Chapter IV (2)

In order to stimulate ingenious chemists and opticians to make experiments on this subject, the Board of Longitude, more than half a century ago, offered a considerable reward for bringing the art of making good flint glass for optical purposes to the requisite perfection. But considerable difficulties arise in attempting improvements of this kind; as the experiments must all be tried on a very large scale, and are necessarily attended with a heavy expence. And although government has been extremely liberal in voting money for warlike purposes, and in bestowing pensions on those who stood in no need of them, it has hitherto thrown an obstruction in the way of such experiments, by the heavy duty of excise, which is rigorously exacted, whether the glass be manufactured into saleable articles or not; and has thus been instrumental in retarding the progress of improvement and discovery. It would appear that experiments of this kind have been attended with more success in France, Germany, and other places on the continent, than in Britain; as several very large achromatic telescopes have been constructed in those countries by means of flint glass which was cast for the purpose in different manufactories, and to which British artists have been considerably indebted; as the London opticians frequently purchase their largest discs of flint glass from Parisian agents. Guinaud, a continental experimenter, and who was originally a cabinet maker, appears to have had his labours in this department of art crowned with great success. Many years were employed in his experiments, and he too frequently, notwithstanding all his attention, discovered his metal to be vitiated by striæ, spects or grains, with cometic tails. He constructed a furnace capable of melting two _cwt_ of glass in one mass, which he sawed vertically, and polished one of the sections, in order to observe what had taken place during the fusion. From time to time, as he obtained blocks, including portions of good glass, his practice was to separate them by sawing the blocks into horizontal sections, or perpendicular to their axes. A fortunate accident conducted him to a better process. While his men were one day carrying a block of this glass, on a hand-barrow, to a saw mill which he had erected at the Fall of the Doubs, the mass slipped from its bearers, and, rolling to the bottom of a steep and rocky declivity, was broken to pieces. Guinaud having selected those fragments which appeared perfectly homogeneous, softened them in circular moulds, in such a manner, that on cooling, he obtained discs that were afterwards fit for working. To this method he adhered, and contrived a way for clearing his glass while cooling, so that the fractures should follow the most faulty parts. When flaws occurred in the large masses, they were removed by cleaving the pieces with wedges; then smelting them again in moulds, which give them the form of discs. The Astronomical Society of London have made trial of discs made by Guinaud, and have found them entirely homogeneous and free from fault. Of this ingenious artist’s flint glass, some of the largest achromatic telescopes on the continent have been constructed. But, it is more than twenty years since this experimenter took his flight from this terrestrial scene, and it is uncertain whether his process be still carried on with equal success.

_Notices of some large Achromatic telescopes on the Continent and in Great Britain._

1. _The Dorpat Telescope._--This is one of the largest and most expensive Refracting telescopes ever constructed. It was made by the celebrated Fraunhofer of Munich for the observatory of the Imperial University of Dorpat, and was received into the observatory by Professor Struve in the year 1825. The aperture of the object glass of this telescope is 9-1/2 English inches, and its solar focal length about fourteen feet, the main tube being thirteen French feet exclusive of the tube which holds the eye pieces. The smallest of the four magnifying powers it possesses, is 175, and the largest 700, which, in favourable weather, is said to present the object with the utmost precision. ‘This instrument,’ says Struve, ‘was sold to us by Privy-Counsellor VON UTZCHNEIDER, the chief of the optical establishment at Munich, for 10,500 florins, (about £950 sterling), a price which only covers the expenses which the establishment incurred in making it.’ The frame work of the stand of this telescope is of oak inlaid with pieces of mahogany in an ornamental manner, and the tube is of deal veneered with mahogany and highly polished. The whole weight of the telescope and its counterpoises is supported at one point, at the common center of gravity of all its parts; and though these weigh 3000 Russian pounds, yet, we are told that this enormous telescope may be turned in every direction towards the heavens with more ease and certainty than any other hitherto in use. When the object end of the telescope is elevated to the zenith, it is sixteen feet four inches, Paris measure, above the floor, and its eye end in this position is two feet nine inches high. This instrument is mounted on an Equatorial stand, and clock work is applied to the Equatorial axis, which gives it a smooth and regular sidereal motion, which, it is said, keeps a star in the exact center of the field of view, and produces the appearance of a state of rest in the starry regions, which motion can be made solar, or even lunar, by a little change given to the place of a pointer, that is placed as an index on the dial plate. Professor Struve considers the optical powers of this telescope superior to those of Schröeter’s twenty-five feet reflector, from having observed σ Orionis with fifteen companions, though Schröeter observed only twelve, that he could count with certainty. Nay, he seems disposed to place it in competition with the late Sir W. Herschel’s forty feet reflector. The _finder_ of this telescope has a focal distance of 30 French inches, and 2-42 aperture.

