(1.) The Telescope, as its name imports, is an instrument for rendering distant objects more clearly visible, which it does by enlarging their apparent angular dimensions, and by introducing into the eye a quantity of light emanating from them, superior to that which it naturally receives from them.

(2.) The early history of this admirable invention is given in detail in the article on Optics, in another part of this work. The limits allowed us in this article will not permit us to recapitulate it, and we have no comment to make on its exactness. We shall only remark that it seems scarcely possible to read the passages in the works of Roger Bacon, Dee, and Thomas Digges, which bear upon this subject, without feeling satisfied that there must have existed some real, practical, experimental ground for their distinct and reiterated assertion of the increased visibility and magnified appearance of distant objects, produced by some combination, of whatever nature, of reflecting or refracting surfaces, prior to the not improbably alleged independent invention of the refracting telescope in Holland.

(3.) When a convex lens or concave mirror is placed before a luminous object (by which we understand any object, whether luminous per se, or illuminated by exterior light), a picture or image of it is formed at a certain distance behind or before the refracting or reflecting surface, determined by the distance of the object from it; whose magnitude is greater or less, according as it is formed farther from or nearer to the surface. This picture is distinct only at one particular distance from the surface, which is called the focal distance; and the place where it is formed, the focus. At every other distance it is hazy and confused. It may be received on a screen of white paper, and viewed on the same side on which it is formed, by an eye anyhow placed within sight of the paper; and either by one or by any number of persons at once; and examined more closely, if needed, by a magnifier. Or it may be formed on a screen of roughened glass, and viewed, in a similar manner, from the hinder side of the screen. In either case, however, we have here, not a telescope, but a camera obscura. Or the image may be fixed photographically, and thus, becoming a real object, may be preserved and subsequently scrutinized at leisure with a microscope. In both methods of procedure it may be very possible to perceive details and minutiae in the picture, which the unaided eye was not competent to discern in the real object. In the telescope, however, no picture is actually produced elsewhere than on the retina of the eye itself; which is so placed as to receive the rays uninterrupted by the screen; the office of the telescope being only to prepare them for forming on the retina a picture larger and clearer than would be formed without its help.

(4.) How this preparation is effected the reader will find described at length in that part of the article on Optics already referred to, which treats of reflections and refractions on spherical and other surfaces; of the formation of images; and of the conditions of their visibility, either by the naked eye, or through convex or concave lenses. To that article, also, we shall refer for most of the data we shall require in the treatment of this special branch of the general subject—the indices of refraction and dispersion of the various kinds of glass or other media used in the construction of telescopes; the reflective powers of different metallic substances; and a variety of other matters which it would lead us too far from our special object to explain ab initio. To the article, also, on the Achromatic Telescope, we may refer for the history of that instrument, and for a general apperception of the principles of its construction, which may be read as a preparation for what we shall have to say upon it.

(5.) We see distinctly every point of an object when the rays which it sends to every part of the surface of the eye are sensibly parallel; or, at least, form so small an angle with each other as to be unnoticeable on one point of the retina, by the adjusting power of the eye. Assuming, then, that the normal eye does this without fatigue in the case of parallel rays, the first condition which a telescope must fulfil is—that it shall dispose all the rays emanating from any single indivisible point in the object, so as to emerge from the instrument parallel to each other, in the usual or medium situation of the mechanism; the next, that the mechanism itself shall be adjustable, so as, by a small movement of its parts inter se, to convert this parallelism into a slight divergence or convergence, to suit the eyes of near or long sighted persons. In the former case, the telescope is said to be in focus, or adjusted for parallel rays; in the latter, to have its focus adjusted for near or long sight.

(6.) The next condition on which the use of a telescope in viewing objects depends, is, that the several pencils of parallel rays which it sends into the eye from different points of the object, should be inclined to each other at angles, differing in some certain ratio from those actually subtended at the eye, by the respective intervals between the points themselves. If the former be greater than the latter, the object will appear magnified when seen through the telescope; if less, diminished. The number expressing this ratio is the measure of the magnifying power of the telescope. The apparent linear dimensions of an object seen with a telescope being in proportion to its magnifying power \( n \), the apparent enlargement of its superficial area will be as the square \((n^2)\) of the magnifying power (it being of course understood that when \( n \) is a fraction less than 1, the term magnifying must be replaced, in common parlance, by diminishing), and that of the apparent solid dimensions as the cube \((n^3)\). Thus, a magnifying power of 100 gives an apparent enlargement of surface to 10,000, and of bulk to 1,000,000 times that seen or judged by the naked eye. In speaking of magnifying power, the apparent linear enlargement is always understood.

(7.) Of the simple refracting telescope.—The simplest construction of a telescope is that in which the images, refracting formed in the focus of a convex lens or object-glass, is viewed by an eye placed behind it (or in the direction of the rays after passing through it), by the intervention of a second lens or eye-glass, so placed as to have the image in the place of its focus for parallel rays incident in the contrary direction, and its axis coincident with that of the other. For, in such a combination, the rays converging to the focus of the object-lens will, after passing through the eye-lens, emerge parallel, and therefore in a condition for distinct normal vision. This parallelism will be slightly deranged, and converted into a slight divergence or convergence, by shifting the place of the eye-lens somewhat to or fro along the common axis of the two lenses; which is accordingly the means by which adjustment to near or long sight is effected, the eye-lens being fitted into a sliding tube for that purpose. And this mode of adjustment is common to every form of telescope.

(8.) In applying this principle, two cases arise, so practically dissimilar as to afford telescopes of very different characters. The one is that originally made by Galileo and the Dutch artists, and thence called the Galilean or Dutch telescope; and which, from its property of showing Telescope objects erect, or in their natural position, was for a long time the only one in use, until superseded, at the suggestion of Kepler, for astronomical purposes, by the other, or "astronomical telescope," in which they appear inverted.

In the Galilean construction, the eye-lens is concave, and is placed at a distance from the object-glass, equal to the difference of their focal lengths, as in fig. 1, in which


**Fig. 1**

OEQ is the common axis, and Q the common focus of the object-glass O, and the eye-glass E. Were the rays proceeding from the several points of a distant object, pqr, after being respectively converged by O to their several foci, P, Q, R, received on a screen at Q, they would depict on it an inverted image PQR; but, being intercepted by E, they are refracted, as in the figure, the several pencils converging to form P, Q, R, respectively, being converted into pencils severally parallel to EP, EQ, ER, which being received by an eye behind E, large enough to take them all in, will be collected on corresponding points of its retina. And it is evident that the image of the lower extremity (p) of the object, being seen by rays entering the eye in the direction EP, will appear as if situated in the direction PES, which, prolonged out into space, falls below the axis QEO, in which direction q, the middle point of the object, is seen; and vice versa for the upper part, r. The object, then, will appear through the telescope in the same position as without it, or erect. But 2dly, it will appear magnified. For the rays by which its extreme points, p, r, are seen, being parallel respectively to EP and ER, incide the angle PER, which is greater than POR or pOr, or that subtended at O by the object itself; in the ratio (when the angles are very small, as they always are in telescopes) of the focal lengths (OQ and EQ) of the object and the eye-glass. Representing then by (F and f) these respective focal lengths, the magnifying power of the telescope will be expressed by \( \frac{F}{f} \).

(9.) The practical defect of this construction is the smallness of the "field of view" of the telescope, or the small angular extent of the visual area which can be brought at once under inspection. For it is evident that, let the object be of whatsoever extent, the portion (p r) of it which can be seen at once is determined by the extent of the image (PR) which can be seen, and which, itself, is determined by joining the corresponding extremities (BC, AD) of the apertures of the object-glass and eye-glass, the course of the extreme rays after refraction being (CM and DN) parallel to EP and ER, and therefore divergent. To receive them, therefore, the eye must be brought close up to the eye-glass, CD, and its pupil must cover the full area of that glass, which is therefore limited in area—or at least its effective portion is so limited—by the natural size of the pupil, or about a quarter of an inch. And if the eye be withdrawn, ever so little, from the lens, the field is diminished, some portion of the divergent cone (CN, DN) escaping and falling outside of the pupil.

(10.) To calculate the field of view in a telescope of this construction, call A and a the apertures of the object-glass and of the pupil of the eye, to which CD is supposed equal (the eye-lens in telescopes of this construction being, however, always made so large as to allow a wide margin all round the opening of the pupil); and F, f, being the focal lengths of O and E, it will be readily seen, by considering the construction of the figure, that we shall have for the measure of the visual angle, POR (or its tangent \( \frac{PR}{OQ} \)) which will be expressed by \( \frac{aF - Af}{F(F-f)} \) which is necessarily less than \( \frac{a}{F-f} \) or than the angle which the pupil of the eye subtends at the object-glass.

(11.) In the astronomical telescope the eye-glass is convex, and is placed at a distance from the object-glass, equal to the sum of their focal lengths, as in fig. 2, which represents the course of the rays entering the eye, after forming an image (PQR) on the distant object (pqr), in the air between them. The rays from p being converged by the object-glass O to P, a point distant from the eye-glass by its focal length, will, after refraction, emerge parallel to PE, joining P and E the centre of the latter, and forming a pencil, of which DV is the extreme lowermost ray, and fit for distinct vision to an eye placed at V, or at any point nearer to the lens, so as to receive the whole of the cone, CVF; as at MN, which represents the aperture of the pupil, whose distance from E, when the aperture (a) of the eye-glass is larger than that of the pupil, is expressed by \( \left(1 - \frac{a}{A}\right) \times (F+f) \times \frac{aF}{Af} \), A, a, F, and f representing the same things as in the former construction. The field of view, then, in this telescope, is determined, not by the aperture of the pupil, but by the magnitude of the image (PR) intercepted between the lines AB, CD, whose angular measure, as seen from O, is given by the expression \( \frac{PR}{OQ} = \frac{aF - Af}{F(F-f)} \). Moreover, since the image of a point, p, above the axis is seen in the direction DV or EPS, which, prolonged into space, falls below it, objects seen with a telescope of this construction appear inverted, and magnified in the ratio of the angle REP : ROP giving the same expression \( \frac{F}{f} \) for the magnifying power as in the Galilean construction. With the same magnifying power, then, the astronomical telescope is longer than the Galilean by twice the focal length of the eye-glass.

