Talescope. theory of refracting telescopes is the forms of the different lenies. Hitherto we have had no occafion to confider any thing but their focal distances; but their aberrations depend greatly on the adjustment of their forms to their situations. When the conjugate focuses of a lens are determined by the fervice which it is to perform, there is a certain form or proportion between the curvatures of their anterior and po fterior furfaces, which will make their aberrations the fmalleft poffible.

It is evident that this proportion is to be obtained by making the fluxion of the quantity within the parenthesis in the formula of par. 2. col. 2. p. 343. equal to nothing. When this is done, we obtain this formula for a, the radius of curvature I 2m2 m 4m+4 for the anterior furface of a lens. 2m+42(m-+-4)r where m is the ratio of the fine of incidence to the fine of refraction, and r is the distance of the focus of incident rays, pofitive or negative, according as they converge or diverge, ail measured on a scale of which the unit is 7, half of the radius of the equivalent ifofceles lens.

1.0

a

It will be fufficiently exact for our purpose to fuppofe

друг

I,

I

b

3

though it is more nearly 3. In this cafe

20

7

2

420+70

Therefore a =

49r

3. col. 2. p. 360. Thus the glafs A of fig. 20. no 2. fhould be Telescopes
moft convex on the fide next the object, that it may produce
little distortion of the pencils. But it fhould be most convex
next the eye, that it may produce diftinct vifion of the image
FG, which is very near it. This image fhould have its con-
cavity turned towards A, whereas it is towards the object-
glafs. We must therefore endeavour to make the vertical
image fg flatter, or even convex. This requires a glafs
very flat before and convex behind. For fimilar reasons
the object-glafs of a microscope and the fimple eye-glafs of
an aftronomical telescope fhould be formed the fame way.

This is a fubject of most difficult difcuffion, and requires
a theory which few of our readers would relifh; nor does
our limits afford room for it. The artifts are obliged to
grope their way. The proper method of experiment would
be, to make eye-pieces of large dimenfions, with extrava-
gant apertures to increase the aberrations, and to provide
for each ftation A, B, C, and D, a number of lenfes of the
fame focal diftance, but of different forms: and we would
advise making the trial in the way of a solar microscope,
Their pictures
and to have two eye pieces on trial at once.
can be formed on the fame fcreen, and accurately compared;
whereas it is difficult to keep in remembrance the perfor-
mance of one eye-piece, and compare it with another.

We have now treated the theory of refracting telescopes
with confiderable minutenefs, and have perhaps exceeded
the limits which some readers may think reasonable. But
we have long regretted that there is not any theory on this
fubject from which a curious perfon can learn the improve-
ments which have been made fince the time of Dr Smith,
or an artist learn how to proceed with intelligence in his
profeffion. If we have accomplished either of thele ends,.
we truft that the public will receive our labours with fatis.
faction.

We cannot add any thing to what Dr Smith has delivered on the theory of reflecting telescopes. There appears 0,875; and to be the fame poffibility of correcting the aberration of the great speculum by the contrary aberration of a convex small fpeculum, that we have practifed in the compound object

These values are parts of a fcale, of which the unit is glass of an achromatic refracting telescope. But this can0,75 inches.

And here we muft obferve that the pofterior furface is con-
cave: for b is a pofitive quantity, becaufe a is a pofi-
tive quantity as well as a; therefore the centre of sphericity
of both surfaces lies beyond the lens.

And this determination is not very different from the ufual practice, which commonly makes this lens a plane convex with its flat fide. next the eye: and there will not be much difference in the performance of these two lenfea; for in all cafes of maxima and minima, even a pretty confider-able change of the best dimenfions does not make a fenfible. change in the result.

The fame confideration leads to a rule which is very fimple, and fufficiently exact for ordinary fituations. This is to make the curvatures such, that the incident and emergent pencils may be nearly equally inclined to the furfaces of the lens. Thus in the eye-piece with five glaffes, A and B fhould be most convex on their anterior fides; C. fhould be most convex on the pofterior fide; D fhould be nearly ifof celes; and E nearly plano-convex..