2. _Sir James South’s Telescope._--About the year 1829, Sir J. South, President of the London Astronomical Society, procured of M. Cauchoix of Paris, an achromatic object glass of 11-2/10 inches, clear aperture, and of 19 feet focal length. The flint glass employed in its construction was the manufacture of the late Guinaud le Pere, and was found to be absolutely perfect. The first observation was made with this telescope, while on a temporary stand, on Feb. 13, 1830, when Sir J. Herschel discovered with it a _sixth_ star in the trapezium in the nebula of Orion, whose brightness was about one third of that of the fifth star discovered by Struve, which is as distinctly seen as the companion to Polaris is in a five feet achromatic. Sir James gives the following notices of the performance of this instrument on the morning of May 14, 1830. ‘At half past two, placed the 20 feet achromatic on the Georgium Sidus, saw it with a power of 346, a beautiful planetary disc; not the slightest suspicion of any ring, either perpendicular or horizontal; but the planet three hours east of the meridian, and the moon within three degrees of the planet.’ At a quarter before three, viewed _Jupiter_ with 252 and 346, literally covered with belts, and the diameters of his satellites might have been as easily measured as himself. One came from behind the body, and the contrast of the colour with that of the planet’s limb was striking. At three o’clock viewed _Mars_. The contrast of light in the vicinity of the poles very decided. Several spots on his body well and strongly marked--that about the south pole seems to overtake the body of the planet, and gives an appearance not unlike that afforded by the new moon, familiarly known as ‘the old moon in the new moon’s arms.’ _Saturn_ has been repeatedly seen with powers from 130 to 928 under circumstances the most favourable; but not any thing anomalous about the planet or its ring could even be suspected. This telescope is erected on an Equatorial stand at Sir J. South’s observatory, Kensington.

3. _Captain Smyth’s Telescope in his private observatory at Bedford._--This Achromatic telescope is 8-1/2 feet focal length, with a clear aperture of 5-9/10 inches worked by the late Mr. Tulley, Senior, from a disk purchased by Sir James South at Paris. It is considered by Captain Smyth to be the finest specimen of that eminent optician’s skill, and, it is said, will bear with distinctness, a magnifying power of 1200. Its distinctness has been proved by the clear vision it gives of the obscure nebulæ, and of the companions of Polaris, Rigel, α Lyræ, and the most minute double stars---the lunar mountains, cavities and shadows under all powers--the lucid polar regions of Mars--the sharpness of the double ring of Saturn--the gibbous aspect of Venus--the shadows of Jupiter’s satellites across his body, and the splendid contrast of colours in α Hercules, γ Andromedæ and other superb double stars.

_Other large Achromatics._--Besides the above, the following, belonging to public observatories and private individuals, may be mentioned. In the Royal observatory at Greenwich, there is an Achromatic of 10 feet focal distance, having a double object glass 5 inches diameter, which was made by Mr. Peter Dollond, and the only one of that size he ever constructed. There is also a 46 inch achromatic, with a triple object glass 3-3/4 inches aperture, which is said to be the most perfect instrument of the kind ever produced. It was the favourite instrument of Dr. Maskelyne, late Astronomer Royal, who had a small room fitted up in the observatory for this telescope. The observatory, some years ago erected near Cambridge, is perhaps the most splendid structure of the kind in Great Britain. It is furnished with several very large achromatic telescopes on Equatorial machinery: but the Achromatic telescope, lately presented to it by the Duke of Northumberland, is undoubtedly the largest instrument of this description which is to be found in this country. The object glass is said to be 25 feet focal distance, and of a corresponding diameter, but as there was no access to this instrument at the time I visited this observatory, nearly six years ago, I am unable to give a particular description of it. In the Royal Observatory at Paris, which I visited in 1837, I noticed, among other instruments, two very large Achromatic telescopes which, measuring them rudely by the eye--I estimated to be from 15 to 18 feet long, and the aperture at the object end, from 12 to 15 inches diameter. They were the largest achromatics I had previously seen; but I could find no person in the observatory at that time, who could give me any information as to their history, or to their exact dimensions, or powers of magnifying.[21]

The Rev. Dr. Pearson, Treasurer to the Astronomical Society of London, is in possession of the telescope formerly alluded to, made by Mr. Tulley, of twelve feet focal distance and seven inches aperture, which is said to be a very fine one. The small star which accompanies the pole star, with a power of a 100, appears through this telescope, as distinct and steady as one of Jupiter’s satellites. With a single lens of 6 inches focus, which produced a power of 24 times, according to the testimony of an observer who noticed it--the small star appeared as it does in an achromatic of 3 inches aperture, which shows the great effect of illuminating power in such instruments. Mr. Lawson, a diligent astronomical observer in Hereford, possesses a most beautiful achromatic telescope of about 7 inches aperture, and 12 feet focal distance, which was made by one of the Dollonds, who considered it as his _chief d’oeuvre_. It is said to bear powers as high as 1100 or 1400; and has been fitted up with mechanism devised by Mr. Lawson himself, so as to be perfectly easy and manageable to the observer, and which displays this gentleman’s inventive talent. In several of his observations with this instrument, he is said to have had a view of some of the more minute subdivisions of the ring of Saturn. A very excellent achromatic telescope was fitted up some years ago by my worthy friend William Bridges, Esq., Blackheath. Its object glass is 5-1/2 inches diameter, and about 5-1/2 feet focal length. It is erected upon Equatorial machinery, and placed in a circular observatory which moves round with a slight touch of the hand. The object glass of this instrument cost about 200 Guineas, the equatorial machinery on which it is mounted cost 150 Guineas, and the circular observatory in which it is placed about 100 Guineas; in all 450 Guineas. Its powers vary from 50 to 300 times.[22]