(12.) From the explanations above given, it will be evident that, in either construction, the object and eye glasses are similarly related to the image which occupies their common focus, and are therefore convertible, so that the telescope may be used to view objects, either end foremost—the only difference being that, when so inverted, it diminishes, instead of magnifying objects; and instead of bringing them apparently nearer, seems to throw them to a greater distance—the distance in either case being judged by the apparent magnitude. This property is not without its use in certain optical experiments where it is desirable to obtain a sunbeam of less angular divergence than the apparent diameter of the sun itself.

(13.) The earlier Galilean telescopes magnified but little, the utmost power obtained by Galileo himself, "with great trouble and expense," not exceeding 33 times. The difficulty of finding and keeping an object in view with a very small field of vision opposed a great obstacle to pro- Telescope, gress in this direction, which was much less felt in the other construction. This, accordingly, very generally and early superseded the Galilean construction, which is now retained only for opera-glasses, and for that other little pocket telescope, formed of a single piece of glass, of a conical form, having a polished convex spherical surface in front, and a concave one next the eye; and roughened and blackened over the rest of its surface (to destroy extraneous light), as in fig. 3; which realizes the notion of Descartes (Doptrica, p. 105) of the mode of action of a telescope, regarded as a prolongation and enlargement of the eye itself, by the substitution of an artificial cornea for the natural one, more remote from the retina, so as to form there a larger image.

![Fig. 2]

(14.) The advantage, as regards the field of view, which the astronomical form of construction possesses over the Galilean, was found to be partly neutralized in practice by an inconvenience of another kind. For it was found that, length for length, and magnifying power for magnifying power, a much higher degree of distinctness was obtained with the latter than with the former telescope. This has been attributed, erroneously, to the crossing of rays in the focus of the astronomical telescope (as if they could jostle), or to the comparative thinness of a concave eye-glass. It arises, however, in fact, from a very different cause—the partial correction both of the spherical and chromatic aberrations of the object-glass by the concave form of the eye-glass (Optics, Pt. iii., §§ 1 and 3), whereas a convex eye-lens exaggerates both defects. The only palliative this evil admitted, before the invention of the achromatic telescope, consisted in obtaining the required magnifying power, by giving great focal length to the object-glass, and so enlarging the actual size of the image to be viewed, while at the same time diminishing the angular deviation from a rectilineal course of the extreme rays transmitted through the edges of the lens: since the size of the image corresponding to a given angular diameter of the object is in the direct proportion of the focal length, while the flexure of the rays which converge to form any point of it is, in the same proportion, inversely. In the case of an object-lens of crown-glass, the angle over which the coloured rays are dispersed is about 1-50th of that flexure. Hence it follows (as a mere inspection of the annexed figure will show, fig. 4) that, supposing the red rays from any point of the object collected into a single point \( r \), the violet will be dispersed over a circle whose radius \( (r v) \) is 1-50th that of the object-glass, \( AB \), without regard to its focal length, and therefore will bear a less ratio to the linear diameter of the image, the greater the image itself, i.e., the longer the focus; and in like manner, the difference of focal length for central and marginal rays due to spherical aberration, being a given fraction of the thickness of the object-lens (Optics, Pt. iii., § 1), is not only diminished by making the lens less convex with the same aperture, but its effect in spreading the rays over a circular space at the focus is further diminished by diminishing the angle of convergence. Now, both the one and the other of these conditions are consequences of lengthening the focus.

(15.) Accordingly, as the demand for increased magnifying power on the part of astronomers grew more urgent, we find the lengths of the telescopes in use rapidly increasing from 20 or 30 inches to 6, 12, 20, and even 50, 100, or 200 feet. The observations of Huygens on Saturn were made with telescopes of 12 and 24 feet, constructed by himself; those of Cassini with 17, 86, 100 feet glasses, made by Campani of Bologna, who, with Eustachio Divini, at Rome, were the first to distinguish themselves as artists in this line. A telescope constructed by Huygens, of 123 feet focus, was used by Pound to furnish the diameters of Jupiter and Saturn, and the elongations of their satellites calculated on by Newton in his Principia; and Rieves and Cox, the most celebrated makers in England in those days, produced telescopes of 50, 60, and 100 feet focus. M. Anzout, in Paris, is stated to have executed one of 600 feet focal length, which, however, proved unmanageable. These long telescopes were of necessity constructed without a tube, and were directed to the object by means of a contrivance invented by Huygens, who placed the object-glass in a short tube or cell, mounted on a ball and socket, on a stage, raised or lowered along a tall vertical pole. The axis of the lens was directed to coincidence with that of the eye-piece (fixed on a stand below) by a long string, held in the observer's hand. This whole apparatus constituted the arrangement known as the "aerial telescope." Three of Huygens' long-focused object-glasses are still in possession of the Royal Society.

(16.) The property, however, which gives the chief superiority to the Astronomical over the Galilean telescope, and renders it an instrument of precision, is the facility it affords for placing in the focus of the object-glass, in the very place where the image is formed in the air between the lenses, a fiducial thread or wire, or network of such threads, or of fine lines engraven on glass, &c.; which being at the same time in the focus of the eye-glass, are seen through it, at the same time and with the same distinctness as the image itself, and as if they formed part and parcel of it. This capital improvement in the use of the Astronomical telescope was made and practically applied by Gascoigne in 1640, and affords, not only the means of directing the axis of the object-glass, or the "line of collimation" of the telescope (as it is technically called), to a precise point of any object, or to a star in the heavens, but also of measuring exactly the angular interval between two such precise points—as, for instance, between two stars very near together, or between the two opposite borders of a planet's disc, &c. &c. This is done by clipping the interval in question between two parallel threads in the focus; one of which is fixed, the other moveable by a fine screw, whose revolutions and parts of a revolution are counted on a graduated circle; the direction of the threads being placed perpendicular to the line of the interval to be measured. Such an instrument is called a Micrometer, or a "Parallel wire micrometer," to distinguish it from other contrivances for the same purpose, which are numerous.

(17.) If a glass or a piece of thin mica, covered with a network of finely-engraved squares, be fixed in a tube halfway between two convex lenses of equal power, and in their common focus, a sort of telescope of no magnifying power is the result, which, as it may be made very short and small, is convenient as a pocket micrometer for esti-

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1 See table of dispersions, art. Optics, &c., p. 582. mating the angular magnitude of distant objects, and thus judging of their distance, as well as for sketching their outlines in true proportion; for which reason it has been called by Martin, its inventor, a "Graphical perspective."

(18.) The great inconvenience of the aerial telescope, and the manifest impossibility of much further progress by mere increase of dimension, made it a matter of vital importance to find some mode of shortening the telescope, by throwing the magnifying power on the eye-glass to the relief of the object-glass, which could only be done by improving the perfection of the image formed by the latter.

The causes of the indistinctness of the image were well understood to be—1st, The spherical aberration of the lens, or the non-convergence of rays transmitted centrally and marginally through it to the same exact point of intersection with the axis (see Optics, Pt. iii.) This might be removed, either by figuring the anterior surface of the object-lens to an elliptic, or the posterior to a hyperbolic form; the other surface being, in the former case, a concave spherical, in the other, a plane one. Proposals for mechanisms to communicate these forms were not wanting, but it does not appear that any very successful attempts were made in this direction. But to destroy the other source of imperfection, the dispersion of the differently-coloured rays, whose effect (as will easily be understood from what is said in art. 14) is much greater (600 times greater, according to Newton) in producing confusion of the image, was not to be so accomplished. It required a further step in physical optics; the discovery of the different dispersive powers of different media—a step long retarded by the dictum of Newton (grounded on a too hasty induction from imperfect experiments), that no such difference existed. This dictum, however, having been called in question on a priori grounds by Euler, that eminent mathematician at once perceived and announced the abstract possibility of operating a correction of the colour by combining lenses of different dispersions—an idea which received its practical application at the hands of Hall and Dollond, and resulted, in those of the latter and of succeeding artists (Tulley, Fraunhofer, Cauchoux, Merz, &c.), in the wonderful achromatic telescopes of modern times.

(19.) The principle of the achromatic telescope cannot be more clearly explained, in a practical manner, than is done in the article on that subject already referred to. In a form adapted to analytical calculation, it may be briefly put as follows:—Let \( \lambda, \lambda', \lambda'' \), &c., represent the focal lengths, and \( L, L', L'' \), &c., their reciprocals, (or the optical powers) of a series of thin lenses placed in contact; the signs being + for convex and − for concave lenses, or those which singly act as such, whether both their surfaces be of like curvature or not. Then will \( L' + L'' + \ldots + \infty \), be the joint power of their combination, and, putting this =L, the focal length of the combination will be given by taking \( \lambda = \frac{1}{L} \), which will be positive (or the compound lens will act as a convex one, and form an image), if \( L' + L'' + \ldots + \infty \), be so—i.e., if the powers of the convex lenses predominate over those of the concave. Now, that the compound lens shall be achromatic, it is necessary that its focal length \( \lambda \), and therefore L the reciprocal of that length, shall be the same for rays of all refrangibilities; or, in other words, shall not vary when \( \mu, \mu', \mu'' \), &c., the indices of refraction of the several lenses, change from their values corresponding to red rays into those corresponding to other colours of the spectrum. Suppose, now, that \( \mu, \mu', \mu'' \), &c., represent the refractive indices of the several lenses for the less refrangible of any two coloured rays which it is proposed to unite in one focus, and \( \mu' + \delta \mu, \mu'' + \delta \mu'' \), &c., the same respective indices for the more refrangible, and \( \delta \mu, \delta \mu', \delta \mu'' \), &c., being very small in proportion to \( \mu, \mu', \mu'' \), &c., so as to allow their squares and higher powers to be neglected) suppose \( \delta L', \delta L'', \ldots \), to be the small variations of \( L', L'' \), &c., separately Telescope, and independently produced by the change from one ray to the other. Then will the condition of achromaticity in the compound lens be expressed by the equation,

\[ \delta L = 0, \quad \text{or} \quad \delta L' + \delta L'' + \ldots + \infty = 0. \]

