33 Orionis. 2″ : 6, 8.
52 Orionis. 1″·8 : 6, 8.
δ Cygni. 1″·8 : 3·5, 9.
2 Camelopardi. 1″·7 : 5·5, 7·5.
π Aquilæ. 1″·7 : 6, 7.
σ^2 Cancri. 1″·4 : 5·5, 7.
9 Leonis. 1″·2 : 7·5, 7·5.
η Orionis. 1″ : 4, 5.
ε Arietis. 1″ : 5, 6·5.
4 Lyncis. 1″ : 6, 7·5.
37 Pegasi. 0″·8 : 6, 7·5.
749ξ Tauri. 0″·8 : 7·1, 7·2.
46 Arietis. 0″·8 : 8, 9.
λ^a Cygni. 0″·7: 5, 6.
β Delphini. 0″·7 : 5, 5·5.
20 Draconis. 0″·7 : 7, 7·5.
287 Draconis. 0″·7 : 7, 8.
178^b Delphini. 0″·6 : 4·5, 6.
φ Draconis. 0″·6 : 4·5, 6·5.
γ^2 Andromedæ. 0″·6 : 8·5, 9.
μ^2 Boötis. 0″·5 : 8, 8·5.
ι^a Boötis. 0″·5 : 4·5, 4·5.
7 Tauri. 0″·5 : 6, 6·5.
108 Draconis. 0″·5 : 9, 9.
η Herculis. 0″·3 : 3, 8.
42 Comæ Berenices. 0″·3 : 4·5, 5.
ω Leonis. 0″·3 : 6·5, 7·5.
Since writing the first edition of my catalogue, the writer has
received many gratifying accounts of the success of the
“Silvered-Glass Reflector.” Many private letters have been received
by him from observers, expressing their delight and satisfaction.
This has been so encouraging that no pains have been spared, nor any
opportunities neglected, in turning to the best purpose every
valuable lesson that continued practice and experience may have
suggested in the manipulation of specula from time to time, in order
to secure the best means for obtaining the highest excellence of
defining power.
Many modifications and improvements have been made in working and
testing mirrors, and special machinery and appliances constructed
for large sizes. But to complete my conditions suitable for truly
figuring and testing specula of considerable size, I found it
necessary to remove from the traffic and tremor of a town to a still
and tranquil situation in the country.
The truth of the curve is so sensibly and seriously affected by
vibration constantly going on in and near a town, that it is liable
to a variety of defects, and the surface becomes wavy and “plucked.”
As an instance, I may mention that my first and most convincing
proof of the advantage of the stiller situation was tested by an
18-inch speculum (on which much labour had been bestowed); it was
laid aside, but successfully finished after removal, and without
undulations or any perceptible defect, and the Observer wrote me,
that in good air, he “saw Sirius as a brilliant white dot, without a
ray or appendage of any kind, and celestial photographs obtained
with it are very fine.” Such results were exceedingly gratifying, as
they were obtained with much less labour and uncertainly, and the
tedious process of the final touches had not to be repeated so many
times.
It is said that the celebrated Alvan Clarke, from the same effects
of tremor, never finished an object-glass to his satisfaction
above-ground; and Dr. Draper, testing his mirrors at the centre of
curvature, to avoid draughts, &c. in an ordinary apartment, resorts
to an underground one.
In this little book of “Hints” it may be useful to remind those who
possess a speculum of fine quality that they are not produced by a
“rule of thumb”—so to speak—and that the difference between _a_
speculum and a really _fine_ one, giving a maximum of defining and
illuminating power, is the result of considerable labour and
thought, and deserves careful usage.
The Rev. Cooper Key, an amateur of much experience, writes in the
“English Mechanic,” that he was eight months (working sometimes
eight hours a day), giving his 18 inch speculum its final touches
and corrections.
A well known correspondent of the “English Mechanic,” “Hyperion,”
tells us he found it impossible to test his 8-1/2 inch mirror in an
ordinary room, and had to resort to a tunnel under the clay of his
garden. Those who have the means and perseverance to make their own
mirror, should be careful not to proceed with the finishing touches
until an hour at night when their workshop, if in a town, is free
from tremor.
First secure a well-ground and carefully-centred disc, let the
polish be as perfect as possible before any attempt is made to
figure. Care must be taken that every square or portion of the
polisher is of the same consistency and temperature, that the disc
may not be acted on irregularly.
To give the pitch this quality it must be well boiled and “pulled,”
so that no air bubbles are in the squares, as these cause expansion
or contraction as the temperature of the apartment varies, or that
of the pitch and glass from friction.
It is much the best plan to keep the workshop to the same uniform
temperature as the polisher was made for, allowing no draughts to
pass over the mirror while working, nor the gas or lamp to be near.