_Achromatic telescopes of a moderate size._

Such telescopes as I have alluded to above, are among the largest which have yet been made on the achromatic principle; they are, of course, comparatively rare, and can be afforded only at a very high price. Few of the _object glasses_ in the telescopes to which I have referred, would be valued at less than 200 Guineas, independently of the tubes, eye pieces and other apparatus with which they are fitted up. It is so difficult to procure large discs of flint glass for optical purposes, to produce the requisite curves of the different lenses, and to combine them together with that extreme accuracy which is requisite, that when a good compound lens of this description is found perfectly achromatic, the optician must necessarily set a high value upon it; since it may happen that he may have finished half a dozen before he has got one that is nearly perfect. The more common sizes of achromatic telescopes for astronomical purposes, which are regularly sold by the London opticians, are the following:--

1. _The 2-1/2 feet Achromatic._--This telescope has an object glass 30 inches in focal length, and 2 inches clear aperture. It is generally furnished with two eye pieces, one for terrestrial objects, magnifying about 30 or 35 times, and one for celestial objects with a power of 70 or 75 times. It might be furnished with an additional astronomical eye-piece--if the object glass be a good one, so as to produce a power of 90 or 95 times. With such a telescope, the belts and satellites of Jupiter, the phases of Venus and the ring of Saturn may be perceived; but not to so much advantage as with larger telescopes. It is generally fitted up either with a mahogany or a brass tube, and is placed upon a tripod brass stand, with a universal joint which produces a horizontal and vertical motion. It is packed, along with the eye-pieces, and whatever else belongs to it, in a neat mahogany box. Its price varies, according as it is furnished with an elevating rack or other apparatus.

The following are the prices of this instrument as marked in the catalogue of Mr. Tulley, Terrett’s Court, Islington, London.

£ s. d.
2-1/2 feet telescopes, brass mounted on plain pillar and claw
stand, with one eye piece for astronomical purposes, and
one for land objects, to vary the magnifying power,
packed in a mahogany box 10 10 0

Ditto, ditto, brass mounted on pillar and claw stand, with
elevating rack, 1 eye piece for astronomical purposes, and
1 for land objects, to vary the magnifying power, packed
in a mahogany box 12 12 0

The following prices of the same kind of telescope are from the catalogue of Messrs. W. and, S. Jones, 30, Lower Holborn, London.

£ s. d.
The improved 2-1/2 feet achromatic refractor, on a brass
stand, mahogany tube, with three eye pieces, two magnifying
about 40 and 50 times for terrestrial objects, and the
other about 75 times for astronomical purposes, in a
mahogany case 10 10 0

Ditto, ditto, the tube all brass, with three eye pieces 11 11 0

Ditto, ditto, with vertical and horizontal rack work
motions 15 15 0

2. _The 3-1/2 feet Achromatic Telescope._--The object glass of this telescope is from 44 to 46 inches focal length, and 2-3/4 inches diameter. It is generally furnished with four eye-pieces, two for terrestrial and two for celestial objects. The lowest power for land objects is generally about 45, which affords a large field of view, and exhibits the objects with great brilliance. The other terrestrial power is usually from 65 to 70. The astronomical powers are about 80 and 130; but such a telescope should always have another eye-piece, to produce a power of 180 or 200 times, which it will bear with distinctness, in a serene state of the atmosphere, if the object glass be truly achromatic. The _illuminating power_ in this telescope is nearly double that of the 2-1/2 feet telescope, or in the proportion of 7, 56 to 4; and therefore it will bear about double the magnifying power with nearly equal distinctness. This telescope is fitted up in a manner somewhat similar to the former, with a tripod stand which is placed upon a table. Sometimes, however, it is mounted on a long mahogany stand which rests upon the floor, (as in fig. 58.), and is fitted with an equatorial motion; and has generally a small telescope fixed near the eye end of the large tube, called a _finder_, which serves to direct the telescope to a particular object in the heavens when the higher powers are applied. It is likewise eligible that it should have an elevating rack and sliding tubes, for supporting the eye end of the instrument, to keep it steady during astronomical observations, and it would be an advantage, for various purposes which shall be afterwards described, to have fitted to it a _Diagonal Eye Piece_ magnifying 40 times or upwards.

The prices of this instrument, as marked in Mr. Tulley’s Catalogue, are as follows:--

£ s. d.
The 3-1/2 feet achromatic telescope 2-3/4 inches aperture, on
plain pillar and claw stand, 2 eye pieces for astronomical
purposes, and 1 for land objects to vary the magnifying
power, packed in a mahogany box 21 0 0

Ditto, ditto, with elevating rack and achromatic finder,
2 eye pieces for astronomical purposes, and 1 for day objects
to vary the magnifying power, packed in a mahogany
box 26 5 0

The following are the prices as marked in Messrs. W. and S. Jones’ Catalogue.