Suppose, now, we denote by \( C, C', \ldots \), the effective convexities of the respective lenses, or the values of \( \frac{1}{r} - \frac{1}{p} \) for each; in which r and p denote the radii of the anterior and posterior surfaces, regarding as positive the radii of anterior convexities and posterior concavities, and vice versa. Then, by Optics, we have \( L' = (\mu' - 1)C'; L'' = (\mu'' - 1)C'' \), &c.; and \( C, C', \ldots \), being invariable,

\[ \delta L' = C'\delta \mu', \quad \delta L'' = C''\delta \mu'' \quad \text{&c.} \]

and eliminating \( C, C', \ldots \),

\[ \delta L' = L'\frac{\delta \mu'}{\mu' - 1}; \quad \delta L'' = L''\frac{\delta \mu''}{\mu'' - 1}, \quad \text{&c.} \]

or putting, for brevity, \( \delta \pi', \delta \pi'' \), &c., for the values of \( \frac{\delta \mu'}{\mu' - 1}, \ldots \), &c., or, as they are termed, the respective dispersive powers of the media of which the lenses consist (i.e., supposing \( \pi = \log(\mu - 1) \), &c.) we have \( \delta L' = L'\delta \pi' \),

\[ \delta L'' = L''\delta \pi'' \quad \text{&c., and therefore} \]

\[ \delta L = L'\delta \pi' + L''\delta \pi'' + \ldots + \infty = 0. \]

(20.) If there be only two lenses, this equation becomes

\[ L'\delta \pi' + L''\delta \pi'' = 0, \quad \text{or} \quad \frac{L'}{\delta \pi'} = -\frac{L''}{\delta \pi''}, \]

the negative sign of which expresses that to unite two differently refrangible rays, the two lenses must have contrary characters, and their powers must be inversely proportional (or, which comes to the same, their focal lengths \( \lambda \) and \( \lambda' \) directly proportional) to the dispersions of the media of which they consist. And if \( \lambda \) the focal length, or L the power of the compound lens, be given, the equation

\[ L = L' + L', \]

combined with the foregoing, will give the focal lengths and powers of both lenses.

(21.) In this case the problem is a determinate one. Take, for instance, crown and flint glass for the convex and concave lenses, the dispersion \( \delta \pi \) of the former being =0.033, and of the latter \( \delta \pi'' = 0.050 \) (Table, p. 582, Optics), and we find \( L'' = -\frac{3}{2}L' \); which shows that a flint concave lens of a power = 2, will achromatize a crown convex one of power 3, leaving the difference of powers (1) outstanding; in other words, a convex with a focal length 33, acting against a concave, focus 50, will produce a compound achromatic lens, focus 100.

(22.) If there be more than two lenses, the problem is Triple and indeterminate, there being only two conditions, \( L = L' + L'' + \ldots + \infty \), and more than two quantities, \( L', L'' \), &c., to be determined; so that we may obtain another and similar condition by uniting in the same focus, not two, but three rays of three different refrangibilities. Denoting then by \( \delta \pi', \delta \pi'' \), &c., the dispersive powers as estimated from the separation of two of the rays (A from B), and by \( \delta \pi', \delta \pi'' \), &c., those of other two (B from C), we shall have simultaneously, to satisfy the three equations,

\[ L = L' + L'' + \ldots + \infty, \]

\[ \delta L = L'\delta \pi' + L''\delta \pi'' + \ldots + \infty, \]

which becomes a determinate problem when three lenses are concerned, and so on.

(23.) For a double object-glass, it is not desirable to unite the very extreme red and violet rays of the spectrum. For the dispersions of crown and flint glasses not following the same law or scale of progression in passing through all the colours from red to violet, the rigorous union of these Telescope. extreme rays, which are very feebly luminous, would leave the intermediate green, which is a very luminous and effective ray, still uncorrected. It would be found far preferable, therefore, in practice, to unite two intermediate and powerfully luminous rays, such as the red and indigo rays, corresponding (Optics, Pt. iv., § 5, p. 590) to those marked, in Fraunhofer's chart of the spectrum, as C and G. These give, for such glasses as occur in practice, $\delta_{\text{C}} = 0.027525$, and $\delta_{\text{G}} = 0.047663$, whence $L' = -0.5772 L$.

(24.) The only very successful attempts to unite more than two coloured rays in the same focus, are those admirable ones of Dr Blair, who enclosed liquid media between lenses of flint and crown glass. A full account of Dr Blair's researches in this direction having, however, been given in both the articles already referred to, especially in Optics, Pt. iv., § 3, we shall not here recapitulate them.

(25.) The great practical difficulty in the way of shortening the refracting telescope being removed by the correction of the coloured aberration, it remained only to deal with that far less obnoxious, but still troublesome, cause of indistinctness which arises from spherical aberrations. What proportion this bears to the former, in an extreme case, may be understood from a computation of their relative values by Newton, in the case of an object-lens of 4 inches in diameter and 100 feet focal length, which results in a ratio of only 1 to 8151, and therefore for the same aperture, and 10 feet focus, 1 to 81-51, the diameter of the least circle of aberration being as the square of the focal length inversely. The spherical aberration, however, is completely removable from a compound object-glass, consisting of two or more lenses, by a proper adjustment of the curvatures of their several surfaces, and that without compromising the achromaticity of the combination. As a problem in analytical optics, this has exercised the ingenuity of many mathematicians. Among the works which treat of this branch of the subject, the reader may consult Euler, Dioptrica, Petersburg, 1769; Clairaut, Mem. de l'Acad. Sci. 1757; D'Alembert, Optique, vol. iii.; Lagrange, Miscel. Turin., III. ii., 152.; and Mem. Acad., Berl., 1778; also Schmidt's Lehrbuch der Analytischen Optik, and Santini's Teorica degli Stromenti Ottici; or he will find in Phil. Tran. R. Soc. 1821, a memoir on the subject by the author of this article, where the approximate formulae which appear best adapted to practical computation are deduced; and to which the practice of the best opticians at present is generally understood pretty closely to conform. They are too complex, and the process of their derivation far too long for insertion here; but as a general conclusion, within the limits of refractive and dispersive power most commonly met with in crown and flint glasses, they indicate a form of object-glass, like that represented in fig. 5, a, b, c, where the anterior or crown lens is double-


Fig.

convex, the second surface being much more curved than the first; and the posterior, concavo-convex, the concavity being turned towards the light, and of much deeper curvature than the convexity. The two interior surfaces, through the whole practical range of the data, approach very nearly indeed to exact coincidence, and under certain conditions exactly fit each other, so as to admit of being cemented together.

(26.) The formulae in question are limited by the conditions, 1st, That the apertures of the lenses of the object-glass are small in proportion to their focal lengths; 2d, That their thicknesses are inconsiderable; and, 3d, That they are placed close together. When these conditions cease to hold good, as in the case of very large achromatics, such as modern art is becoming familiar with, they still afford an available first approximation to the proper curvatures; and there is no real difficulty of a mathematical nature, though there is much of tedious and laborious calculation, in following out by trigonometrical computation the course of the rays in any assigned case; and in determining, to any required precision, the proper forms of spherical surfaces which shall unite the central and marginal, or these and intermediate rays, in one point, for any two refrangibilities. For a general and perfectly rigorous process of this kind, the reader is referred to an excellent memoir by the late M. Littrow, in vol. iii., Mem. Astron. Soc. Lond.

(27.) The mathematical difficulties presented by the construction of a perfect achromatic object-glass may be of course regarded, then, as completely overcome. The only practical ones consist, first, in a sufficiently delicate workmanship; and, secondly, in obtaining discs of perfectly pure and limpid glass, free from veins, of any required size, and differing in its sufficiently in dispersive power. To a very considerable extent, modern art has overcome this difficulty. When the Dollond first commenced the manufacture of achromatics, discs of flint-glass of more than two or three inches in diameter, free from veins, were hardly procurable. Up to the year 1820, specimens of 5 or 6 inches were of the utmost rarity; and even so late as 1839, Mr Simms reported a disc of 7½ inches (and that perfect only over 6) to be, up to that time, unique in the history of English glass-making. A Swiss artist, M. Guinand of Brenets, near Neuchatel, however, devoting himself to the object, succeeded, in the early part of the present century, in manufacturing discs of large dimensions, with considerable certainty. He is stated (Biblioth. Universelle, Feb. and Mar. 1824) to have been engaged, on the strength of this success, by Messrs Fraunhofer and Utzschneider, to conduct the manufacture of the glass used in their celebrated establishment at Benedictbauer, in Bavaria, where he worked for nine years, from 1805 to 1814. From that period, achromatics of 6, 7, 8, and 9 inches in aperture, of exquisite quality, began to emanate from that establishment: to be followed, after the decease of Fraunhofer, by still larger, and, if possible, more perfectly executed instruments of the same kind, from their successors, Merz and Mahler of Munich, as well as from M. Cauchoux of Paris.

(28.) The ultimate perfection of the achromatic telescope would be attained could other species of glass be manufactured, having either a much lower dispersive power than crown or plate glass, or a widely different scale of action on the rays of intermediate refrangibility from those of the last-named glasses. In the former case, by forming the convex lens of the less dispersive medium, we should greatly diminish the total amount of colour to be contended with, in consequence of being enabled to use crown-glass for the concave lens, and so to render the secondary spectrum of little or no importance. This is far from hopeless. The fluoric compounds are well known to hold a remarkably low place in the dispersive scale. The dispersive index, both of cryolite and fluate of lime, is 0.022, or only two-thirds of that of plate-glass (0.033), and therefore holding nearly the same place relative to this glass that the latter does to flint. It is probable, moreover, from the very low dispersion of sulphate of strontia, as compared with that of sulphate of lime, that the fluoride of strontium would be found to possess a dispersion inferior to that of any yet known substance. Now, it does not seem too much to hope, in the present advanced state of the chemical arts, that Telescope. glasses into which one or both of these elements enter largely should one day be manufactured. M. Jamin, by replacing the oxide of lead by that of zinc in flint-glass, has succeeded in forming a zinc-flint glass of the most exquisite limpidity, of low refractive and dispersive power, and capable of being wrought into discs of any size.

