Chapter IV (1)

ON THE DIFFERENT KINDS OF REFRACTING TELESCOPES.

There are two kinds of telescopes, corresponding to two modes of vision, namely, those which perform their office by _refraction_ through lenses, and those which magnify distant objects by _reflection_ from mirrors. The telescope which is constructed with lenses, produces its effects solely by refracted light, and is called a Dioptric, _or refracting telescope_. The other kind of telescope produces its effects partly by reflection, and partly by refraction, and is composed both of mirrors and lenses; but the mirrors form the principal part of the telescope; and therefore such instruments are denominated _reflecting telescopes_. In this chapter I shall describe the various kinds of _refracting_ telescopes.

SECT 1.--THE GALILEAN TELESCOPE.

This telescope is named after the celebrated Galileo, who first constructed, and probably _invented_ it in the year 1609. It consists of only two glasses, a _convex_ glass next the object, and a _concave_ next the eye. The convex is called the _object-glass_, and the concave to which the eye is applied, is called the _eye-glass_. Let C (fig. 43.) represent the convex object-glass, presented to any object in the direction DEI, so that the rays fall parallel upon it;--if these rays, after passing through it, were not intercepted by the concave lens K, they would pass on, and cross each other in the focus F, where an inverted image of the object would be formed. But the concave lens K, the virtual focus of which is at F, being interposed, the rays are not suffered to converge to that point, but are made less convergent,[19] and enter the pupil almost parallel, as GH, and are converged by the humours of the eye to their proper foci on the retina. The object, through this telescope, is seen upright, or in its natural position, because the rays are not suffered to come to a focus, so as to form an inverted picture. The concave eye-glass is placed as far within the focus of the object-glass, as is equal to its own virtual focus; and the magnifying power is as the focal length of the object-glass to that of the eye-glass, that is, as CF to BF. Thus, suppose the focus of the object-glass to be 10 inches, and the focus of the eye-glass to be 1 inch, the magnifying power will be 10 times--which is always found by dividing the focal length of the object-glass by that of the eye-glass. The interval between the two glasses, in this case, will be 9 inches, which is the length of the telescope, and the objects seen through it will appear under an angle ten times greater than they do to the naked eye. These propositions might be proved mathematically; but the process is somewhat tedious and intricate, and might not fully be understood by general readers. I shall therefore only mention some of the general properties of this telescope, which is now seldom used, except for the purpose of _opera-glasses_.

1. The focal distance of the object-glass must be greater than that of the eye-glass, otherwise it would not magnify an object: if the focal distance of the eye-glass were greater than that of the object-glass, it would diminish objects, instead of magnifying them. 2. The visible area of the object is greater, the nearer the eye is to the glass; and it depends on the diameter of the pupil of the eye, and on the breadth of the object-glass; consequently the field of view in this telescope is very small. 3. The distinctness of vision in this construction of a telescope exceeds that of almost any other. This arises from the rays of light proceeding from the object directly through the lenses, _without crossing_ or intersecting each other; whereas in the combination of convex lenses, they intersect one another to form an image in the focus of the object-glass, and this image is magnified by the eye-glass with all its imperfections and distortions. The thinness of the centre of the concave lens also contributes to distinctness. 4. Although the field of view in this telescope is very small, yet where no other telescope can be procured, it might be made of such a length as to show the spots on the Sun, the crescent of Venus, the satellites of Jupiter, and the ring of Saturn; and, requiring only two glasses, it is the cheapest of all telescopes. It has been found that an object-lens 5 feet focal distance, will bear a concave eye-glass of only 1 inch focal distance, and will consequently magnify the diameters of the planets 60 times, and their surfaces 3600 times, which is sufficient to show the phenomena now stated. And, although only a small portion of the sun and moon can be seen at once, yet Jupiter and all his satellites may sometimes be seen at one view; but there is some difficulty in finding objects with such telescopes. 5. Opera-glasses, which are always of this construction, have the object-lens generally about 6 inches focus and 1 inch diameter, with a concave eye-glass of about 2 inches focus. These glasses magnify about 3 times in diameter, have a pretty large field, and produce very distinct vision. When adjusted to the eye, they are about 4 inches in length. To the object end of an opera-glass there is sometimes attached a plane mirror, placed at an angle of 45 degrees, for the purpose of viewing objects on either side of us. By this means, in a theatre or assembly, we can take a view of any person without his having the least suspicion of it, as the glass is directed in quite a different direction. The instrument with this appendage is sometimes called a _Polemoscope_.

SECT. 2.--THE COMMON ASTRONOMICAL REFRACTING TELESCOPE.