£ s. d.
The 3-1/2 feet achromatic, plain mahogany tube 18 18 0

Ditto, ditto, brass tube 21 0 0

Ditto, all in brass, with rack work motions, &c. 26 5 0

Ditto, the object glass of the largest aperture, and the
rack motions on an improved principle _from_ 37l. 16s. to 42 0 0

Ditto, fitted up with Equatorial motion, framed mahogany
stand, divided altitude, and azimuth arches, or declination
and right ascension circles, &c. &c. _from_ 60l to 80 0 0

This is the telescope which I would particularly recommend to astronomical amateurs, whose pecuniary resources do not permit them to purchase more expensive instruments. When fitted up with the eye pieces and powers already mentioned, and with a finder and elevating rack,--price 25 guineas--it will serve all the purposes of general observation. By this telescope, satisfactory views may be obtained of most of the interesting phenomena of the heavens, such as the spots of the sun--the mountains, vales, and caverns on the lunar surface--the phases of Mercury and Venus--the spots on Mars--the satellites and belts of Jupiter--the ring of Saturn--many of the more interesting nebulæ, and most of the double stars of the second and third classes. When the object glass of this telescope is accurately figured and perfectly achromatic, a power of from 200 to 230 maybe put upon it, by which the division of Saturn’s ring might occasionally be perceived. It is more easily managed and represents objects considerably brighter than reflecting telescopes of the same price and magnifying power, and it is not so apt to be deranged as reflectors generally are. A telescope of a less size would not in general be found satisfactory for viewing the objects I have now specified, and for general astronomical purposes. It may not be improper for the information of some readers, to explain what is meant in Mr. Tulley’s catalogue, when it is stated that this instrument has ‘one eye piece for day objects, _to vary the magnifying power_.’ The eye piece alluded to is so constructed, that by drawing out a tube next the eye, you may increase the power at pleasure, and make it to vary, say from 40 to 80 or 100 times; so that such a construction of the terrestrial eye piece (to be afterwards explained) serves in a great measure, the purpose of separate eye-pieces. The whole length of the 3-1/2 feet telescope, when the terrestrial eye piece is applied, is about 4-1/2 feet from the object glass to the first eye glass.

When the aperture of the object glass of this telescope exceeds 2-3/4 inches its price rapidly advances.

The following is Mr. Tulley’s scale of prices, proportionate to the increase of aperture:--

£ s. d.
3-1/2 feet telescopes 3-1/4 inches aperture, with vertical and
horizontal rack work motions, achromatic finder, 3 eye
pieces for astronomical purposes, and one for day objects
to vary the magnifying power, packed in a mahogany box 42 0 0

Ditto, ditto, 3-3/4 inches diameter, mounted as above 68 5 0

Ditto, with universal Equatorial, instead of pillar and
claw stand 84 0 0

Here, in the one case, the increase of half an inch in the diameter of the object-glass, adds about £16. to the expense; and in the other case no less than £26. 5s. The proportion of light in those two telescopes, compared with that of 2-3/4 inches aperture, is as follows:--The square of the 2-3/4 object-glass is 7.56; that of 3-1/4, 10.56, and that of the 3-3/4, 14.06; so that the light admitted by the 3-1/4 compared with the 2-3/4 aperture, is nearly as 10 to 7; and the light admitted by the 3-3/4 object-glass is nearly double that of the 2-3/4 aperture, and will bear nearly a proportional increase of magnifying power.

3. _The 5 feet Achromatic telescope._ The focal length of the object-glass of this telescope is 5 feet 3 inches, and the diameter of its aperture 3-8/10 inches. The usual magnifying powers applied to it are, for land objects 65 times; and for celestial objects, 110, 190, 250, and sometimes one or two higher powers. The quantity of light it possesses is not much larger than that of the 3-1/2 feet telescope, with 3-3/4 inches aperture; but the larger focal length of this telescope is considered to be an advantage; since the longer the focus of the object-glass, the less will be its chromatic and spherical aberrations, and the larger may be the eye-glasses, and the flatter the field of view.

The following are the prices of these telescopes as marked in Mr. Tulley’s catalogue.

£ s. d.
5 feet telescopes 3-3/4 inches aperture, on an universal
equatorial stand, with achromatic finder, 4 eye pieces for
astronomical purposes, and 1 for day objects to vary the
power, packed in a mahogany box 100 guineas to 157 10 0

7 feet ditto, 5 inches aperture, on a newly improved
universal equatorial stand, 6 eye pieces for astronomical
purposes, and 1 for day objects to vary the magnifying
power, with achromatic finder, and Troughton’s Micrometer 207 5 0

The above are all the kinds of achromatic telescopes _generally_ made by the London opticians. Those of the larger kind, as 5 and 7 feet telescopes, and the 3-1/2 feet with 3-3/4 inches aperture, are generally made to order, and are not always to be procured. But the 2-1/2 and 3-1/2 feet achromatics of 2-3/4 inches aperture, are generally to be found ready-made at most of the optician’s shops in the metropolis. The prices of these instruments are nearly the same in most of the optician’s shops in London. Some of them demand a higher price, but few of them are ever sold lower than what has been stated above, unless in certain cases, where a discount is allowed.

The stands for these telescopes, and the manner in which they are fitted up for observation are represented in figures 57, 58, and 59. Fig. 57 represents either the 2-1/2 or the 3-1/2 feet telescopes mounted on a plain brass stand, to be placed on a table. A is the long eye-piece for land objects, and B the small eye-piece for astronomical observation, which is composed of two lenses, and represents the object in an inverted position. These eye-pieces are screwed on, as occasion requires, at E, the eye-end of the telescope. The shorter of the two astronomical eye-tubes which accompany this telescope, produces the highest magnifying power. For adjusting the telescope to distinct vision, there is a brass knob or button at _a_, which moves a piece of rack-work connected with the eye-tube, which must be turned either one way or the other till the object appears distinctly; and different eyes frequently require a different adjustment.