(29.) In the other direction, the salts of lead are no less remarkable for their high dispersion. The borate of this metallic oxide was indicated by the author of this article so long ago as 1820 (on account of its definite chemical composition, its easy fusibility, and the tendency of the boracic compounds to form glasses), as eminently fit for optical uses. A specimen produced in Sir James South's laboratory in that year, had a refractive index of 1·880, Telescopa, and a dispersion considerably exceeding that of flint-glass.

Subsequently (1829), in the hands of Prof. Faraday, in union with silicate of lead, it has been made the basis of a "heavy glass" of extraordinary refractive and dispersive power (1·8735 and 0·0703), perfectly adapted for the use of the optician. On the whole, then, we are justified in regarding the manufactory of new species of glass as a field still open, and holding out every prospect for the future.

(30.) The following list comprises some of the most considerable achromatic telescopes which have been constructed up to the present time:

| Artist's Name and Residence | Public or Private Observatory of | Aperture in English Inches | Focal length in Feet | |-----------------------------|---------------------------------|---------------------------|---------------------| | Peter Dollond, London | Sir James South, Camden Hill, Kensington | 3·75 | 60 | | George Dollond | G. Bishop, Esq., Regent's Park, London | 7 | 129 | | Tulley, London | Dr Lee, Harwell House, Aylesbury (formerly Adml. Smyth's) | 5·9 | 102 | | Tulley | Sir J. Herschel, Slough and Feldhausen, Cape of Good Hope | 5 | 84 | | Tulley | Radcliffe Observatory, Oxford (Equatorial) | 7·1 | 120 | | Fraunhofer, Munich | Imperial Observatory, Dorpat (Equatorial) | 9·6 | 174 | | Merz and Mahler, or Merz and Son, Munich | Royal Observatory, Berlin (Equatorial) | 9·6 | 174 | | Merz and Son | Royal Observatory, Munich (Equatorial) | 11·2 | 192 | | | Royal Observatory, Palermo, Sicily | 9·8 | 173 | | | Observ. of Collegio Romano, Rome (Equatorial) | 9·6 | ... | | | Royal Observatory, Cape of Good Hope (Equatorial) | 7 | 102 | | | Observatory, Liverpool (Equatorial) | 8·5 | 144 | | | Royal Observatory, Greenwich (Equatorial) | 12 | 210 | | | National Observatory, Washington, United States (Equatorial) | 9·6 | 183 | | | Observatory of Cincinnati, United States (Equatorial) | 12 | 204 | | | Observatory of Cambridge, United States (Equatorial) | 15 | 270 | | | Imperial Observatory, Poulkova, Russia (Equatorial) | 15·9 | 289 | | | Northumberland Equatorial Observatory, Cambridge | 11·5 | 234 | | | Sir J. South, Camden Hill, Middlesex | 11·7 | 228 | | | Sheepshanks, Equatorial Royal Observatory, Greenwich | 6·7 | 98 | | | E. Cooper, Esq., Observatory, Markree, Ireland | 14 | 302 | | | Royal Observatory, Greenwich (Transit Circle) | 8·0 | 138 | | | Do. do. do. Cape of Good Hope, do. do. | 8·0 | 142 | | | Observatory, San Fernando, do. do. | 8·0 | 142 | | | Imperial Observatory, Paris (only 8·4 ft., quite perfect) | 9·2 | 132 | | | Do. do. | 12·3 | 192 | | | Observatory, Madras (Equatorial) | 6·3 | 96 | | | Imperial Observatory, Poulkova, Russia (Vertical Circle) | 6·3 | 96 | | | Do. do. (Great Meridian Telescope) | 6·2 | 109 | | | National Obs., Washington, United States (Refraction Circle) | 7·0 | 162 | | | Rev. W. R. Dawes, Hopefield Lodge, Haddenham, Berks | 9·25 | 110 | | | Observatory, Amherst College, United States (Equatorial) | 7·25 | 101 | | | Strutt, Esq., Worcester | 5 | ... | | | — King, Esq., Ipwich | 5 | 76 | | | Made by order of W. Dalarus, Esq. | 5 | 60 | | | In process of completion by Mr Dallmeyer | 8 | ... | | | J. Fletcher, Esq., Tarn Bank, Cockermouth (Equatorial) | 6 | 84 | | | In progress for Mr F., to replace the above, and nearly completed | 9·4 | 144 | | | — Barclay, Esq., Walthamstow (Equatorial) | 7·5 | 120 | | | Sir W. K. Murray, Ochtertyre | 9 | 156 | | | Rev. C. Pritchard, Clapham (Equatorial) | 6·6 | 100 | | | Observatory, Madras | 6·0 | 90 | | | Imperial Observatory, Paris (Equatorial) | 12·4 | 206 | | | Imperial Observatory, Poulkova (Meridian Circle) | 6 | 84 | | | Under trial at the Imperial Observatory, Paris | 9·45 | 163 | | | In progress. (No precise report of performance) | 20·5 | 590 | | | Washington, United States (Prime Vertical Transit) | 5·0 | 78 | | | Royal Observatory, Berlin (Meridian Circle) | 5·5 | 60 | | | Queen's College Observatory, Cork, Ireland | 8 | 126 | | | Equatorially mounted, complete | 12 | 232 |

* Mr Dallmeyer (son-in-law of the late A. Ross), working for the latter, with his mechanism and under his instructions, is understood to lay claim to the personal execution of these glasses, and the computation of their curvatures.

(31.) *Dialytic Telescopes.*—Attempts, however, have not been wanting to evade the difficulty of constructing large object-glasses, arising from the small sizes readily obtainable of good flint-discs, by effecting the correction of the coloured dispersion of a single crown object-lens, by a smaller concave lens, or combination of lenses of high dispersive power.

The effective aperture is in a few cases acknowledged to be some few tenths of an inch less than the nominal aperture here set down. Thus, in the Markree telescope of Mr Cooper 13'3 is considered by its owner to be the effective aperture. We cannot, of course, answer for the performance of all these glasses, but there can be no doubt that the large majority of them are of first-rate excellence. Telescope power placed at a distance in the narrower part of the converging cone of rays. This is the principle of Mr. Roger's construction, fully described in Mem. Astr. Soc., vol. iii., p. 229 (1828); and since (1839) reduced to practice under the name of the Dialytic Telescope, by M. Pfössl of Vienna, a very artificial and beautiful invention, highly deserving further trial. The construction is as follows:—AB is the large crown lens, which, acting alone, would unite the red rays in F and the violet in f. They are intercepted, however, at G, by a smaller compound lens, consisting of a convex crown lens (ab) and a concave flint (a'b') of equal and opposite powers for red rays, so that the red ray shall pass through both undeviated, and continue its course to F; but the flint lens (a'b') being more dispersive, will more than counteract the crown (ab) for violet rays. On these, then, the combination will act as a concave lens, and throw the violet focus f farther from O, and that the more, the greater the power of either of these two lenses separately. By properly adjusting their powers, then, the violet focus may be brought to exact coincidence with the red. Thus, a correction of colour is operated, while leaving the radii of the four surfaces of the small lenses, as well as those of the large one, free to satisfy the other essential condition, the destruction of spherical aberration in the triple combination; inasmuch as the power of a lens depends on the difference of the curvatures of its surfaces, and not on the absolute curvature of either. Thus, both the corrections are completely under command, and radii may be calculated to suit any given state of the data. But what gives this construction a capital advantage is, that, in point of practice, no calculation is necessary beyond the very simple one which suffices to determine the powers of the lenses. For these once ascertained, and the lenses placed close together in situ, if it be found, on trial, that the colour is not completely destroyed, we have only to bring the double lens nearer to the object-glass, if the violet focus be longer than the red; or withdraw it farther, if shorter, to bring about an exact union. And as regards the correction of the spherical aberration: by constructing the two lenses so that, when placed close together, their compound spherical aberration shall somewhat over-compensate the convex aberration of the object-lens, which is easily accomplished, the excess may be destroyed, and the compensation rendered exact, by merely separating the two lenses from each other by a very small interval. Both these adjustments are of the readiest practical attainment.

The two glasses are mounted in a common cell, allowing of being separated from contact by a fine screw motion; and the cell itself is made moveable along the axis by a sliding motion, tube within tube. Mr Rogers gives the following formula for finding the powers of the correcting lenses (L' and L'' = -L'), or their focal lengths (X' and -X'' = X):

\[ L' = \frac{F}{\delta_{\pi'} - \delta_{\pi}} \times \frac{A^2}{a^2} \]

\[ \lambda' = \phi \cdot \frac{\delta_{\pi'} - \delta_{\pi}}{\delta_{\pi'}} \times \frac{A^2}{a^2} \]

where \( \phi \) and F are respectively the focal length, and the power of the object-glass and A, a, the apertures of the object-glass and of the compound smaller lens, a formula whose correctness is evident on a mere inspection of the figure.