When the polisher is warmed—which it should be after laying aside
for any time—it should be warmed _equally_. Neglect of the above in
making the polisher, or any incautious handling of either the disc
or polisher, will be sure to cause defects, which cannot be cured
but by retracing the early steps in the fine grinding with an
accurately centered tool.
The polishing successfully accomplished, the process of correcting
for parallel rays is next proceeded with. At every step all possible
care must be taken to prevent the mirror from running into an
irregular curve. The importance of this cannot be too strongly
urged, if a speculum capable of doing the _best_ work is desired, as
the curve _must_ be true, regular, or uniform, to give the _highest_
defining and illuminating power. An under-corrected mirror, if of a
regular curve, will perform much better than a compound correction,
exhibiting at the focal point much less lateral aberration.
A brief explanation of this may be of use as far as the limits of
these pages will admit. It would be impossible to teach, by a mere
description of methods, how to commence and finish off a speculum of
good quality, even if every working secret and minute detail were
unreservedly explained. The only way is to master sufficient theory,
and the rest will come by prolonged care and perseverance. I state
this because amateurs who have been desirous of enjoying the
gratification of observing with a mirror of their own making have
written for information which they have been quite willing even to
pay for liberally, but have felt disappointed, and perhaps thought
it somewhat discourteous, on being told that what they wanted was
impracticable and could not be satisfactorily attempted by the
Optician in writing. In some cases I have finished amateurs’ work on
agreeable terms, and which has led to a pleasant correspondence or
acquaintance. These remarks may prevent some future disappointment.
Every one is familiar with the fact that the parabola is the only
concave surface that can reflect rays of light falling on its
surface from an object at an infinite distance—such as the stars and
planets practically are—to one common focus, or without aberration.
This series or column of rays (which is equal in diameter to the
opening of the speculum), reach the mirror without making an angle
to it or to each other, they travel side by side, they are all of
one length, and are reflected to a point, and are therefore all of
the same length at the proper focal distance, viz., half the radius
of the curvature of the concave. The properties of the parobola make
the nearest possible approach to it of the utmost importance.
It has been said that a considerably under-corrected surface, if of
a true and uniform curve, is better than one with less aberration,
with zones or sections of various curves. To explain this, let us
suppose an artificial star at some short distance, say 50 yards, the
parabola would not form an image of this at the eye-piece without
aberration; it has for this distance too short a focus for the
central rays, and the best disc is inclined to the inner focus,
because the rays from the object _diverge_ towards it, instead of
travelling parallel; and they reach the surface (the central rays
compared with the marginal), at an angle equal to the semi-diameter
of the mirror.
But, if instead of a parabolic mirror an elliptical one be used,
which has one of its foci at 50 yards’ distance, the image will be
perfect. Now place the artificial star at 500 yards, the image will
now be attended with perceptible aberration. The longer focus of the
ellipse must be worked further and further from the mirror by
shortening the focus of the central rays. Correct it for this
distance, and again remove the artificial star to a still greater
distance, repeating the corrections as before and carrying the outer
focus towards the object, and the inner towards the mirror, until
the rays from the object become more and more parallel, and the
curve is nearer and nearer to the parabola, or that eccentricity of
ellipse which acts better and better for distant objects or parallel
rays.
It is evident from this that if the ellipse is corrected very
considerably towards the parabola, without irregularities, and
_every part_ of the surface corrected regularly from the centre to
the edge (no part hastening more than another), that such a surface,
though under-corrected, is much better than if one portion is fully
and another under-corrected, especially if the more imperfect
portion is towards the edge. Such a compound correction may show
little or no _outstanding_ aberration at the focal point, but the
rays do not find a focus at the same regular pace as they would from
a regular curve—one edge of a zone will be coming into focus when
another would be going out. With the focussing screw they are
focussed to the place where they appear to collapse, and are most
satisfactory, though, _in reality_, the rays at the best place bend
over each other, and the definition is imperfect. From a star, which
is only a point, this may be more tolerated, but on the planets,
where the image has a sensible diameter, and is perhaps magnified
many times, this imperfect curve is very inferior to the regular
one, whose error is all of _one kind_. The light is all there
_somewhere_, but not with any good effect. There is no _proper_
illumination or definition, as rays are employed which are crossing
the optical axis at _varying_ angles, and the result is confusion.
So the amateur who sets himself the pleasant task of making his own
speculum (for there are many who can better afford the labour than
the capital to purchase, and whose capabilities are thus superior to
their means), need not be discouraged and give up the pursuit
because he cannot obtain the best results by getting a perfectly
parabolic glass. But if he has been successful in removing a
considerable amount of the spherical error, and advanced to the
elongated ellipse by maintaining a truthful curve, “let well alone”
with this disc, and proceed no further, but commence _another_,
taking care not to alter the first until the second is _better_, and
_then_ an improvement of the first may be attempted.