Fig. 58, represents a 5 feet telescope fitted up for astronomical observations. It is mounted on a mahogany stand, the three legs of which are made to close up together by means of the brass frame _aaa_, which is composed of three bars, connected with three joints in the centre, and three other joints, connected with the three mahogany bars. It is furnished with an apparatus for equatorial motions. The brass pin is made to move round in the brass socket _b_, and may be tightened by means of the finger screw _d_, when the telescope is directed nearly to the object intended to be viewed. This socket may be set perpendicular to the horizon, or to any other required angle; and the quantity of the angle is ascertained by the divided arc, and the instrument made fast in that position by the screw _e_. If this socket be set to the latitude of the place of observation, and the plane of this arc be turned so as to be in the plane of the meridian, the socket _b_ being fixed to the inclination of the pole of the earth, the telescope when turned in this socket, will have an equatorial motion, so that celestial objects may be always kept in view, when this equatorial motion is performed. The two handles at _k_ are connected with rack-work, intended to move the telescope in any required direction. The two sets of brass sliding rods _ii_ are intended to render the telescope as steady as possible, and to elevate and depress it at pleasure, and are so constructed as to slide into each other with the utmost ease.

The _Finder_ is placed at AE, either on the top or the left side of the tube of the telescope. When high magnifying powers are applied to any telescope, it is sometimes difficult, on account of the smallness of the field of view, to direct the main tube of the telescope to the object. But the Finder, which is a telescope with a small power, and consequently has a large field of view--when directed to any object, it is easily found, and being brought to the centre of the field, where two cross hairs intersect each other, it will then be seen in the larger telescope. B is the eye-tube for terrestrial objects, containing 4 glasses, and C, one of the astronomical eye-pieces. A socket is represented at _g_, containing a stained glass, which is screwed to any of the eye-pieces, to protect the eye from the glare of light, when viewing the spots of the sun. The brass nut above _f_, is intended for the adjustment of the eye-piece to distinct vision. The 3-1/2 feet telescope is sometimes mounted in this form.

Fig. 59, represents a 5 or 6 feet telescope, mounted on a stand of a new construction by Dollond. It possesses the advantage of supporting the telescope in two places, which renders it extremely steady--a property of great importance when viewing celestial objects with high magnifying powers. It possesses likewise, the advantage of enabling the observer to continue seated at the same height from the floor, although the telescope be raised to any altitude--_the elevation being entirely at the object end_, although it may be changed from the horizon to the zenith. The frame-work is composed of bars of mahogany, and rests on three castors, two of which are made fast to their respective legs in the usual way, and the third stands under the middle of the lower horizontal bar that connects the two opposite legs, so that the frame has all the advantages of a tripod. As it becomes very inconvenient to stoop to the eye end of a telescope, when the altitude of an object is considerable, and the centre of motion at the middle of the tube, this construction of a stand serves to remedy such inconvenience.

_Proportions of curvature of the lenses which form an achromatic object-glass._

As some ingenious mechanics may feel a desire to attempt the construction of a compound achromatic object-glass, I shall here state some of the proportions of curvature of the concave and convex lenses, which serve to guide opticians in their construction of achromatic instruments. These proportions are various; and even when demonstrated to be mathematically correct, it is sometimes difficult to reduce them to practice, on account of the different powers of refraction and dispersion possessed by different discs of crown and flint-glass, and of the difficulty of producing by mechanical means, the exact curves which theory requires. The following table shows the radii of curvature of the different surfaces of the lenses necessary to form _a double achromatic object-glass_--it being supposed that the sine of refraction in the crown-glass is as 1.528 to 1, and in the flint as 1.5735 to 1; the ratio of their dispersive powers being as 1 to 1.524. It is also assumed that the curvatures of the concave lens are as 1 to 2, that is, that the one side of this lens is ground on a tool, the radius of which is double that of the other. The 1st column expresses the compound focus of the object-glass in _inches_; the 2nd column states the radius of the _anterior_ surface of the _crown_, and column 3rd, its _posterior_ side. Column 4th expresses the radius of the anterior surface of the _concave_ lens, and column 5th its posterior surface, which, it will be observed, is exactly double that of the other.

-------+-----------+-----------+-----------+-----------
Focus |Radius of |Radius of |Radius of |Radius of
in |anterior |posterior |anterior |posterior
inches.|surface, |surface. |surface, |surface.
|convex. | |concave. |
-------+-----------+-----------+-----------+-----------
|Inc. Dec. |Inc. Dec. |Inc. Dec. |Inc. Dec.
12 | 3 | 4. 652 | 4. 171 | 8. 342
24 | 6 | 9. 304 | 8. 342 | 16. 684
30 | 7. 5 | 11. 063 | 10. 428 | 20. 856
36 | 9 | 13. 956 | 12. 513 | 25. 027
48 | 12 | 18. 608 | 16. 684 | 33. 369
60 | 15 | 23. 260 | 20. 856 | 41. 712
120 | 30 | 46. 520 | 41. 712 | 83. 424

From the above table it will be seen, that to construct, for example, a 30 inch compound object-glass, the radius of the anterior side of the crown must be 7-1/2 inches, and that of the posterior side 11.63 inches; the radius of the anterior surface of the concave 10.428, and that of the posterior 20.856 inches. It may be proper to observe, that in these computations, the radius of the anterior surface of the concave is less than the posterior side of the convex, and consequently admits of its approach, without touching in the centre--a circumstance which always requires to be guarded against in the combination of achromatic glasses. The following table shows the radii of curvature of the lenses of a _triple_ object-glass, calculated from formula deduced by Dr. Robison of Edinburgh.