(32.) Another construction, bearing considerable analogy to this, has been proposed and practised with much success by the late Mr P. Barlow. It consisted in placing in the structure narrowing cone of rays from a plate-glass object-lens, a concave lens consisting of two plate-glass capsules, of equal thickness throughout, enclosing between them a very highly dispersive fluid,—that selected being the bi-sulphuret of carbon, whose refractive index is 1.678, and dispersive power 0.115, or more than double that of flint-glass. The fluid lens is made concavo-convex, and the curves are calculated to destroy the spherical aberration, the power of the lens being so adjusted as to destroy, as nearly as by calculation it can be done, the chromatic. When this is the case, it has been shown by Mr Airy, in Camb. Phil. Tr. vol. ii. p. 233, and by the author of this article (Encyc. Metropol. art. Light, sec. 479), that an exact achromaticity can be produced by varying the distance between the two lenses. The principle was tested by Mr Barlow, by the actual construction of a telescope, of 8 inches aperture, and 12 feet focal length (the shortening might be carried farther), the cost being borne by the Board of Longitude. The trial proved highly satisfactory, and thus, to use his own expression, "less than an ounce of sulphuret of carbon, value three shillings," was made to perform the office of a very costly flint disc of eight inches. Mr Barlow's account of his invention, and of the construction and performance of his telescope, will be found in the Transactions of the Royal Society, for 1828, 1829, and 1831.

(33.) In a work by Wolfius, about the early part of the Wolf's last century, we find it suggested, to interpose between the object-glass of the common astronomical telescope and its focus, a concave lens, as a means of increasing the magnifying power, without a proportional corresponding increase of the length of the telescope. The mode in which it effects this will be evident on inspection of the figure 7,

where A is the object-glass, Q its focus, B the interposed lens, q the focus after refraction through B; PQR the image formed by A alone at Q, and pqr the enlarged image virtually formed at q. If AP and AR be joined and produced, they will mark out on pr the portion, pr', which would be the magnitude of the image formed by A were its focal length Ag instead of AQ. Practically speaking, this construction is objectionable in its simple form, as proposed by Wolf, on the ground of colour produced by the refraction through B, which, supposing the object-glass achromatic, would destroy the achromaticity of the image. Nothing, however, prevents a negative or concave lens from being rendered achromatic, as well as a positive or convex one. In the equation of art (20) \( L = L' + L'' \), L may be negative as well as positive. We have only to make the stronger lens of the combination (the crown) concave, and the weaker convex, and the result will be a negative achromatic lens, which, interposed on Wolf's intermediate principle, will be free from the objection. Such is the modification embodied in the "Barlow lens," which forms

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1 Meyer (Grosse Conversations-Lexicon, art. "Fernrohr"), in describing this invention, suppresses all mention of Mr Rogers, and ascribes it wholly to M. M. Littrow and Pfössl, with what justice may best be inferred from M. Littrow's own memoirs in the Trans. Astron. Soc. Nor does he once mention Mr Barlow in reference to the fluid-correcting lens of art. 32 which he describes! It is not in France only that English invention is ignored. Telescope, the subject of two papers by Messrs Dollond and Barlow (in Phil. Trans. 1834), and which has been found by Mr Dawes (Ast. Soc. Notices, vol. x. 175) to work with excellent effect when applied to a good achromatic object-glass. It is evident that, by giving the interposed concave a motion to and fro along the axis, the magnifying power may be varied within very extensive limits, so that it becomes a sort of variable eye-piece, though, as Mr Barlow justly remarks, the interposed lens is rather to be considered as part and parcel of the object-glass, and may be used with any description of eye-piece. And this leads us now to speak of this latter adjunct to the telescope.

(34.) The telescope, generally considered, consists of two parts—an object-glass, to form the image; an eyeglass, to view and magnify it. We have seen what may be done towards producing a perfect object-glass; in other words, a perfect image. But we have hitherto said nothing of any improvement at the other end of the instrument. The "eye-piece" is, however, no less an essential feature of the telescope, and its perfection no less important than that of the object-glass or speculum. The first, or nearly the first, step in its improvement, consisted in obviating one of the chief annoyances in the use of the achromatic telescope, when directed to day objects, viz., its inverted representation of them. It is obvious that, if optical means can invert an object, a repetition of the same means can re-invert the picture, and so rectify the representation. This, accordingly, was the first application of a compound eye-piece, due to Rheita, and called by his name. He applied behind the convex lens constituting the original simple eye-glass, a second short telescope, consisting of two convex lenses, their distance being the sum of their focal lengths. This is the simplest form of the "day eye-piece," or "common terrestrial telescope."

(35.) The next improvement was of a more thoughtful and elaborate kind. It is known as the Huygenian eye-piece, from its inventor, Huygens, one of those enlightened men of the Archimedean, Galilean, and Newtonian school, who make science walk hand in hand with common sense, and, of the two, work out the directive power of all human progress. It consists of two convex lenses, as in fig. 8, the anterior or "field-glass," having its focal length to that of the posterior or "eye-glass," as 3 to 1, the distance between them being twice the focal length of the latter, and the combination being so placed as to form the visible image half-way between the two. This combination possesses several capital advantages. 1st, It is achromatic, in the sense in which an eye-piece is said to be so, viz., that a colourless image, or real white object, seen through it, does not appear bordered with coloured fringes, which is the case when a single lens is used, or Rheita's eye-piece. This is a consequence, not, as in the achromatic object-glass, of all the central coloured rays being collected in one focus, which, in the case of an eye-piece, is a condition comparatively of little moment, but of its possessing the same magnifying power for rays of all colours, on an object of sensible angular diameter, so as not to form overlapping coloured pictures of it on the retina. This condition it is, which, translated into algebraic language, furnishes the "equation of achromaticity" of an eye-piece. An expression for the magnifying power of a telescope provided with a certain eye-piece, is formed in general terms, involving the focal length of its lenses, their distances from each other, and their refractive indices; and this being made to vary by the variation of the last-mentioned elements only, the variation is equated to zero. The algebraic working, even for a two-glass eye-piece, is a little complex, and for a more compounded one, very much so. The reader will find it very well given in Dr Lloyd's Treatise on Light and Vision, and in an elaborate paper by Professor Litrow, in the fourth volume of the Trans. R. Astron. Soc., p. 599, from the former of which we extract the following proposition, viz., that an eye-glass of two Telescope lenses of the same medium, is achromatic when the interval between the lenses is an arithmetical mean between their focal length, a condition which the Huygenian construction evidently satisfies. The rationale of this, in the case of that eye-piece, will be obvious, independently of algebraic analysis, by inspection of the course of the rays in fig. 8, where AC, BD, are the lenses, PQ the image which would be formed by the object-glass alone, pq that really formed by the action of the field-glass. The object-glass being supposed achromatic, a ray, as OC, of white light going to form the image of a point, Q, will be refracted by the field-glass at C towards the corresponding point, q, of the new image, but not as a single white ray. It will be separated into coloured rays, following different courses. The red ray (Cr) being less refracted, will fall on a point (r) of the eye-glass more remote from its centre (B) than the violet ray (Ce), and (the prismaticity of the lens increasing from the centre outwards) will be more bent aside by the second transmission, in proportion, than the violet, and thus a compensation is effected, and the two rays finally emerge parallel, their exact parallelism being secured by the proportion of their focal lengths.

(36.) The Huygenian eye-piece possesses, also, other important advantages. The total deflection of the light, to produce the magnifying power, is, in this construction, equally divided between the two glasses, a condition the most favourable for diminishing that distortion which is always perceived in looking obliquely through a lens; and finally, the field of view is greatly enlarged, in proportion to the size of the eye-lens, being such as would require to produce the same magnifying power, a single lens, of the much greater semi-diameter, bd, found by drawing Qb parallel to qB, and erecting bd.

(37.) The inconvenience of this eye-piece (which has occasioned its being improperly termed a negative eye-piece) is, that the image being formed between the lenses of which it consists, undergoes a certain amount of distortion by the field-glass; owing to which equal linear portions of it do not correspond precisely to equal angular measures of the distant object. Equal parts, then, of a micrometer, applied at the place of the image, so as to be seen at the same time through the eye-lens, will not correspond to precisely equal angular intervals.

(38.) To give the greatest distinctness to the Huygenian Best forms eye-piece, Mr Airy recommends that the first lens should be a meniscus, having the radii of its surfaces as 11 : 4, and its convexity towards the object-glass; and the second, a "crossed lens" (radii as 1 : 6), with the more convex side towards the first; and that a "field-bar," or pierced diaphragm, should be placed in the focus of the eye-lens. (Airy on the "Spherical Aberration of Eye-pieces," Camb. Phil. Trans., vol. iii., i. p. 61.)

(39.) The common astronomical (or positive) eye-piece, described by Ramsden (Phil. Trans. 1783), consists of two positive plano-convex lenses of equal lengths, having their convexities turned towards each other, and separated by two-thirds of the focal length of either, as in fig. 9. This combination is placed behind the image PQ, formed by the object-glass, at a distance, AP, equal to one-fourth of the focal length of A. The first, or field-glass, therefore, forms an enlarged Telescope image, pg, at a distance one-third of that focal length, which places it in the focus of the eye-glass. This eye-piece is not properly achromatic, but its spherical aberration is much less than in any of the other constructions, and it has the advantage of giving what is called a flat field of view, requiring no change of focus to see the centre and borders of the field with equal distinctness.

(40.) Lastly, if for the third or eye-lens of the Rheita eye-piece, as described in Art. 34, we substitute a Huygenian eye-piece, we shall have the four-glass eye-piece, devised by Dollond, for his admirable day-telescopes or perspective glasses; and finally rested in by him, and by many succeeding opticians, as combining, with a proper adjustment of the distances and foci of the two anterior lenses, the greatest number and amount of advantages, viz., an erect representation, achromaticity, a large field of view, and a high degree of distinctness in all parts of it. If this eye-piece be divided into two, by separating the first pair of lenses from the last, and mounting the latter in a tube, sliding within that which carries the former, while at the same time the whole combination is adjustable, bodily, by a sliding movement along the axis of the telescope, we have the late Mr G. Dollond's "Panoramic" eye-piece, whose magnifying power may be varied within considerably extensive limits. For astronomical purposes, however, the Huygenian eye-piece, for low magnifying powers, or, in some cases, a combination of two equi-convex lenses placed close together (which, by dividing the refraction, materially diminishes the distortion at the edges of the field); the Ramsden double eye-glass for higher powers; and for extremely high ones, a single lens of short focus,—are those most generally employed.