In the second attempt, should the amateur lose control over the
_regularity_ of the surface, let him try it as an experiment against
the first on the planets, and he will not fail to appreciate the
difference, and will be stimulated by fresh courage to get as near
to the parabola as possible with the same accurate curve.
To produce a true and uniform curve is, however, the acme of
troubles, whether it is desired to obtain the spherical, or
parabola, or any other curve. It is generally supposed that the
spherical curve is a very easy matter, so easy indeed that it is
difficult to avoid. This is a very great mistake—a spherical curve
of undeviating truth is as difficult a problem as a true parabola.
The spherical curve is the _only uniform_ curve, it has but _one_
focus, and the polisher must coincide with, and be of the same
radius as the glass, at every instant. This is why the optician
strives to obtain a semi-polish with the grinder to lessen the risk
of losing his curve on the polisher, for the curves of an object
glass are spherical. The curve most liable to be obtained by the
amateur is the spheroidal, a curve with its marginal rays _shorter_
than the central, or half the radius of curvature.
There are no means with the _telescope_ of telling the spheroidal,
approximating to the sphere, _from_ the sphere. There are _no_ means
of analyzing the exact character of a curve _equal_ to certain
methods at the centre of the curvature, but to accomplish this
requires much practice and observation, with “surroundings”
perfectly free from vibration. If the amateur can overcome this, and
lives in or very near a town, he should only work at the polishing
and figuring during the late hours of the night, when traffic, &c.
have subsided. Then, by carefully preventing any draughts in the
apartment, and with the mirror of the same temperature as the air in
the room, he will then be able to see how varied and numerous are
the chances of error in working a mirror, and the great care
necessary to avoid or cure them. He will find the surface
exceedingly prone to receive zones and irregularities during work,
and much more so than to “work true.”
The necessity for avoiding incautious handling or heating may be
realized by the following little experiment when one can manage and
understand it:—Place the tip of one finger on the surface, as it
hangs in the dark room ready for testing, and with very gentle
pressure let it remain long enough to spell one’s name; it will then
be seen that the feeble heat of the finger has, by expansion, raised
a mound on the surface of the glass, and though this amount of
swelling must be _very_ small, yet it is enough to cast a shadow
across the surface, as if something were laid on it, and quite ten
minutes will elapse before the heat will leave this spot and the
surface again become level. Now if the polisher were placed on the
glass while this hillock was there, a permanent hollow would be the
result. For a full account of these methods (of which Foucault was
the discoverer) the reader is referred to Sir John Herschel’s and
Dr. Draper’s works on the telescope.
Care must be taken not to leave too much aberration, as then the
central disc is formed too positively outside the focus, and the
rest of the light from the object appears as obtrusive rings and
false light. The over-correction is bad, and acting as a negative
lens the disc is formed too near the mirror. Such a correction,
besides being objectionable on almost all classes of objects,
prevents the use of the “Barlow” lens, and acts badly with all kinds
of positive or Ramsden eye-pieces, which improve _under_-corrected,
but “make bad worse” with over-corrected surfaces.
If these few and brief hints should stimulate the industrious and
persevering student to make his own telescope, and thus enjoy the
fruits of his own labours (which may add a relish and a pleasure to
his astronomical work), they will have served the purpose for which
they are written.
After a “Hint” on the choice of focus for the mirror, it only
remains to say a few words about the plane, as this, with the large
speculum, are the only parts that need be home-made as far as the
optical work is concerned. Never adopt a “dumpy” for general use
where high powers are sometimes wanted, for small and moderate
sizes, say 8 to 12 diameters, and for large sizes not less than
about 6 diameters of the mirror, as the larger ones practically
admit of a shorter focus. The short ones can be mounted somewhat
cheaper, but never choose them on _this_ account, they will not make
so satisfactory an instrument, and no adaptation of “Barlow’s” will
make it so.
To make the plane, provide three well-turned metal discs of 7 inches
or 9 inches diameter. Iron is the best, as the work will go down
closer, and the plates or discs may be very thick—say an inch—and
not so liable to “spring.” These turned discs must be scraped and
ground perfectly flat on each other, until they are in good contact
all over, so that there is nothing between the faces when testing
them. In the earlier stage of “truing,” oil and colour can be used.