-------+--------------------+---------------------+-------------------
Focal | Convex lens of | Concave lens of | Convex lens of
length.| crown glass. | flint glass. | crown glass.
-------+--------------------+---------------------+-------------------
Inches |Inc. Dec. Inc. Dec. |Inc. Dec. Inc. Dec. |Inc. Dec Inc. Dec.
6 | 4. 54 3. 03 | 3. 03 6. 36 | 6. 36 0. 64
9 | 6. 83 4. 56 | 4. 56 9. 54 | 9. 54 0. 92
12 | 9. 25 6. 17 | 6. 17 12. 75 | 12. 75 1. 28
18 | 13. 67 9. 12 | 9. 12 19. 08 | 19. 08 1. 92
24 | 18. 33 12. 25 | 12. 25 25. 50 | 25. 50 2. 56
30 | 22. 71 15. 16 | 15. 16 31. 79 | 31. 79 3. 20
36 | 27. 33 18. 25 | 18. 25 38. 17 | 38. 17 3. 84
42 | 31. 87 21. 28 | 21. 28 44. 53 | 44. 53 4. 48
48 | 36. 42 24. 33 | 24. 33 50. 92 | 50. 92 5. 12
54 | 40. 96 27. 36 | 27. 36 57. 28 | 57. 28 5. 76
60 | 45. 42 30. 33 | 30. 33 63. 58 | 63. 58 6. 40

The following table contains the proportions of curvature, said to be employed by the London opticians.

--------+-----------------------+-------------+------------------------
| | |
| | Radius of |
| | both the |
Focal | Convex of crown | surfaces of | Convex lens of
length. | glass. | the concave | crown glass.
| | of flint |
| | glass |
--------+-----------------------+-------------+------------------------
| | | | |
Inches. | Inc. Dec. | Inc. Dec. | Inc. Dec. | Inc. Dec. | Inc. Dec.
6 | 3. 77 | 4. 49 | 3. 47 | 3. 77 | 4. 49
9 | 5. 65 | 6. 74 | 5. 21 | 5. 65 | 6. 74
12 | 7. 54 | 8. 99 | 6. 95 | 7. 54 | 8. 99
18 | 11. 30 | 13. 48 | 10. 42 | 11. 30 | 13. 48
24 | 15. 08 | 17. 98 | 13. 90 | 15. 08 | 17. 98
36 | 22. 61 | 26. 96 | 20. 84 | 22. 61 | 26. 96
42 | 26. 38 | 31. 45 | 24. 31 | 26. 38 | 31. 45
48 | 30. 16 | 35. 96 | 27. 80 | 30. 16 | 35. 96
54 | 33. 91 | 40. 45 | 31. 27 | 33. 91 | 40. 45
60 | 37. 68 | 44. 94 | 34. 74 | 37. 68 | 44. 94

From this table it appears, that the two convex lenses, have the same radii of their respective sides and that the concave flint lens has its two surfaces equally concave, so that a triple object-glass formed according to these proportions, would require only three pair of grinding tools. The following are the curves of the lenses of one of the best of Dollond’s achromatic telescopes, the focal length of the compound object-glass being 46 inches. Reckoning from the surface next the object--the radii of the crown-glass were 28 and 40 inches: the concave lens 20.9 inches, and the inner crown-glass lens, 28.4 and 28.4 inches. This telescope carried magnifying powers of from 100 to 200 times.

Although I have inserted the above tables, which might in some measure guide an ingenious artist, yet on the whole, a private amateur has little chance in succeeding in such attempts. The diversity of glasses, and the uncertainty of an unpractised workman’s producing the precise curvatures he intends, is so great, that the object-glass, for the most part, turns out different from his expectations. The great difficulty in the construction is to find the exact proportion of the dispersive powers of the crown and flint glass. The crown is pretty constant, but there are hardly two pots of flint glass which have the same dispersive power. Even if constant, it is difficult to measure it accurately; and an error in this greatly affects the instrument; because the focal distances of the lenses must be nearly as their dispersive powers. In the two preceding tables, the sine of incidence, in the crown glass, is supposed to be to the sine of refraction as 1.526 to 1; and in the flint glass, as 1.604 to 1. Opticians who make great numbers of lenses both of flint and crown glass, acquire, in time, a pretty good guess of the nature of the errors which may remain after they have finished an object-glass; and having many lenses intended to be of the same form, but unavoidably differing a little from it, they try several of the concaves with the two convexes, and finding one better than the rest, they make use of it to complete the set. In this way some of the best achromatic telescopes are frequently formed. I have sometimes found, when supplying a concave flint glass to a telescope where it happened to be wanting, that, of four or five concave lenses which appeared to be the same as to curvature and other properties, only one was found to produce a distinct and colourless image. Should any one, however, wish to attempt the construction of an achromatic lens, the best way for preventing disappointments in the result is, to procure a _variety_ of tables of the respective curvatures founded on _different conditions_, and which, of course, require the surfaces of the several lenses to be of different curves. Having lenses of different radii at his command, and having glass of different refractive or dispersive powers, when one combination does not exactly suit, he may try another, and ultimately may succeed in constructing a good achromatic telescope; for, in many cases, it has been found that chance, or a happy combination of lenses by trial, has led to the formation of an excellent object-glass.