The astronomical telescope is the most simple construction of a telescope, composed of convex lenses only, of which there are but two essentially necessary, though a third is sometimes added to the eye-piece for the purpose of enlarging the field of view. Its construction will be easily understood from a description of the following figure. Its two essential parts are, an object-glass AD, and an eye-glass EY, so combined in a tube that the focus F of the object-glass is exactly coincident with the focus of the eye-glass. Let OB (fig. 44.) represent a distant object, from which rays nearly parallel proceed to the object-lens AD. The rays passing through this lens will cross at F, and form an image of the object at IM. This image forms as it were an object to the eye-glass EY, which is of a short focal distance, and the eye is thus enabled to contemplate the object as if it were brought much nearer than it is in reality. For the rays, which after crossing proceed in a divergent state, fall upon the lens EY, as if they proceeded from a real object situated at F. All that is effected therefore, by such a telescope is, to form an image of a distant object by means of the object-lens, and then to give the eye such assistance as is necessary for viewing that image as near as possible, so that the angle it shall subtend at the eye shall be very large compared with the angle which the object itself would subtend in the same situation.

Here it may be expedient to explain, 1. how this arrangement of glasses shows distant objects distinctly, and 2. the reason why objects appear magnified when seen through it. As to the first particular, it may be proved as follows:--The rays OA and BD, which are parallel before they fall upon the object-glass, are by this glass refracted and united at its focus: In order, then, to distinct vision, the eye-glass must re-establish the parallelism of the rays,--which is effected by placing the eye-glass so that its focus may be at F, and consequently the rays will proceed from it parallel to each other and fall upon the eye in that direction. For distinct vision is produced by _parallel_ rays. 2. The reason why the object appears magnified will appear, if we consider that, if the eye viewed the object from the centre of the object-glass, it would see it under the angle OCB; let OC and BC then be produced to the focus of the glass, they will then limit the image IM formed in the focus. If then, two parallel rays are supposed to proceed to the eye-glass EY, they will be converged to its focus H, and the eye will see the image under the angle EHY. The apparent magnitude of the object, therefore, as seen by the naked eye, is to the magnitude of the image as seen through the telescope, as OCB to EHY, or as the distance CF to the distance FG, in other words, _as the focal length of the object-glass to that of the eye-glass_.

It is obvious from the figure, that, through this telescope, all objects will appear _inverted_; since the object OB is depicted by the object-glass in an inverted position at IM, and in this position is viewed by the eye-glass EY; and, therefore this kind of telescope is not well adapted for viewing terrestrial objects, since it exhibits the tops of trees, houses, and other objects as undermost, and the heads of people as pointing downwards. But this circumstance is of no consequence with respect to the heavenly bodies, since they are round, and it can make little difference to an observer which side of a globular body appears uppermost or undermost. All astronomical refracting telescopes invert objects; but they are preferred to any other telescopes, because they have few glasses, and consequently more light. This telescope however, can be transformed into a common day telescope for land objects, by the addition of two other eye-glasses, as we shall afterwards explain; but in this case a quantity of light is lost by refraction at each lens; for there is scarcely any transparent substance that transmits all the rays of light that fall upon it.

The _magnifying power_ of this telescope is found _by dividing the focal distance of the object-glass by the focal distance of the eye-glass_: the quotient gives the magnifying power, or the number of times that the object seen through the telescope, appears larger or nearer than to the naked eye. Thus, for example, if the focal distance of the object-glass be 28 inches, and the focal distance of the eye-glass 1 inch, the magnifying power will be 28 times. If we would enlarge the telescope and select an object-glass 10 feet, or 120 inches focus, an eye-glass of 2 inches focal length might be applied, and then the diameter of objects would be magnified 60 times, and their surfaces 3600 times. If we would use an object-glass of 100 feet, it would be necessary to select an eye-glass about 6 inches focus, and the magnifying power would be 200 times, equal to 1200 inches divided by 6. Since, then, the power of magnifying depends on the proportion of the focal length of the object and eye-glasses, and this proportion may be varied to any degree, it may seem strange to some that a short telescope of this kind will not answer that purpose as well as a long one. For instance, it may be asked why an object-glass of 10 feet focus, may not be made to magnify as much, as one of 100 feet focal length, by using an eye-glass of half an inch focus, in which case, the magnifying power would be 240 times? But it is to be considered, that if the power of magnifying be increased, while the length of the telescope remains the same, it is necessary to diminish the focal length of the eye-glass in the same proportion, and this cannot be done on account of the great distortion and colouring which would then appear in the image, arising both from the deep convexity of the lens and the different refrangibility of the rays of light. It is found that the length of common refracting telescopes must be increased in proportion to the square of the increase of their magnifying power; so that in order to magnify twice as much as before, with the same light and distinctness, the telescope must be lengthened four times; to magnify 3 times as much, 9 times; and to magnify four times as much, sixteen times; that is--suppose a telescope of 3 feet to magnify 33 times,--in order to procure a power four times as great, or 132 times, we must extend the telescope to the length of 48 feet, or 16 times the length of the other. Much likewise depends upon the breadth or aperture of the object-glass. If it be too small, there will not be sufficient light to illuminate the object; and if it be too large, the redundance of light will produce confusion in the image.

The following table, constructed originally by Huygens, and which I have re-calculated and corrected, shows the linear aperture, the focal distance of the eye-glass, and the magnifying power of astronomical telescopes of different lengths, which may serve as a guide to those who wish to construct telescopes of this description.