When these discs are proved true, a disc of plate glass, same size,
is cemented with pitch on one of them, or on a thick disc of glass,
and care must be taken that it is not strained while on the block
during working. Truly grind this plate on one of the tools to a fine
semi-polish. Polish on the same tool with a piece of thick silk or
alpaca, laid over and cemented down by a solution of resin dissolved
in turpentine (as much resin as the turpentine will dissolve), then,
with the tip of the finger, thinly smear over the tool and bind
round the edge with cord, and the silk will keep in place. Fill up
the texture of the silk or alpaca evenly with damp rouge, keep it
uniformly damp, and never let the rouge and water work about. It may
be polished on very hard strained pitch, but pitch for the amateur
is not so safe, as it is liable in his hands to alter its form and
destroy the truth of the plane, but it is the quickest and handiest
if it can be managed.
After the polish is _perfect_ remove the plate from the support and
cut into squares a little larger than the size of the intended flat.
Test these in the telescope on a _star_. If one plane turns out bad,
the whole will most likely be so, and another plate must be worked
with renewed energy and care, for a bad plane will spoil the action
of the speculum however good, for there is no way of counteracting
the curved surface of the flat or second reflector. The edge of the
plate for about an inch should not be used.
When a good plane is found it can be edged by turning a piece of
wood a little less in diameter than the minor axis of the plane
required, turn the end square, and mark a line around it distant
from the end equal to the diameter, and cut through to the opposite
edge, and it will give the oval and will appear round at 45°, this
will mount nicely in brass tubes of the proper size, and a cover
should be made to fit easy.
“THE EQUATORIAL.”
Fig. 1 is a modification of the German principle, and it should be a
sufficient recommendation to remark that it is the principle used by
a maker of such experience as Mr. John Browning, and is, without
doubt, the very best style of mounting for a fixed equatorial,
especially when clockwork is employed, because clock power is
applied to the polar axis itself direct from the driving worm.
The driving part, viz., the worm and wheel, which is out of the
observer’s way (being between the standards), is not liable to meet
with accident, and the driving wheel being near the lower end of the
axis, is at the most rigid part, viz., the foundation of the
instrument. As it has a long and very firm polar axis, and is
connected with the foundation plate, it secures the utmost
steadiness and freedom from strain.
An equatorial mounting, with two long and stiff shafts for the axes,
has always the advantage of firmness; the _holding_ portions of the
instrument being in masses, are not liable to receive injury from
blows, and thus be put radically out of order. _No means should be
resorted to to make an equatorial of light weight_; an instrument
cannot be light and slim and at the same time _firm_ and _steady_—no
amount of steadying rods, splines or strings, will make a slender
tripod for a refractor so steady as a firmly made one, with proper
size and weight in the parts.
Another important advantage of this kind of mount for a large size
is, that although it has considerable weight, it is very convenient
to move and set up, being built of convenient parts, which are easy
of separation and removal. The uprights or standards are separate,
and are bolted to the bed-plate, the upper and lower discs are
readily detached from the stand. The cradle and tube are in this
construction separable. The tube of the telescope being suspended
over the _side_ of the stand, is in the most convenient position for
observing objects at any altitude, as the stand is out of the way
and clear of the telescope. The various disadvantages and objections
to the driving clock being _carried_ by the telescope are here
avoided. The clock, which is large and very powerful, is bolted down
to the iron bed-plate, and the telescope, not having to carry the
clock or weight, the balance is never altered nor the rate of the
clock disturbed, and thus a strong clock, keeping regular time, and
working much longer can be used. They will drive 2-1/2 hours. It
will be readily understood that a driving clock to enable the
instrument to do the most exact and best work must be powerful and a
good time-keeper. Lord Lindsay has said that “the clock should have
twice as much power as is _used_,” otherwise the spindles, &c. are
pent up, and it is moreover sensible to any extra weight or work
being put upon the instrument.
To give an idea of the efficiency and regularity of this clock, I
may mention that a Newtonian telescope of 18 inches aperture,
intended to carry a photographic camera of 112 lbs. weight, needed
no additional provisions to do the extra work, the rate and power
not being affected. There is a mechanism in the clock “for making up
of time” and in setting the hour circle can be used with a joint
handle or hooks as a fine screw-motion, and can be applied whether
the clock is going or not. There is also a provision at the
foundation for throwing the instrument out of the meridian, to
follow the motion of the moon or planets with the clock and “maker
up.” The above mounting is equally suitable for “Cassegrains” and
“Newtonians,” to both of which forms it has been successfully
applied up to 18 inches of aperture. It is well suited for large
telescopes.
Fig. 2 is a mounting on the same principle, but with a shorter polar
axis, and the column is in one casting. It is well suited for
moderate sizes, and the circles, &c. are applied exactly as in Fig.
1, but when a clock is wanted there is no mounting equal to the
former.
The “Educational” is a plain 6-1/2 inch, of 4 to 6 feet focus, and
is made to this pattern, with revolving body and screw-motion for
following. It is made as portable as it can be, and is a steady,
good-working instrument, and much approved of.