_Achromatic telescopes composed of fluid lenses._

The best achromatic telescopes, when minutely examined, are found to be in some respects defective, on account of that slight degree of colour which, by the aberration of the rays, they give to objects, unless the object-glass be of small diameter. When we examine with attention a good achromatic telescope we find that it does not show white or luminous objects perfectly free from colour, their edges being tinged on one side with a claret-coloured fringe, and on the other with a green fringe. This telescope, therefore, required farther improvement, to get rid of these secondary colours, and Father Boscovich, to whom every branch of optics is much indebted, displayed much ingenuity in his attempts to attain this object. But it is to Dr. Blair, professor of astronomy in Edinburgh, that we are chiefly indebted for the first successful experiments by which this end was accomplished. By a judicious set of experiments, he proved that the quality of dispersing the rays in a greater degree than crown-glass, is not confined to a few mediums; but is possessed by a great variety of fluids, and by some of these in a most extraordinary degree. Having observed that when the extreme red and violet rays were perfectly united, the green were left out, he conceived the idea of making an achromatic concave lens which should refract the green less than the united red and violet, and an achromatic convex lens which should do the same, and as the concave lens refracted the outstanding green _to_ the axis, while the concave one refracted them _from_ the axis, it followed, that, by a combination of these two opposite effects, the green would be united with the red and violet.

By means of an ingenious prismatic apparatus, he examined the optical properties of a great variety of fluids. The solutions of metals and semi-metals proved in all cases more dispersive than crown glass. Some of the salts, such as sal-ammoniac, greatly increased the dispersive power of water. The marine acid disperses very considerably, and this quality increases with its strength. The most dispersive fluids were accordingly found to be those in which this acid and the metals were combined. The chemical preparation called _causticum antimoniale_, or butter of antimony, in its most concentrated state, when it has just attracted sufficient humidity to render it fluid, possesses the quality of dispersing the rays in an astonishing degree. The great quantity of the semi-metal retained in solution, and the highly concentrated state of the marine acid, are considered as the cause of this striking effect. Corrosive sublimate of mercury, added to a solution of _sal-ammoniacum_ in water, possesses the next place to the butter of antimony among the dispersive fluids, which Dr. Blair examined. The essential oils were found to hold the next rank to metallic solutions, among fluids which possess the dispersive quality, particularly those obtained from bituminous minerals, as native petrolea, pit coal, and amber. The dispersive power of the essential oil of sassafras, and the essential oil of lemons, when genuine, were found to be not much inferior to any of these. But of all the fluids fitted for optical purposes, Dr. Blair found that _the muriatic acid mixed with a metallic solution_, or, in other words, a fluid in which the marine acid and metalline particles, hold a due proportion, most accurately suited his purpose. In a spectrum formed by this fluid the green were among the most refrangible rays, and when its dispersion was corrected by that of glass, there was produced an inverted secondary spectrum, that is, one in which the green was above, when it would have been below with a common medium. He therefore placed a concave lens of muriatic acid with a metallic solution between the two lenses, as in fig. 60, where AB is the concave fluid lens, CF a plano-convex lens, with its plane side next the object, and ED, a meniscus. With this object-glass the rays of different colours were bent from their rectilineal course with the same equality and regularity as in reflection.

Telescopes constructed with such object-glasses were examined by the late Dr. Robison and professor Playfair. The focal distance of the object-glass of one of these did not exceed 17 inches, and yet it bore an aperture of 3-1/2 inches. They viewed some single and double stars and some common objects with this telescope; and found, that, in magnifying power, brightness, and distinctness, it was manifestly superior to one of Mr. Dollond of 42 inches focal length. They had most distinct vision of a star, _when using an erecting eye-piece_, which made this telescope magnify more than a 100 times; and they found the field of vision as uniformly distinct as with Dollond’s 42 inch telescope magnifying 46 times; and were led to admire the nice figuring and centering of the very deep eye-glasses which were necessary for this amplification. They saw double stars with a degree of perfection which astonished them. These telescopes, however, have never yet come into general use; and one reason perhaps, is, that they are much more apt to be deranged, than telescopes constructed of object-glasses which are solid. If any species of glass, or other solid transparent substance could be found with the same optical properties, instruments might perhaps be constructed of a larger size, and considerably superior to our best achromatic telescopes.[23] It is said that Mr. Blair, the son of Dr. Blair, some years ago, was engaged in prosecuting his father’s views, but I have not heard any thing respecting the result of his investigations.

_Barlow’s refracting telescope with a fluid concave lens._

Professor Barlow, not many years ago, suggested a new fluid telescope, which is deserving of attention; and, about the year 1829 constructed one of pretty large dimensions. The fluid he employs for this purpose is the _sulphuret of Carbon_, which he found to be a substance which possessed every requisite he could desire. Its index is nearly the same as that of the best flint glass, with a dispersive power more than double. It is perfectly colourless, beautifully transparent, and although very expansible, possesses the same, or very nearly the same optical properties under all circumstances to which it is likely to be exposed in astronomical observations--except perhaps, direct observations on the solar disc, which will probably be found inadmissible. Mr. Barlow first constructed an object-glass with this fluid of 3 inches aperture, with which he could see the small star in Polaris with a power of 46, and with the higher powers several stars which are considered to require a good telescope, for example 70, ρ Ophinchi, 39 Bootis, the quadruple star ε Lyræ, ζ Aquarii, α Herculis, &c. He next constructed a 6 inch object-glass. With this instrument the small star in Polaris is so distinct and brilliant, with a power of 143, that its transit might be taken with the utmost certainty. As the mode of constructing these telescopes is somewhat novel, it may be expedient to enter somewhat into detail.