---------------+----------------------------------+-----------
Focal distance | Linear aperture Focal distance | Magnifying
of the | of the of the | power.
object-glass. | object-glass. eye-glass. |
---------------+-----------------+----------------+-----------
Feet. | Inch. Dec. | Inch. Dec. |
1 | 0. 545 | 0. 605 | 20
2 | 0. 76 | 0. 84 | 28.5
3 | 0. 94 | 1. 04 | 34.6
4 | 1. 08 | 1. 18 | 40
5 | 1. 21 | 1. 33 | 45
6 | 1. 32 | 1. 45 | 50
7 | 1. 43 | 1. 58 | 53
8 | 1. 53 | 1. 69 | 56.8
9 | 1. 62 | 1. 78 | 60.6
10 | 1. 71 | 1. 88 | 63.8
15 | 2. 10 | 2. 30 | 78
20 | 2. 43 | 2. 68 | 89.5
30 | 3. 00 | 3. 28 | 109
40 | 3. 43 | 3. 76 | 127
50 | 3. 84 | 4. 20 | 142
60 | 4. 20 | 4. 60 | 156
70 | 4. 55 | 5. 00 | 168
80 | 4. 83 | 5. 35 | 179
90 | 5. 15 | 5. 65 | 190
100 | 5. 40 | 5. 95 | 200
120 | 5. 90 | 6. 52 | 220

In the above table, the first column expresses the focal length of the object-glass in feet; the second column, the diameter of the aperture[20] of the object-glass, the third column, the focal distance of the eye-glass, and the fourth, the magnifying power, which is found by reducing the feet in the first column to inches, and dividing by the numbers in the third column. From this table it appears that, in order to obtain a magnifying power of 168 times, by this kind of telescope, it is requisite to have an object-glass of 70 feet focal distance, and an eye-glass five inches focus, and that the aperture of the object-glass ought not to be more than about 4-1/2 inches diameter. To obtain a power of 220 times requires a length of 120 feet.

The following is a summary view of the properties of this telescope. 1. The object is always inverted. 2. The magnifying power is always in the proportion of the focal distance of the object-glass to the eye-glass. 3. As the rays emerging from the eye-glass, should be rendered parallel for every eye, there is a small sliding tube next the eye, which should be pushed out or in till the object appears distinct. When objects are pretty near, this tube requires to be pulled out a little. These circumstances require to be attended to in all telescopes. 4. The apparent magnitude of an object is the same wherever the eye be placed, but the visible area, or field of view, is the greatest when the eye is nearly at the focal distance of the eye-glass. 5. The visual angle depends on the breadth of the eye-glass; for it is equal to the angle which the eye-glass subtends at the object-glass; but the breadth of the eye-glass cannot be increased beyond a certain limit, without producing colouring and distortion.

If the general principles on which this telescope is constructed be thoroughly understood, it will be quite easy for the reader to understand the construction of all the other kinds of telescopes, whether refracting or reflecting. A small astronomical telescope can be constructed in a few moments, provided one has at hand the following lenses:--1. A common reading-glass, eight or ten inches focal distance; 2. A common magnifying lens, such as watchmakers or botanists use, of about 1-1/2 or 2 inches focus. Hold the reading-glass--suppose of ten inches focus--in the left hand opposite any object, and the magnifying lens of two inches focus, in the right hand near the eye, at twelve inches distance from the other in a direct line, and a telescope is formed which magnifies five times. I have frequently used this plan, when travelling, when no other telescope was at hand.

SECT. 3.--THE AERIAL TELESCOPE.

The Aerial is a refracting telescope of the kind we have now described, intended to be used without a tube in a dark night; for the use of a tube is not only to direct the glasses, but to make the place dark where the images are formed. It appears from the preceding table inserted above, that we cannot obtain a high magnifying power, with the common astronomical telescope, without making it of an extreme length, in which case the glasses are not manageable in tubes--which are either too slight and apt to bend, or too heavy and unwieldy if made of wood, iron or other strong materials. The astronomers of the seventeenth century, feeling such inconveniences in making celestial observations with long tubes, contrived a method of using the glasses without tubes. Hartsocker, an eminent optician, contrived to fix them at the top of a tree, a high wall, or the roof of a house; but the celebrated Huygens, who was not only an astronomer, but also an excellent mechanic, made considerable improvements in the method of using an object-glass without a tube. He placed it at the top of a very long pole, having previously enclosed it in a short tube, which was made to turn in all directions by means of a ball and socket. The axis of this tube he could command with a fine silken string, so as to bring it into a line with the axis of another short tube which he held in his hand, and which contained the eye-glass. The following is a more particular description of one of these telescopes. On the top of a long pole or mast _ab_ (fig. 45), is fixed a board moveable up and down in the channel _cd_: _e_ is a perpendicular arm fixed to it, and _ff_ is a transverse board that supports the object glass enclosed in the tube _i_, which is raised or lowered by means of the silk cord _rl_; _gg_ is an endless rope with a weight _h_, by which the apparatus of the object-glass is counterpoised; _kl_ is a stick fastened to the tube _i_; _m_ the ball and socket, by means of which the object-glass is moveable every way: and to keep it steady, there is a weight _n_ suspended by a wire; _l_ is a short wire to which the thread _rl_ is tied; _o_ is the tube which holds the eye-glass; _q_ the stick fixed to this tube, _s_ a leaden bullet, and _t_ a spool to wind the thread on; _u_ is pins for the thread to pass through; _x_ the rest for the observer to lean upon, and _y_ the lantern. Fig. 46 is an apparatus contrived by M. de la Hire for managing the object-glass; but which it would be too tedious particularly to describe. To keep off the dew from the object-glass, it was sometimes included in a pasteboard tube, made of spongy paper, to absorb the humidity of the air. And to find an object more readily, a broad annulus of white pasteboard was put over the tube that carried the eye-glass; upon which the image of the object being painted, an assistant who perceived it, might direct the tube of the eye-glass into its place.