But this is not fo eafy a matter as appears at first fight. The lenfes of an eye-piece have not only to bend the feveral pencils of light to and from the axis of the telescope; they have alfo to form images on the axes of these pencils. Thele offices frequently require oppofte torms, as mentioned in par.

In

not be, unless we make the radius of the convex fpeculum ·
exceedingly large, which deftroys the magnifying power
and the brightness. This therefore must be given up.
deed their performance, when well executed, does already
vantages in what he calls the front view, not using a plane -
furpaís all imagination. Dr Herfchel has found great ad-
mirror to throw the pencils to one fide. But this cannot
be practifed in any but telescopes fo large, that the lofs of
light, occafioned by the interpofition of the obferver's head,
may be difrega:ded.

NOTHING remains but to defcribe the mechanifm of fome : of the most convenient forms.

To defcribe all the varieties of fhape and accommodation which may be given to a telescope, would be a task as trifling as prolix. The artifts of London and of Paris have racked their inventions to please every fancy, and to fuit every purpose. We fhall content ourfelves with a few general maxims, deduced from the scientific confideration of a telescope, as an inftrument by which the visual angle sub-~tended by a diftinct object is greatly magnified.

i

Telescope. fhows it erect. This is owing to the magnifying power,
because the apparent angular motion is greater than what
we naturally connect with the motion of the telescope.
This
does not happen when we look through a tube with
out glaffes.

*

But this apparatus is not portable, and it is fadly deficient in elegance. The following is the best method we have feen of combining thefe circumftances with the indifpenfable. requifites of a good telescope.

may be almoft annihilated by having a flender rod coming Telescope. from a hook's joint in the fide of the window, and paffing through fuch another joint clofe by the pin F. We have feen an inftrument of this form, having AB parallel to the earth's axis. The whole apparatus did not coft 50 fhillings, All fhaking of the inftrument therefore makes the object and we find it not in the leaft fenfible manner affected by a dance before the eye; and this is disagreeable, and hinders ftorm of wind. It was by obfervations with this instrument us from feeing it diftinctly. But a tremulous motion, how that the tables of the motions of the Georgium Sidus, pubeyer fmall, is infinitely more prejudicial to the performance lifhed in the Edinburgh Tranfactions, were conftructed, of a telescope, by making the object quiver before us. A and they are as accurate as any that have yet appeared. person walking in the room prevents us from feeing diftinct. This is an excellent equatorial. Ty; nay, the very pulfation in the body of the observer, agitates the floor enough to produce this effect, when the telescope has a great magnifying power: For the vilible motion of the object is then an imperceptible tremor, like that of an harpfichord wire, which produces an effect precifely fimilar to optical indiftinctness, and every point of the ob ject is diffused over the whole space of the angular tremor, and appears coexiftent in every part of this space, juft as a harpfichord wire does while it is founding. The more rapid this motion is, the indiftinctness is the more complete. Therefore the more firm and elaftic and well bound together the frame-work and apertures of our telescope is, the more hurtful will this confequence be. A mounting of lead, were it practicable, would be preferable to wood, iron, or brafs. This is one great caufe of the indiftinctness of the very fineft reflecting telescopes of the ufual conftructions, and can never be totally removed. In the Gregorian form, it is hardly poffible to damp the elaftic tremor of the Imall fpeculum, carried by an arm fupported at one end only, even though the tube were motionless. We were witneffes of a great im. provement made on a four-feet reflecting telescope, by fupporting the fmall fpeculum by a ftrong plate of lead placed across the tube, and led by an adjufting fcrew at each end. But even the great mirror may vibrate enough to produce indistinctness. Refracting telescopes are free from this in conveniency, because a small angular motion of the objectglafs round one of its own diameters has no fenfible effect on the image in its focus. They are affected only by an angular motion of the axis of the telescope or of the eye-, glaffes.