In the usual construction of achromatic telescopes, the two or three lenses composing the object-glass are brought into immediate contact; and in the fluid telescope of Dr. Blair, the construction was the same, the fluid having been enclosed in the object-glass itself. But in Mr. Barlow’s telescope, the fluid correcting lens is placed at a distance from the plate lens equal to half its focal length; and it might be carried still farther back, and yet possess dispersive power to render the object-glass achromatic. By this means the fluid lens--which is the most difficult part of the construction--is reduced to one half or to less than one half of the size of the plate lens; consequently, to construct a telescope of 10 or 12 inches aperture involves no greater difficulty in the manipulation, than in making a telescope of the usual description of 5 or 6 inches aperture, except in the simple plate lens itself; and, hence, a telescope of this kind, of 10 or 12 feet length, will be equivalent in its focal power to one of 16 or 20 feet. By this means, the tube may be shortened several feet and yet possess a focal power more considerable than could be conveniently given to it on the usual principle of construction. This will be better understood from the annexed diagram. (fig. 61.)

In this figure ABCD represent the tube of the 6 inch telescope, CD, the plate object-glass, F the first focus of rays, _de_ the fluid concave lens, distant from the former 24 inches. The focal length MF being 48, and consequently, as 48 : 6 :: 24 : 3 inches, the diameter of the fluid lens. The resulting compound focus is 62.5 inches. It is obvious, therefore, that the rays _df_, _ef_, arrive at the focus under the same convergency, and with the same light as if they proceeded from a lens of 6 inches diameter, placed at a distance beyond the object-glass CD (as GH,) determined by producing those rays till they meet the sides of the tube in GH, namely at 62.5 inches beyond the fluid lens. Hence, it is obvious, the rays will converge as they would do from an object-glass GH of the usual kind with a focus of 10 feet 5 inches. We have thus, therefore, shortened the tube 38.5 inches, or have at least the advantage of a focus 38.5 inches longer than our tube; and the same principle may be carried much farther, so as to reduce the usual length of refracting telescopes nearly one half without increasing the aberration in the first glass beyond the least that can possibly belong to a telescope of the usual kind of the whole length. It should likewise be observed that the adjustment for focus may be made either in the usual way, or by a slight movement of the fluid lens, as in the Gregorian Reflectors, by means of the small speculum.

Mr. Barlow afterwards constructed another and a larger telescope on the same principle, the clear aperture of which is 7.8 inches. Its tube is 11 feet, which, together with the eye-piece, makes the whole length 12 feet, but its effective focus is on the principle stated above, 18 feet. It carries a power of 700 on the closest double stars in South’s and Herschel’s catalogue, and the stars are, with that power, round and defined, although the field is not then so bright as could be desired. The telescope is mounted on a revolving stand, which works with considerable accuracy as an azimuth and altitude instrument. To give steadiness to the stand it has been made substantial and heavy; its weight by estimation being 400 pounds, and that of the telescope 130 pounds, yet its motions are so smooth, and the power so arranged, that it may be managed by one person with the greatest ease, the star being followed by a slight touch, scarcely exceeding that of the keys of a piano-forte. The focal length of the plate lens is 78 inches, and of the fluid lens 59.8 inches--which at the distance of 40 inches produce a focal length of 104 inches, a total length of 12 feet, and an equivalent focus of 18 feet. The curves of the parallel meniscus checks for containing the fluid are--30 inches, and 144 inches, the latter towards the eye. The curves for the plate lens are 56.4 and 144. There is an interior tube 5 inches diameter, and 3 feet 6 inches long, which carries the cell in which the fluid is enclosed, and an apparatus by which it may be moved backwards and forwards, so that the proper adjustment may be made for colour, in the first instance, and afterwards the focus is obtained by the usual rack-work motion. The following is the mode by which the fluid was enclosed. After the best position has been determined practically for the checks forming the fluid lens, these, with the ring between them ground and polished accurately to the same curves, are applied together, and taken into an artificial high temperature, exceeding the greatest at which the telescope is ever expected to be used. After remaining here with the fluid some time, the space between the glasses is completely filled, immediately closed, cooled down by evaporation, and removed into a lower temperature. By this means a sudden condensation takes place, an external pressure is brought on the checks, and a bubble formed inside, which is of course filled with the vapour of the fluid; the excess of the atmospheric pressure beyond that of the vapour being afterwards always acting externally to prevent contact. The extreme edges are then sealed with the serum of human blood, or by strong fish-glue, and some thin pliable metal surface. By this process, Mr. Barlow says, ‘I have every reason to believe the lens becomes as durable as any lens of solid glass. At all events I have the satisfaction of stating, that my first 3 inch telescope has now been completed more than fifteen months, and that no change whatever has taken place in its performance, nor the least perceptible alteration either in the quantity or the quality of the fluid.’