, for that would certainly injure the
figure, but performs a slow motion of rotation, so that in no two
successive strokes are the same parts of the edge pressed against them.
[Illustration: Fig. 26. Hypocycloidal Curve.]
The local polishers are made of lead, alloyed with a small proportion
of antimony, and are 8, 6, and 4 inches in diameter, respectively. The
largest and smallest are most used, the former on account of its size
polishing most quickly, but the latter giving the truest surface. The
rosin that covers them is just indentable by the thumb nail, and is
arranged in a novel manner. The leaden basis, as seen at _t_, Fig. 25,
is perforated in many places with holes, which permit evaporation,
serve for the introduction of water where needed, and allow the rosin
to spread freely. Grooves are made from one aperture to another, and
the rosin thus divided into irregular portions. The effects of the
production of heat are in this way avoided.
The mirror may be ground and fined on this machine, in the same manner
as on that described at page 21, or it may be ground with a small
tool 8 inches in diameter, as recently suggested by M. Foucault, the
results in the latter case being just as good a surface of revolution
as in the former. It is best polished with the 8 inch, and a moderate
pressure may be given by the screw _q_, if the pitch is not too soft.
This, however, tends to leave an excavated place at the centre of the
mirror, the size depending on the stroke of the crank _m_, which should
be about 2 inches. The pin _q_ ought to be half way from the centre to
the edge of the mirror, but must be occasionally moved right or left an
inch along the slot. When the surface is approaching a perfect polish,
the warmed 4 inch polisher must be put in the place of the 8 inch.
The pin _q_ must be set exactly half-way between the centre and edge
of the mirror, and the crank must have a stroke of two inches radius.
The polisher then just goes up to the centre of the glass surface
with one edge, and to the periphery with the other, while the outer
excursion of the inner edge and inner excursion of the outer edge meet,
and neutralize one another at a midway point. Wherever the edge of a
polisher changes direction many times in succession, on a surface, a
zone is sure to form, unless avoided in this manner. All the foregoing
description is for a 15-1/2 inch mirror.
By this system of local polishing the difficulties of heat,
distribution of polishing powders, irregular contact of the rosin,
&c. that render the attainment of a fine figure so uncertain usually,
entirely disappear. A spherical surface is produced as above described,
and afterwards by moving _q_ towards the edge, and at the same time
increasing the stroke, it is converted into a paraboloid. The fleecy
appearance spoken of on a former page is not perceived, and the surface
is good almost up to the extreme edge.
(4.) EYE-PIECES, PLANE MIRRORS AND TEST OBJECTS.
The telescope is furnished with several eye-pieces of various
construction, giving magnifying powers from 75 to 1200, or if it were
desired even higher. For the medium powers 300 and 600 Ramsden, or
rather positive eye-pieces have been adopted. They differ, however,
from the usual form in being achromatic, that is, each plano-convex
is composed of a flint and crown, arranged according to formulas
calculated by Littrow. In this way a large flat field and absence of
color are secured, and the fine images yielded by the mirror are not
injured. For the higher powers, single achromatic lenses are used, and
for the highest of all a Ross microscope.
With these means it has been found that the parabolic surfaces
yielded by the processes before described, will define test objects
excellently. Of close double stars they will separate such as γ^{2}
Andromedæ, and show the colors of the components. In the case of
unequal stars which seem to be more severe tests, they can show the
close companion of Sirius--discovered by Mr. Alvan Clark’s magnificent
refractor--the sixth component of θ^{1} Orionis, and a multitude of
other difficult objects.
As an example of light collecting power, Debillisima between ε and 5
Lyræ is found to be quintuple, as first noticed by Mr. Lassell. In the
18-1/2 inch specula of Herschel, it was only recorded as double, and,
according to Admiral Smyth, Lord Rosse did not notice the fourth and
fifth components. Jupiter’s moons show with beautiful disks, and their
difference in diameter is very marked. As for the body of that planet,
it is literally covered with belts up to the poles. The bright and dark
spots on Venus, and the fading illumination of her inner edge, and its
irregularities are perceived even when the air is far from tranquil.
Stars are often seen as disks, and without any wings or tails, unless
indeed the mirror should be wrongly placed, so that the best diameter
for support is not in the perpendicular plane, passing through the axis
of the tube.