Such was the construction of the telescopes with which Hevelius, Huygens, Cassini, and other eminent astronomers of the seventeenth century made their principal discoveries. With such telescopes, Huygens discovered the fourth satellite of Saturn, and determined that this planet was surrounded with a ring; and with the same kind of instrument Cassini detected the first, second, third, and fifth, satellites of Saturn, and made his other discoveries. When the night was very dark, they were obliged to make the object-glass visible, by means of a lantern so constructed as to throw the rays of light up to it in a parallel direction. In making such observations, they must have taken incredible pains, endured much cold and fatigue, and subjected themselves to very great labour and expense--which almost makes us wonder at the discoveries they were instrumental in bringing to light--and should make modern philosophers sensible of the obligations they are under to such men as Newton and Dollond, through whose inventions such unwieldy instruments are no longer necessary. Telescopes of the description now stated were made of all sizes, from 30 to above 120 feet in length. Divini at Rome, and Campani at Bologna, were famed as makers of the object-glasses of the long focal distance to which we have alluded, who sold them for a great price, and took every method to keep the art of making them a secret. It was with telescopes made by Campani, that Cassini made his discoveries. They were made by the express order of Louis XIV, and were of 86, 100, and 136 Paris feet in focal length. M. Auzout made one object-glass of 600 feet focus; but he was never able to manage it, so as to make any practical observations with it. Hartsocker is said to have made some of a still greater focal length. The famous aerial telescope of Huygens was 123 feet in focal length, with six inches of aperture. At his death, he bequeathed it to the Royal Society of London, in whose possession it still remains. It required a pole of more than a hundred feet high, on which to place the object-glass for general observations. It was with this glass, that Dr. Derham made the observations to which he alludes in his preface to his ‘Astro-Theology.’ When this glass was in the possession of Mr. Cavendish, it was compared with one of Mr. Dollond’s forty-six inch treble object-glass Achromatics, and the gentlemen who were present at the trial, said that ‘the Dwarf was fairly a match for the Giant.’ It magnified 218 times, and the trouble of managing it, was said to be extremely tiresome and laborious.

SECT. 4.--THE COMMON REFRACTING TELESCOPE FOR TERRESTRIAL OBJECTS.

This telescope is constructed on the same principle as the astronomical telescope already described, with the addition of two or three glasses. In fig. 47, OB represents a distant object, LN, the object glass, which forms the image IM in its focus, which is, of course, in an inverted position, and, if the eye were applied at the lens EE, the object would appear, exactly as through the astronomical telescope, every object being apparently turned upside down. To remedy this inconvenience, there are added two other glasses FF and GG, by which a second image is formed from the first, in the same position as the object. In order to effect this, the first of these two glasses, namely FF, is placed at twice its focal distance from the former glass EE, and the other lens GG, next the eye, is placed at the same distance from FF. For all the three glasses are supposed to be of the same focal distance. Now, the lens FF, being placed at twice the focal distance for parallel rays from EE, receives the pencils of parallel rays after they have crossed each other at X, and forms an image at _i m_ similar to that at IM and equal to it, but contrary in position, and consequently erect; which last image is viewed by the lens GG, in the same manner as the first image IM would be viewed by the lens EE. In this case, the image IM is considered as an object to the lens FF of which it forms a picture in its focus, in a reverse position from that of the first image, and of course, in the same position as the object.

The magnifying power of this telescope is determined precisely in the same way as that of the astronomical telescope. Suppose the object-glass to be thirty inches focal distance, and each of the eye-glasses 1-1/2 inch focal distance, the magnifying power is in the proportion of 30 to 1-1/2, or 20 times, and the instrument is, of course, considerably longer than an astronomical telescope of the same power. The distance, in this case, between the object-glass and the first eye-glass EE is 31-1/2 inches; the distance between EE, and the second glass FF, is 3 inches, and the distance between FF and the glass GG next the eye, 3 inches; in all 37-1/2 inches, the whole length of the telescope. Although it is usual to make use of three eye-glasses in this telescope, yet two will cause the object to appear erect, and of the same magnitude. For suppose the middle lens FF taken away, if the first lens EE be placed at X, which is double its focal distance from the image IM, it will at the same distance X _m_, on the other side, form a secondary image _i m_ equal to the primary image IM, and also in a contrary position. But such a combination of eye-glasses produces a great degree of colouring in the image, and therefore is seldom used. Even the combination now described, consisting of three lenses of equal focal distances, is now almost obsolete, and has given place to a much better arrangement consisting of _four_ glasses, of different focal distances--which shall be afterwards described.