(41.) Professor Littrow, in the memoir referred to in Art. 35, gives the following table of the focal lengths and distances of several of Fraunhofer's four-glass terrestrial eye-pieces; in which F represents the focal length of the object-glass in inches (Vienna measure); \( f_1, f_2, f_3, f_4 \), those of the four lenses of the eye-piece; M, the magnifying power; and D, D', D'', the respective intervals between the first and second, second and third, and third and fourth lenses, reckoning from the object-glass:

| M | F | \( f_1 \) | \( f_2 \) | \( f_3 \) | \( f_4 \) | D | D' | D'' | |---|---|---|---|---|---|---|---|---| | 28 | 20-22 | 1-56 | 1-91 | 2-18 | 1-20 | 2-23 | 3-58 | 1-84 | | 42 | 31-15 | 1-45 | 1-78 | 2-02 | 1-11 | 1-16 | 3-32 | 1-71 | | 60 | 56-56 | 1-82 | 2-23 | 2-55 | 1-40 | 2-72 | 4-19 | 2-15 | | 66 | 58-61 | 1-71 | 2-09 | 2-38 | 1-31 | 2-55 | 3-92 | 2-01 | | 70 | 44-43 | 1-22 | 1-49 | 1-70 | 0-94 | 1-81 | 2-79 | 1-43 |

In all which \( \frac{f}{F} = 0-82 \), \( \frac{f}{f_1} = 0-71 \), \( \frac{f}{f_2} = 1-30 \), \( \frac{D}{D'} = 0-65 \); and \( \frac{D}{D''} = 1-26 \); ratios which he finds to accord almost precisely with those which the theory delivered by him would assign as productive of a very large field of view, with complete achromaticity.

1 We find an eye-piece of four glasses, by Ramsden, strongly recommended, as perfectly achromatic, and possessed of extraordinary distinctness, formed by placing the four lenses A, B, C, D, whose focal distances are in the proportions of 0-775, 1-025, 1-01, and 0-79 respectively, at the following respective distances from each other: AB=1-18, BC=1-83, CD=1-63. A, is plano-convex, plane side first, the others equi-convex. Of Reflecting Telescopes.

(44.) An optical image may be formed by reflexion on a polished surface of glass or metal, wrought into a regular convexity or concavity, on the same principles of the divergence and convergence of the reflected rays as by refraction through polished transparent surfaces. There seems, indeed, some reason to believe that the contrivances for distant (i.e., telescopic) vision, obscurely indicated in the passages of Roger Bacon's and Digges's works, which have been cited in support of their possession of some means for effecting it, refer rather to images originally formed by reflecting, than by refracting surfaces. Be that as it may, the idea of employing metallic concave mirrors, instead of convex lenses, very early suggested itself to Mersenne, as an abstract theoretical possibility; to Gregory, as a practical application by which the length of a telescope might be deduced, and (perhaps) the image improved; and, finally, to Newton, who clearly perceived that it would be so, his discoveries having led him to form a just estimate of the vastly greater amount of indistinctness produced by the aberration of colour than by that of sphericity. From this cause of indistinctness reflectors enjoy an inherent immunity; and it was this consideration which led Newton, despairing of a remedy for the coloured aberration, to turn his thoughts to the construction of reflecting telescopes, and to that improvement on the construction first suggested by Gregory, known as the Newtonian reflector.

(45.) The Gregorian Telescope.—The construction of this telescope, first described by James Gregory in his Optica Promota, in 1663, is as follows:—A and B are two concave mirrors, a larger and smaller, having a common axis, and their concavities facing each other. The larger A, in strictness, should be a segment of a paraboloid, forming its focus at q an inverted image p of a very distant object PQ, which we will suppose to subtend a very small angle (1') at the centre of A. The small mirror B should be a segment of an ellipsoid of revolution, having its two foci, the one in q, the other in q', the centre of an aperture in AA, equal to the diameter BB of the small mirror. Under these circumstances, by reason of the property of the ellipse, in which lines drawn from the two foci to any point in the curve make equal angles with it, q and q' will be conjugate optical foci; and therefore, taking C for the centre of curvature of BB, or of a sphere approximately coincident with the ellipsoid, and bisecting BC in E, G will be the principal focus of the small mirror for parallel rays, and qG x q'G = GB². These distances, therefore, being so adjusted, a second image q'p', or an image of qp, will be formed by reflection at B, inverted with respect to qp, and therefore erect with respect to the object QP, and enlarged in the ratio of q'p' to qp, or of q'C to qC; that is, of Bq' to Bq. This image is then viewed either by a simple convex lens placed behind it, as at O, or by means of any of the eye-pieces already described. We will here suppose the simpler case. The magnifying power, then, will be thus determined. The first image and object subtending equal angles at the aperture in A, the linear magnitude of the image or qp will = F tan 1', calling F the focal length of A; and therefore that of the second will be F Bq' / Bq . tan 1', which, at the distance of the eye-glass from it (f), will subtend the angle F Bq' / Bq × 1', so that the magnifying power will be expressed by M = F Bq' / Bq. F', then, representing the focal length for parallel rays of the small mirror, and D, d, denoting the distances Bq' and Bq, we have, by the principles of optical reflection, 1 / D + 1 / d = 1 / F', and M = F D / f d = F(D - F') / fF', from which expression, where all the focal lengths, and the distance between the mirrors, are known, the magnifying power can be calculated. The field of view may be computed from the formula 1 / Mf(a + A / M)

where M is the magnifying power determined as above, a the aperture of the eye-glass, and A that of the large mirror. This expression supposes the aperture of the small one to be equal to A · d / F or A · DF' / (D - F'), which will just enable it to receive the whole cone of reflected rays incident parallel to the axis of the telescope. It will evidently, therefore, not receive the whole of a cone reflected obliquely to form a point of the image out of the centre of the field, and the defalction will be greater the greater the obliquity. The illumination of the field, therefore, will degrade in intensity in proceeding from the centre outwards, unless the small mirror be made somewhat larger, which will be attended with some additional interception of light from the large mirror, but will afford a central area uniformly illuminated.

(46.) Among the advantages offered by the Gregorian advancement, besides its affording an erect image, is, that tages and a considerable proportion of the magnifying power is due disadvantage to the action of the small mirror, and is therefore so far performed without introducing colour, so that a feebler eye-glass, ceteris paribus, being necessary to produce a given amplification, its defects of achromaticity, if any, is of less moment. This advantage, however, is balanced by some serious practical defects, viz.:—1st, The loss of light consequent on two metallic reflexions at a nearly perpendicular incidence, which cannot be calculated at less than 0·44 of the whole; 2ndly, The necessity for a deep concavity in the small mirror, which renders it extremely difficult to give a truly elliptic form to its surface, without which its aberration is very injurious, and the more so, since, supposing both the mirrors worked to spherical forms, their aberrations conspire; and that of the large mirror is even violently exaggerated by the action of the small one. This will be evident on inspection of fig. 11, where e is the focus of central rays incident on AC and a; that of marginal ones, lying (Optics, § iii.) nearer to C or farther from D than a. Were the figure of DB then truly elliptic, and such as to form the image of c at C, that of a would be formed, not at C, but at a much nearer point a', because conjugate optical foci move in contrary directions, and the Telescope. motion of the more distant is much the more rapid. But DB being supposed spherical, the ray aB being lateral, will not be converged to a' the focus of a for central rays, but to a point (a") still nearer to B. Optics, ut supra, fig. 65.

(47.) It does not appear that Gregory ever succeeded in getting a satisfactory trial of his invention. Artists in later times have, however, produced telescopes of no contemptible merit on this construction; and some of "Short's Gregorians" (an Edinburgh artist of great reputation as a constructor of reflectors about 1734) have attained celebrity.

(48.) The Cassegrain Telescope.—Before describing the Newtonian, we shall here briefly pass in review a construction of the reflecting telescope suggested by Cassegrain in or about 1672, which differs only from the Gregorian in the substitution of a convex hyperbolic for a concave elliptic small mirror. Granting the perfection of the forms, it is evident that this construction would equally fulfill all the conditions of a rigorously perfect image; and that with the advantage of requiring a shorter tube—the distance of the mirrors being the difference, instead of the sum, of their focal distances. The Cassegrain construction possesses another, and that not an inconsiderable, advantage over the Gregorian, analogous to that pointed out in art. 14, when comparing the Galilean with the astronomical form of refractors. The aberrations of the two mirrors tend to correct each other (as is easily seen by following out the reasoning of art. 46, for a convex form of BD mutatis mutandis); and this renders it more readily possible than in the Gregorian form, by trying one and the same large mirror in combination with several small ones, to select one whose defects shall suit and counteract the opposite defects of the other, and so produce perfect vision. In spite of this (partly by reason of its forming an inverted image), the construction is now almost entirely disused, though excellent telescopes (by Short and others) have been so constructed; and so lately as 1813, Captain Kater found, or conceived himself to have found, with equal apertures of both mirrors, and equal magnifying powers, not only better definition, but a greater illumination, in the Cassegrain (in the proportion of three to two); a fact (if really such) which would seem altogether inexplicable on any theory of light yet put forward.

(49.) In both these constructions, the adjustment of the focus to distinct vision is performed by giving a small motion to or fro along the axis of the tube, by a fine screw. The eye-piece most commonly used is the Huygenian, on account of its great aperture and field of view.

(50.) The Newtonian Reflector.—In this construction, the image which would be formed by a large speculum placed at the bottom of the tube is simply deflected, and thrown out, laterally, by a small plane-reflecting surface, inclined at an angle of 45°, to the axis of the large one. It is thus rendered visible to the observer's eye, placed outside of the tube, as in fig. 12, in which AB is a parabolic reflector, which alone would form an image (PQR) of a distant object in its focus, but the rays being intercepted by the small oval plane reflector ab, inclined as aforesaid, nearer than the focus by somewhat more than half the linear aperture (AO) of the large one, the image is really formed at pqr, just outside of the tube, and is viewed by an eye-glass at E. In this construction, as will be sufficiently obvious on tracing the course of the rays, the object is seen inverted, and in a direction at right angles to the real one.