This fingle confideration gives us great help towards judging of the merits of any particular apparatus. We fhould ftudy it in this particular, and fee whether its form makes the tube readily fufceptible of fuch tremulous motions. If it does, the firmer it is and the more elaftic it is, the worse. All forms therefore where the tube is fupported only near the middle, or where the whole immediately or remotely depend on one narrow joint, are defective

Reafoning in this way, we fay with confidence, that of all the forms of a telescope apparatus, the old fashioned fimple and reprefented in fig. 21. is by far the beft, and that others are fuperior according as the difpofition of the points of fupport of the tube approaches to this. Let the pivots A, B, be fixed in the lintel and fole of a window. Let the four braces terminate very near to these pivots. Let the telescope lie on the pin Ff, refting on the fhoulder round the eye-piece, while the far end of it refts on one of the pins 1, 2, 3, &c.; and let the diftance of these pins from F very little exceed the length of the telescope. The trembling of the axis, even when confiderable, cannot affect the pofition of the tube, because the braces terminate almost at the pivots. The tremor of the brace CD does as little harm, because it is nearly perpendicular to the tube. And if the object glafs were clole at the upper fupporting pin, and the focus at the lower pin F, even the bending and trembling of the tube will have no effect on its optical axis. The inftrument is only subject to horizontal tremors. These

The pillar VX (fig. 22.) rifes from a firm ftand, and has a horizontal motion round a cone which completely fills it. This motion is regulated by a rack-work in the box at V. The fcrew of this rack-work is turned by means of the handle P, of a convenient length, and the fcrew may be dif engaged by the click or detent V, when we would turn the inftrument a great way at once. The telescope has à vertical motion round the joint Q placed near the middle of the tube. The lower end of the tube is fupported by the ftay OT. This confifts of a tube RT, faftened to the pil lar by a joint I', which allows the ftay to move in a vertical plane. Within this tube flides another, with a ftiff motion. This tube is connected with the telescope by another joint O, alfo admitting motion in a vertical plane. The fide M of this inner tube is formed into a rack, in which works a ́ pinion fixed to the top of the tube RT, and turned by the flat finger-piece R. The reader will readily fee the advantages and the remaining defects of this apparatus. It is very portable, because the telescope is eafily difengaged from it, and the legs and ftay fold up. If the joint Q were immediately under A, it would be much freer from all tremor in the vertical plane. But nothing can hinder other tremors arifing from the long pillar and the three springy legs. Thefe communicate all external agitations with great vigour. The inftrument fhould be fet on a stone pedestal, or, what is better, a cafk filled with wet fand. This pedeltal, which neceffity perhaps fuggefted to our fcientific navigators, is the beft that can be imagined.

Fig. 23 is the stand usually given to reflecting telescopes. The vertical tube FBG is faftened to the tube by finger fcrews, which pafs through the flits at F and G. This arch turns round a joint in the head of the divided pillar, and has its edge cut into an oblique rack, which is acted on by the horizontal ferew, furnifhed with the finger-piece A. This fcrew turns in a horizontal fquare frame. This frame turns round a horizontal joint in the off fide, which cannot be feen in this view. In the fide of this frame next the eye there is a finger-fcrew 'a, which paffes through the frame, and preffes on the round horizontal plate D. By fcrewing down this finger-fcrew, the frame is brought up, and preffes the horizontal screw to the rack. Thus the elevation of the. telescope is fixed, and may be nicely changed by the finger applied to A' and turning this fcrew. The horizontal round plate D moves ftiffly round on another plate of nearly equal diameter. This under plate has a deep conical hollow focket, which is nicely fitted by grinding to a folid cone formed on the top of the great upright pillar, and they may be firmly fixed in any polition by the finger-fcrew E. To the under plate is taftened a box c, containing a horizontal ferew C, which always works in a rack cut in the edge of the upper plate, and cannot be difengaged from it. When a great vertical or horizontal motion is wanted, the fcrews a and E are flacked, and by tightening them the telescope may be

fixed

G

ظر منظورم

Red
Orange

Yellow
Green

A

Blue
Purple

Ficlet

C

M

E

K

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