The following figures, 48, 49, 50 represent the manner in which the rays of light are refracted through the glasses of the telescopes we have now described. Fig. 48 represents the rays of light as they pass from the object to the eye in the Galilean telescope. After passing in a parallel direction to the object-glass, they are refracted by that glass, and undergo a slight convergence in passing towards the concave eye-glass, where they enter the eye in a parallel direction, but no image is formed previous to their entering the eye, till they arrive at the retina. Fig. 49 represents the rays as they pass through the glasses of the astronomical telescope. The rays, after entering the object-glass, proceed in a converging direction, till they arrive at its focus, about A, where an image of the object is formed; they then proceed diverging to the eye-glass, where they are rendered parallel, and enter the eye in that direction. Fig. 50 represents the rays as they converge and diverge in passing through the four glasses of the common day-telescope described above. After passing through the object-glass, they converge towards B, where the first image is formed. They then diverge towards the first eye-glass where they are rendered parallel; and passing through the second eye-glass, they again converge and form a second image at C; from which point they again diverge, and passing through the first eye-glass enter the eye in a parallel direction. If the glasses of these telescopes were fixed on long pieces of wood, at their proper distances from each other, and placed in a darkened room, when the sun is shining, the beam of the sun’s light would pass through them in the same manner as here represented.

SECT. 5.--TELESCOPE FORMED BY A SINGLE LENS.

This is a species of telescope altogether unnoticed by optical writers, so far as I know; nor has the property of a single lens in magnifying distant objects been generally adverted to or recognised. It may not therefore be inexpedient to state a few experiments which I have made in relation to this point. When we hold a spectacle-glass of a pretty long focal distance--say, from 20 to 24 inches--close to the eye, and direct it to distant objects, they do not appear sensibly magnified. But if we hold the glass about 12 or 16 inches from our eye, we shall perceive a sensible degree of magnifying power, as if distant objects were seen at less than half the distance at which they are placed. This property of a spectacle-glass I happened to notice when a boy, and, on different occasions since that period have made several experiments on the subject, some of which I shall here relate.

With the object-glass of a common refracting telescope 4-1/2 feet focal distance, and 2-1/2 inches diameter, I looked at distant objects--my eye being at about 3-1/2 feet from the lens, or about 10 or 12 inches within its focus--and it produced nearly the same effect as a telescope which magnifies the diameters of objects 5 or 6 times. With another lens 11 feet focal distance and 4 inches diameter--standing from it at the distance of about 10 feet, I obtain a magnifying power of about 12 or 14 times, which enables me to read the letters on the sign-posts of a village half a mile distant. Having some time ago procured a very large lens 26 feet focal distance, and 11-1/2 inches diameter, I have tried with it various experiments of this kind upon different objects. Standing at the distance of about 25 feet from it, I can see distant objects through it magnified about 26 times in diameter, and consequently 676 times in surface, and remarkably clear and distinct, so that I can distinguish the hour and minute hands of a public clock in a village two miles distant. This single lens, therefore answers the purpose of an ordinary telescope with a power of 26 times. In making such experiments our eye must always be _within_ the focus of the lens, at least 8 or 10 inches. The object will, indeed, be seen at any distance from the glass within this limit; but the magnifying power is diminished in proportion as we approach nearer to the glass. Different eyes, too, will require to place themselves at different distances, so as to obtain the greatest degree of magnifying power with distinctness, according as individuals are long or short-sighted.