(51.) The practical advantages of this, as compared with its predecessor of the former constructions, are—1st, That the excessive difficulty of truly figuring the small mirror is avoided; it being far less difficult to give a truly plane surface to a small reflector, than a very concave or convex elliptic or hyperbolic one; 2dly, That by placing the small mirror properly, the emergent central ray may be diverted out horizontally, or obliquely upwards, so that the observer is not constrained to gaze upwards, which is very distressing when long continued, but may look horizontally, or, if he please, obliquely or vertically downwards, without fatigue; 3dly, That the second reflexion is performed at an incidence of 45°, by which materially less light is lost than at a perpendicular incidence, and the loss may be still further diminished by effecting the second reflexion (as suggested by Sir David Brewster) at a more oblique incidence, elongating for that purpose the oval form of the small mirror, from an ellipse, whose axes are as $\sqrt{2}$ to 1, into one more eccentric. Or, which is far preferable (as originally suggested by Newton himself) a glass prism bda may be substituted for the metallic reflector ab, having a right angle at d, and the angles ab each 45°. In this arrangement the second reflexion is performed internally at the hypotenuse, or base of the prism ab, and whether in the case of crown or flint glass, is total; so that no more light is lost by this second reflexion than would be lost in passing through a thick plate of the same kind of glass; that is to say, about 5 per cent., if the glass be quite limpid and colourless. So effectual was the construction for a reflector found, that very soon after its proposal by Newton, Hadley constructed (in 1723) one of 5½ inches in aperture, and 62 inches focus, which bore a magnifier from 190 to 230 times, and surpassed in effect Huygen's aerial telescope of 122 feet.

(52.) The magnifying power and the field of view, in magnifying the Newtonian reflector, are found in the same manner as in the simple astronomical telescope, provided the small field mirror be sufficiently large to catch the rays reflected from the extreme margin of the great one to the opposite extreme border of the eye-glass; just as, in the construction last named, would be the case were a plane reflector interposed between the object-glass and its focus. If A be the semi-aperture of the large mirror, and F its focal length, the shorter semi-diameter of the small mirror must not be less than $\frac{A^2}{F}$; but if limited to this precise measure, the central point only of the field of view (as in the Gregorian) will be fully illuminated.

(53.) The usual method of mounting the Newtonian reflector, when the large speculum is not very weighty, or of more than a few feet in focal length, is to suspend the tube in such a manner, that when its inclination to the horizon varies, the situation of the eye-piece shall change but little, so that the observer shall not need to shift his position much. This may be done precisely, by making the eye-tube itself one of the two opposite pivots of a metal frame, embracing the eye-end of the tube (being pierced along its axis, to admit a sliding-tube, carrying the eye-lens or lenses). In this arrangement, the small mirror must be fixed; and the focus must be adjusted, not (as is usually done) by moving it to and fro along the axis, but by sliding in or out the eye-tube within the hollow pivot. If destined to carry a micrometer, the place of the small mirror must be so near the large one as to throw the focus out to a distance beyond the bearing of the pivot. For an instrument destined... Telescope, for meridional astronomical observation only, this construction might be adapted to a reflector of any size. The eye-axis might be supported on a pier of convenient height above the ground, enlarged into a platform for the observer and his writing materials, &c., who might sit at his ease (and under shelter), while the lower end of the tube might be depressed when necessary, into a pit or sunken area below the ground level, by suitable mechanism, whose working might be eased by applying a counterpoising weight, nearly but not quite equal to that of the tube charged with the speculum, applied at the centre of gravity of the tube so loaded, according to an ingenious principle devised by Lord Rosse (of which more hereafter).

(54.) When a prism of glass is used for the second reflection in the Newtonian telescope, it requires to be protected from dew, the deposition of which on its surface is fatal to its performance. The same may be said of the object-glasses of refracting telescopes. No dew forms on the surface of polished metal, but glass, from its peculiar relations to radiant heat, is extremely liable to contract it, when exposed to a clear sky at night. This may be obviated by slightly warming the prism, and by embedding it in a case stuffed with warm felt or other non-conducting substance; or by the same means which succeed perfectly in the case of a refractor, viz., prolonging the tube of the telescope some distance beyond it, either permanently or by attaching to it a "dew-cap," i.e., a light tube of thin metal, blackened within and polished without, of a length about three times the diameter of the tube.

(55.) The Simple Reflector.—When the aperture of a reflecting telescope is so large that the interception of the light from a few square inches of its area, by the portion of the observer's head outside of his eye, will cause a less loss of light than would arise from the interposition of a small mirror, together with the imperfect reflection from its surface, the small mirror may be suppressed, and we have then the construction first imagined by Le Maire (and afterwards adopted by Sir W. Herschel), and hence sometimes called the Herschelian telescope. In this construction the axis of the mirror is inclined to that of the tube of the telescope, so as to bisect the angle between the axis of the latter and a line from its centre to the edge of the opening of the tube, and thus to form an image in its focus, on that edge where the eye-piece is placed to receive it. The loss of light, by the intervention of the observer's head, and the greater inconvenience arising from the disturbance of the air by its warmth, may be avoided by applying a right-angled prism close to the last lens of the eye-piece, so as to effect a total internal reflection on its base at right angles, outwards; or still better, by working the faces of the prism itself into spherical convexities (thereby converting it into a thick lens), and suppressing the eye-glass entirely if a single lens, or else using the prism-lens to supply the place of any one of those of which it consists, as may be most eligible.

(56.) A great advantage of this construction, besides its economy of light, is, that the observer, in astronomical observations (for which alone it is ever used), looks always downwards. Those only who are in the habit of observing for many hours consecutively can appreciate this benefit. Among its disadvantages, it must be considered that the aberration of the mirror is much increased by the oblique incidence of the central rays; insomuch as the area of the mirror must be regarded as a circular portion cut out from the half of a centred reflector of twice the aperture. It is evident, too, that in grinding and figuring such a reflector, it is needless to insist on a parabolic form in preference to a good spherical one, unless it were possible to work the surface to a portion of a paraboloid, having its vertex at the circumference of the mirror. And here we may once for all remark, that that is a good form which gives a good image; and that the geometrical distinctions between the Telescope parabola, sphere, and hyperbola, become mere theoretical abstractions in the figuring and polishing of specula, there being no practical mode of ascertaining, by any system of measurements on a scale, what form the surface has, apart from its optical effect on the rays of light. How great the delicacy of workmanship required in such operations may be appreciated by considering that the total thickness to be abraded from the edge of a spherical speculum 48 inches in diameter and 40 feet focus, to convert it into a paraboloid, is only one 21,333rd part of an inch.

(57.) In the large reflectors which are at present used for Sir Wm. astronomical purposes, the two last forms of construction are Herschel's exclusively employed; and, from the facility with which glass prisms of sufficient purity and silver mirrors on glass can now be obtained, it seems probable that the Newtonian will supersede all other forms. At the epoch when Sir William Herschel commenced his astronomical labours (1776), the apparent hopelessness of constructing very large achromatic object-glasses, rendered the reflecting principle the only one which offered the prospect of an unlimited increase of optical power. Devoting himself to this object, he succeeded in constructing reflectors, gradually increasing in dimension from 7, 10, 14, up to 20, 25, and even 40 feet in focal length, and with apertures proportional of 6, 8, 12, 18, 24, as far as 48 inches. (See Phil. Trans. 1787.) Even this limit has been surpassed by Lord Rosse, who, after satisfactorily testing his new and refined modes of casting, figuring, and polishing, by the successful construction of two specula of 36 inches aperture and 27 feet focus (described by him in Phil. Trans. 1840), finally surpassed every former attempt, by the completion of a reflector, on the Newtonian principle, of 6 feet aperture and 53 feet focus (Phil. Trans. 1848). Mr Lassell has also succeeded in constructing reflectors of Mr Lasell's very great size and perfection. Commencing about the year sell's 1819, with Newtonian telescopes of 7 and 9 inches aperture, and 7 and 9 feet focus; and proceeding onwards, in 1844, to 24 inches aperture and 20 feet focus, he has quite recently succeeded in the construction and equatorial mounting of a Newtonian reflector; 4 feet in aperture and 39 feet focus. M. Delamé, also, and Mr Nasmyth, have Mr Delamé achieved great success in this line of optical construction, and Before proceeding, however, to give any more particular Mr Nasmyth account of these instruments, and the processes employed in their construction; it will be advisable to devote some attention, 1st, To the kind of advantages accruing from increased dimensions as a source of optical power; and, 2ndly, To the comparative Advantages and defects of large reflectors and refractors; both in reference to their convenience in use and construction, and to the conditions which determine the perfect action of each.

(58.) Illuminating, Magnifying, and Space-penetrating powers of Telescopes.—Perfect distinctness being supposed, illuminating and magnifying power are the two great elements of telescopie vision. Except an object, whether a real one or an optical image, be sufficiently bright, it cannot be seen at all; and except the details contemplated cover a certain angular area, or subtend a certain amount of visual angle at the eye, they cannot be distinguished, however great the illumination. Experience assigns, for Illumination, the generality of eyes, an angle of about $2\frac{1}{2}$ or 3 minutes, ing, mag., as the minimum below which the form of an object (whether nifying, round, square, &c.) cannot be discerned, though its existence, and space, as dark on a light ground, or vice versa, may be perceived ing powers under a much smaller angle. A printed page, for instance, of tele- may be read in a good light, if the letters subtend this scope angle. If further removed, they must be magnified by the intervention of a telescope. Now, at first sight, it would seem that, as the magnifying power of a telescope may be increased indefinitely (supposing a perfect image), we need only apply a sufficiently powerful eye-piece to see any Telescope, details, as to read a page, however distant. This, however, is not the case. As the magnifying power is increased, the degree of illumination of the magnified surface diminishes. For supposing the whole light which goes to form the image of (say) one square second of an object's visible surface received into the eye, it will be spread on the retina over an area greater in proportion to the square of the magnifying power; and the illumination of the sensitive surface will of necessity be diminished in the same ratio. Now, considering only the illumination of the centre of the field of view (which that at the borders can in no case exceed), and denoting by $A$ and $a$ the linear apertures of the object-glass (or speculum) and the eye, and by $m$ the magnifying power of the telescope; if the whole light incident on the object-glass from $(1')^2$ of the object were received into the eye, it would illuminate the magnified image of $(m')^2$ in the ratio of $\frac{A^2}{m^2}$ while that of the natural image formed by the eye alone would be $\frac{A^2}{1'}$. The ratio of these is $\frac{A^2}{m^2} \times \frac{1}{m^2}$. And if we take $e$ for the extinction of light due to imperfect transparency of glasses or imperfect reflexion of metal, this will be further reduced to $(1-e)\frac{A^2}{m^2}$. Now, in no case can $\frac{A^2}{m^2}$ exceed unity.