This kind of telescope stands in no need of a tube, but only of a small pedestal on which it may be placed on a table, nearly at the height of the eye, and that it be capable of a motion in a perpendicular or parallel direction, to bring it in a line with the eye and the object. The principle on which the magnifying power, in this case, is produced, is materially the same as that on which the performance of the Galilean telescope depends. The eye of the observer serves instead of the concave lens in that instrument; and as the concave lens is placed as much within the focus of the object-glass, as is equal to its own focal distance, so the eye, in these experiments, must be placed at least its focal distance within the focus of the lens with which we are experimenting; and the magnifying power will be nearly in the proportion of the focal distance of the lens to the focal distance of the eye. If, for example, the focal distance of the eye, or the distance at which we see to read distinctly, be 10 inches, and the focal distance of the lens, 11 feet, the magnifying power will be as 11 feet, or 132 inches to 10, that is, about 13 times. Let A (fig. 51.) represent the lens placed on a pedestal; the rays of light passing through this lens from distant objects will converge towards a focus at F. If a person then, place his eye at E, a certain distance within the focal point, he will see distant objects magnified nearly in the proportion of the focal distance of the lens to that of the eye; and when the lens is very broad--such as the 26 feet lens mentioned above--two or three persons may look through it at once, though they will not all see the same object. I have alluded above to a lens made by M. Azout of 600 feet focal distance. Were it possible to use such a lens for distant objects, it might represent them as magnified 5 or 600 times, without the application of any eye-glass. In this way the aerial telescope of Huygens would magnify objects above 100 times, which is about half the magnifying power it produced with its eye-piece. Suppose Azout’s lens had been fitted up as a telescope, it would not have magnified above 480 times, as it would have required an eye-glass of 14 or 15 inches focal distance, whereas, without an eye-glass, it would have magnified objects considerably above 500 times. It is not unlikely that the species of telescope to which I have now adverted, constituted one of those instruments for magnifying distant objects which were said to have been in the possession of certain persons long before their invention in Holland, and by Galileo in Italy--to which I have referred in p. 182. Were this kind of telescope to be applied to the celestial bodies, it would require to be elevated upon a pole in the manner represented, fig. 45, p. 226.

SECT. 6.--THE ACHROMATIC TELESCOPE.

This telescope constitutes the most important and useful improvement ever made upon telescopic instruments; and, it is probable, it will, ere long, supersede the use of all other telescopes. Its importance and utility will at once appear when we consider, that a good achromatic telescope of only 4 or 5 feet in length will bear a magnifying power as great, as that of a common astronomical telescope 100 feet long, and even with a greater degree of distinctness, so that they are now come into general use both for terrestrial and celestial observations. There are, indeed, certain obstructions which prevent their being made of a very large size; but from the improvement in the manufacture of achromatic glass which is now going forward, it is to be hoped that the difficulties which have hitherto impeded the progress of opticians will soon be removed. In order to understand the nature of this telescope, it will be necessary to advert a little to the _imperfections_ connected with common refracting telescopes.

The first imperfection to which I allude is this, that _spherical surfaces do not refract the rays of light accurately to a point_; and hence the image formed by a single convex lens is not perfectly accurate and distinct. The rays which pass near the extremities of such a lens meet in foci nearer to the lens than those which pass nearly through the centre, which may be illustrated by the following figure. Let PP (fig. 52) be a convex lens and E_e_ an object, the point E of which corresponds with the axis, and sends forth the rays EM, EN, EA, &c., all of which reach the surface of the glass, but in different parts. It is manifest that the ray EA which passes through the middle of the glass, suffers no refraction. The rays EM, EM, likewise, which pass through near to EA, will be converged to a focus at F, which we generally consider as the focus of the lens. But the rays EN, EN, which are nearer to the edge of the glass will be differently refracted, and will meet about G, nearer to the lens, where they will form another image G_g_. Hence, it is evident, that the first image F_f_, is formed only by the union of those rays which pass very near the centre of the lens; but as the rays of light proceeding from every point of an object are very numerous, there is a succession of images formed, according to the parts of the lens where they penetrate, which necessarily produces indistinctness and confusion. This is the imperfection which is distinguished by the name of _spherical aberration_, or the error arising from the spherical form of lenses.

The second and most important imperfection of single lenses, when used for the object-glasses of telescopes, is, that the rays of compounded light being differently refrangible, come to their respective foci at different distances from the glass; the more refrangible rays, as the _violet_, converging sooner than those which are less refrangible, as the _red_. I have had occasion to illustrate this circumstance, when treating on the colours produced by the prism, (see p. 128, and figures 32 and 33,) and it is confirmed by the experiment of a paper painted red, throwing its image, by means of a lens, at a greater distance than another paper painted blue. From such facts and experiments, it appears, that the image of a white object consists of an indefinite number of coloured images, the violet being nearest, and the red farthest from the lens, and the images of intermediate colours at intermediate distances. The aggregate, or image itself, must therefore be in some degree confused; and this confusion being much increased by the magnifying power, it is found necessary to use an eye glass of a certain limited convexity to a given object glass. Thus, an object glass of 34 inches focal length will bear an eye-glass of only 1 inch focus, and will magnify the diameters of objects 34 times; one of 50 feet focal distance will require an eye-glass of 4-1/2 inches focus, and will magnify only 142 times; whereas, could we apply to it an eye-glass of only 1 inch focus, as in the former case, it would magnify no less than 600 times. And were we to construct an object-glass of 100 feet focal length, we should require to apply an eye-glass, not less than 6 inches focus, which would produce a power of about 200 times; so that there is no possibility of producing a great power by single lenses, without extending the telescope to an immoderate length.

Sir Isaac Newton, after having made his discoveries respecting the colours of light, considered the circumstance we have now stated as an insuperable barrier to the improvement of refracting telescopes; and therefore turned his attention to the improvement of telescopes by _reflection_. In the telescopes which he constructed and partly invented, the images of objects are formed by reflection from speculums or mirrors; and being free from the irregular convergency of the various coloured rays of light, will admit of a much larger aperture and the application of a much greater degree of magnifying power. The reflector which Newton constructed was only 6 inches long, but it was capable of bearing a power equal to that of a 6 feet refractor. It was a long time, however, after the invention of these telescopes before they were made of a size fitted for making celestial observations. After reflecting telescopes had been some time in use, Dollond made his famous discovery of the principle which led him to the construction of the _achromatic_ telescope. This invention consists of a compound object glass formed of two different kinds of glass, by which both the spherical aberration and the errors arising from the different refrangibility of the rays of light are, in a great measure corrected. For the explanation of the nature of this compound object glass and of the effects it produces; it may be expedient to offer the following remarks respecting the dispersion of light and its refraction by different substances.

The _dispersion_ of light is estimated by the variable angle formed by the red and violet rays which bound the solar spectrum;--or rather, it is the excess of the refraction of the most refrangible ray above that of the least refrangible ray. The dispersion is not proportional to the refraction--that is, the substances which have an equal mean refraction, do not _disperse_ light in the same ratio. For example, if we make a prism with plates of glass, and fill it with oil of Cassia, and adjust its refracting angle ACB, (fig. 31, p. 127,) so that the middle of the spectrum which it forms falls exactly at the same place where the green rays of a spectrum formed by a glass prism would fall--then we shall find that the spectrum formed by the _oil of Cassia_ prism will be two or three times _longer_ than that of the _glass_ prism. The oil of Cassia, therefore, is said to _disperse_ the rays of light more than the glass, that is, to separate the extreme red and violet rays at O and P more than the mean ray at _green_, and to have a greater _dispersive power_. Sir I. Newton appears to have made use of prisms composed of different substances, yet, strange to tell, he never observed that they formed spectrums, whose lengths were different, when the refraction of the green ray was the same; but thought that the dispersion was proportional to the refraction. This error continued to be overlooked by philosophers for a considerable time, and was the cause of retarding the invention of the achromatic telescope for more than 50 years.

Dollond was among the first who detected this error. By his experiments it appears, that the different kinds of glass differ extremely with respect to the divergency of colours produced by equal refractions. He found that two prisms, one of white flint glass, whose refracting angle was about 25 degrees, and another of crown glass whose refracting angle was about 29 degrees, refracted the beam of light nearly alike; but that the divergency of colour in the white flint was considerably more than in the crown glass; so that when they were applied together, to refract contrary ways, and a beam of light transmitted through them, though the emergent continued parallel to the incident part, it was, notwithstanding, separated into component colours. From this he inferred, that, in order to render the emergent beam white, it is necessary that the refracting angle of the prism of crown glass should be _increased_, and by repeated experiments he discovered the exact quantity. By these means he obtained a theory in which refraction was performed without any separation or divergency of colour; and thus the way was prepared for applying the principle he had ascertained to the construction of the object glasses of refracting telescopes. For the edges of a convex and concave lens, when placed in contact with each other, may be considered as two prisms which refract contrary ways; and if the excess of refraction in the one be such as precisely to destroy the divergency of colour in the other, a colourless image will be formed. Thus, if two lenses are made of the same focal length, the one of flint glass and the other of crown, the length or diameter of the coloured image in the first will be to that produced by the crown glass, as 3 to 2 nearly. Now, if we make the focal lengths of the lenses in this proportion, that is, as 3 to 2, the coloured spectrum produced by each will be equal. But if the flint lens be concave, and the crown convex--when placed in contact--they will mutually correct each other, and a pencil of white light refracted by the compound lens will remain colourless.

The following figure may perhaps illustrate what has been now stated. Let LL (fig. 53.) represent a convex lens of _crown glass_, and _ll_ a concave lens of _flint glass_. A ray of the sun S, falls at F on the convex lens which will refract it exactly as the prism ABC, whose faces touch the two surfaces of the lens at the points where the ray enters and quits it. The solar ray, SF, thus refracted by the lens LL, or prism ABC, would have formed a spectrum PT on the wall, had there been no other lens, the violet ray F crossing the axis of the lens at V, and going to the upper end P of the spectrum; and the red ray FR, going to the lower end T. But as the flint-glass lens _ll_, or the prism A_a_C which receives the rays FV, FR, at the same points, is interposed, these rays will be united at _f_, and form a small circle of white light; the ray SF of the sun being now refracted without colour from its primitive direction SFY into the new direction F_f_. In like manner the corresponding ray SM will be refracted to _f_, and a white and colourless image of the sun will be there formed by the two lenses. In this combination of lenses it is obvious that the spherical aberration of the flint lens corrects to a considerable degree that of the crown-glass, and by a proper adjustment of the radii of the surfaces, it may be almost wholly removed. This error is still more completely corrected in the _triple_ achromatic object-glass, which consists of three lenses--a concave flint lens placed between convexes of crown glass. Fig. 54 shows the _double_ achromatic lens, and fig. 55, the _triple_ object-glass, as they are fitted up in their cells, and placed at the object end of the telescope. In consequence of their producing a focal image free of colour they will bear a much larger aperture and a much greater magnifying power than common refracting telescopes of the same length. While a common telescope whose object-glass is 3-1/2 feet focal distance will bear an aperture of scarcely 1 inch, the 3-1/2 feet Achromatic will bear an aperture of 3-1/4 inches, and consequently transmits 10-1/2 times the quantity of light. While the one can bear a magnifying power of only about 36 times, the other will bear a magnifying power for celestial objects of more than 200 times.

The theory of the achromatic telescope is somewhat complicated and abstruse, and would require a more lengthened investigation than my limits will permit. But what has been already stated may serve to give the reader a general idea of the _principle_ on which it is constructed, which is all I intended. The term _achromatic_ by which such instruments are now distinguished was first given to them by Dr. Bevis. It is compounded of two Greek words which signify, ‘free of colour.’ And, were it not that even philosophers are not altogether free of that pedantry which induces us to select Greek words which are unintelligible to the mass of mankind, they might have been contented with selecting the plain English word _colourless_, which is as significant and expressive as the Greek word _achromatic_. The _crown-glass_, of which the convex lenses of this telescope are made, is the same as good common window-glass; and the _flint-glass_ is that species of glass of which wine-glasses, tumblers, decanters and similar articles are formed, and is sometimes distinguished by the name of crystal-glass. Some opticians have occasionally formed the concave lens of an achromatic object-glass from the bottom of a broken tumbler.

This telescope was invented and constructed by Mr. John Dollond, about the year 1758. When he began his researches into this subject, he was a silk weaver in Spitalfields, London. The attempt of the celebrated Euler to form a colourless telescope, by including water between two meniscus glasses, attracted his attention, and, in the year 1753, he addressed a letter to Mr. Short, the optician, which was published in the Philosophical Transactions of London, ‘concerning a mistake in Euler’s theorem for correcting the aberrations in the object glasses of refracting telescopes.’ After a great variety of experiments on the refractive and dispersive powers of different substances, he at last constructed a telescope in which an exact balance of the opposite dispersive powers of the crown and flint lenses made the colours disappear, while the predominating refraction of the crown lens disposed the achromatic rays to meet at a distant focus. In constructing such object glasses, however, he had several difficulties to encounter. In the first place, the focal distance as well as the particular surfaces must be very nicely proportioned to the densities or refractive powers of the glasses, which are very apt to vary in the same sort of glass made at different times. In the next place, the centers of the two glasses must be placed truly in the common axis of the telescope, otherwise the desired effect will be in a great measure destroyed. To these difficulties is to be added--that there are four surfaces (even in double achromatic object glasses) to be wrought perfectly spherical; and every person practised in optical operations will allow, that there must be the greatest accuracy throughout the whole work. But these and other difficulties were at length overcome by the judgment and perseverance of this ingenious artist.

It appears, however, that Dollond was not the only person who had the merit of making this discovery--a private gentleman, Mr. Chest, of Chest-hall, a considerable number of years before, having made a similar discovery, and applied it to the same purpose. This fact was ascertained in the course of a process raised against Dollond at the instance of Watkins, optician at Charing-cross, when applying for a patent. But as the other gentleman had kept his invention a secret, and Dollond had brought it forth for the benefit of the public, the decision was given in his favour. There was no evidence that Dollond borrowed the idea from his competitor, and both were, to a certain extent, entitled to the merits of the invention.

One of the greatest obstructions to the construction of large achromatic telescopes is, the difficulty of procuring large discs of flint glass of an uniform refractive density--of good colour, and free from veins. It is said that, fortunately for Mr. Dollond, this kind of glass was procurable when he began to make achromatic telescopes, though the attempts of ingenious chemists have since been exerted to make it without much success. It is also said, that the glass employed by Dollond in the fabrication of his best telescopes, was of the same melting, or made at the same time, and that, excepting this particular treasure, casually obtained, good dense glass for achromatic purposes, was always as difficult to be procured as it is now. The dispersion of the flint glass, too, is so variable, that, in forming an achromatic lens, trials on each specimen require to be made before the absolute proportional dispersion of the substances can be ascertained. It is owing, in a great measure, to these circumstances, that a large and good achromatic telescope cannot be procured unless at a very high price. Mr. Tulley of Islington--who has been long distinguished as a maker of excellent achromatic instruments--showed me, about six years ago, a rude piece of flint glass about five inches diameter, intended for the concave lens of an achromatic object glass, for which he paid eight guineas. This was before the piece of glass was either figured or polished, and, consequently, he had still to perform the delicate operation of figuring, polishing, and adjusting this concave to the convex lenses with which it was to be combined; and during the process some veins or irregularities might be detected in the flint glass which did not then appear. Some years before, he procured a disc of glass from the continent about seven or eight inches diameter, for which he paid about thirty guineas, with which an excellent telescope, twelve feet focal length, was constructed for the Astronomical Society of London. It is obvious therefore, that large achromatic telescopes must be charged at a pretty high price.