For even in the extreme case of $m=1$, in which case the eye-lens $E$ must equal the object-glass $O$ in aperture, and be equally distant from the focus $F$ (see fig. 13), if $a$ be less than $A$, all the light exterior to the cone marked by the dotted lines will fall outside of the pupil; in other words, the effective portion of the object-glass will be limited to $a$, and therefore $(1-e)$ is the maximum of superficial illuminating power of which any telescope is susceptible.

(59.) The value of $1-e$, or the ratio of the effective to the incident light, after any number of successive transmissions or reflexions in a telescope, may be found by multiplying together the numbers set down in the following table for each surface, in whatever order the surfaces occur:

| After transmission through one surface of glass not in contact with any other surface | 0.957 (a) | |------------------------------------------|-----------| | After transmission through the common surface of two glasses cemented together | 1.000 | | After reflexion on polished speculum metal at a perpendicular incidence | 0.632 (b) | | After reflexion on polished speculum metal at 45° obliquity | 0.690 (c) | | After reflexion on pure polished silver at a perpendicular incidence | 0.905 (d) | | After reflexion on pure polished silver at 45° obliquity | 0.910 (e) | | After reflexion on glass (external) at a perpendicular incidence | 0.043 (f) |

And thence we calculate the effective light in refracting telescopes composed of lenses not in contact, or the percentage of the incident light transmitted by simple or compound eye-pieces, as follows, viz.—

| Percentage transmitted through 1 lens | 0.915 | |-------------------------------------|-------| | Do, do, do, 2 lenses | 0.838 | | Do, do, do, 3 do | 0.767 | | Do, do, do, 4 do | 0.702 |

A mean of Sir W. Herschel's and Lambert's experiments would make these values somewhat higher,—viz., 0.94, 0.89, 0.84, 0.80, respectively.

And for the effective light in reflectors (irrespective of the eye-pieces), as follows:—

| Herschelian (Lord Ross's speculum metal) | A...0.632 | | Newtonian (both mirrors ditto) | B...0.436 | | Do, small mirror & glass prism | C...0.632 | | Gregorian or Cassegrain | D...0.399 |

The same telescopes, all the metallic reflections being from pure silver.

| A...0.905 | | B...0.824 | | C...0.905 | | D...0.819 |

(60.) When the visual angle, subtended by an illuminated surface, is too small to be discerned as a thing having figure, its impression on the eye (all other light being absent) is simply proportional to the total quantity of light which it brings to bear on that (sensibly) one and indivisible point of the retina on which it falls. Such is the case with stars seen either with the naked eye or in telescopes, provided the quantity of light is not so much increased as to give rise to the curious phenomena of spurious discs and rings (see Optics, vol. xvi. p. 618); and hence it arises that, as the aperture of a telescope is increased, it brings into view, when directed to the heavens, still smaller and smaller stars, and that, apparently, ad infinitum; while those which telescopes of inferior dimensions barely render visible as just discernible points of light, appear more conspicuous and brilliant, though not magnified into any visible size or shape.

From this (which is purely a physiological effect, and of which no a priori reason can be rendered) arises what is termed the space-penetrating power of a telescope. Taking as unity the "space-penetrating power of the eye," or that which just enables it to see the least visible star at its actual distance (1), a telescope which collects in one point of the retina a quantity of light $n^2$ times as great, would render it equally visible at $n$ times the distance; and $n$ therefore is the space-penetrating power of such a telescope. It is evident that this is independent of the magnifying power; so that the power in question ($P$) will be represented by

$$\sqrt{\frac{1-e}{a}} \cdot \frac{A}{a}$$

in the notation above employed. Thus, for a telescope on the Newtonian construction, of 72 inches aperture, with a glass prism for a second reflector and a double eye-piece, we find

$$P = \sqrt{0.632 \times (0.915)^2} \times \frac{72}{0.25} = 209.5;$$

and for one of 18.8 inches aperture on the Herschelian construction, with a single eye-lens,

$$P = \sqrt{0.632 \times 0.915} \times \frac{18.8}{0.25} = 57.2.$$

(61.) When the natural illumination of an object is very feeble, magnifying power in a telescope will to a certain extent compensate for deficiency of light. Thus it is that we can read with spectacles in the fading light of evening long after the page becomes illegible without their aid; and thus Sir Wm. Herschel found that, with a telescope whose space-penetrating power was thirty-nine times that of the natural eye, he could read the figures on the dial-plate of a distant church-clock when the daylight had so Telescope, far failed that the steeple itself was invisible to the naked eye.

(62.) Comparative merits of Refracting and Reflecting Telescopes, and conditions requisite for securing distinct Vision with either.—The great obstacle to the indefinite increase of dimension of metallic reflectors is their enormous weight. The 48-inch reflector of Sir W. Herschel weighed 25 cwt.; the 6-feet speculum of Lord Rosse no less than 80 cwt. Not only does this necessitate the use of very powerful and very costly machinery, both for their construction and their management when constructed, but it entails a great and serious inconvenience of another kind. The metal of which they are made, though highly elastic and rigid, perhaps as much so as glass, is yet so much heavier that, with an equal thickness, it is far more liable to bend by the mere action of its own weight in different positions of the mass; and what is of still more importance, such flexure, by altering the inclination of the polished surface to the incident rays, acts directly to deviate the reflected rays from their proper paths, and produce aberration. Now this is not the case in a glass lens. In refraction through an object-glass, single or compound, the convergence of the ray towards its focus is effected by the prismaticity of the surface or surfaces at the point of incidence, and so long as this prismaticity remains unaltered, is very little affected by a minute change in the inclination of the surfaces to the incident light, such as flexure of the general mass would produce. The flexure of an object-glass by its own weight, then, is productive of little or no appreciable disturbance of its optical action, and it is fortunate that it is so, since no way of supporting it could be devised without the obstruction of its light. In reflectors the case is far otherwise. A speculum of 18 inches, an aperture 20 feet focus and 2 inches in thickness, was found to be totally spoiled by supporting it on three points at its circumference; and when reclined against a flat and strong wooden back, with a single thin pack-thread interposed down the middle, all trace of figure was destroyed, and the surface divided into two lobes, each producing its own image of a star, and that a most imperfect one, connected by an irregular burr of light. No thickness that can be given to a mirror (unless quite extravagant) can obviate this; and hence a perfect uniformity of support over every part of the back, and in every angle of inclination to the horizon, is the first requisite (after a good original figure) towards the good performance of a speculum. The necessity of such equable support is not obviated; it must be observed, only palliated, by the use of glass as the material of the speculum.

(63.) There are several ways of giving such support. The first and most obvious is to rest the back of the reflector on a soft and equable cushion of elastic material. This succeeds perfectly well when the weight of the metal does not exceed 200 or 300 lbs., in which case, a bed consisting of several layers of even-textured woollen blanket, or other similar material, is completely successful, and leaves nothing to desire in respect of simplicity, economy, or efficiency, provided the whole be supported on a back so strong as not to yield under the pressure in any part more than a small aliquot of the total compression of the cushion. A similar condition is requisite if the mirror be sustained by a multitude of feeble springs distributed over the whole extent of its back. For small mirrors or light ones, as of glass, an air cushion may be advantageously used. For very heavy ones, however, the following ingenious contrivance has been adopted by Lord Rosse. The back of the mirror, supposed of uniform thickness, may be considered as divided into three sectors of 120°. Suppose the centre of gravity Telescope, of each of these to be sustained by a projecting knob at one of the angular points of a slab of iron, in the form of an equilateral triangle, which is itself sustained by a supporting point under its centre of gravity. Under such circumstances it is evident—First, that each sector being separately and independently supported, would bring no strain on the others; and, secondly, that the whole weight would be equally distributed among the three points of support. It remains now to obviate the separate individual flexure of each sector. To effect this, each may be conceived as again subdivided into three of equal area (or rather of equal weight), and the centre of gravity of each of these being found, suppose each again to be sustained by making it rest on a pin or knob at one angle of a smaller, or secondary, iron slab, which in its turn should be supported on its centre of gravity by making it rest on one of the points of our primary triangle. Lastly (for a 6-feet speculum), each of these secondary areas may be again conceived as subdivided into three equal tertiary areas, which may be in like manner supported on tertiary triangular slabs, each sustained at its centre of gravity on one angle of a secondary one. Thus the whole mirror would be ultimately subdivided into twenty-seven equal areas, each separately and independently supported at its centre of gravity. A speculum thus sustained would obviously be quite secured against flexure from its own weight. The idea is an extension of that of the common "splitter bar," by which, or by a combination of which the pull of two, four, or eight horses drawing at once is equalized so as to distribute the work equally among them. In its practical application by Lord Rosse, it is modified by the introduction of certain levers, which add somewhat to the complexity of the mechanism, and whose action could not be rendered intelligible in few words, or without diagrams, but which do not alter the principle of the method.

(64.) To give perfect freedom, however, to every part of the metal to take its bearing on its cushion, or any other by a band support, it is absolutely necessary that it should be quite free from stickage of any kind, and therefore that it should not be in any way fastened to its points of support, but be free to glide upon them with the least possible amount of friction; and moreover, that it should not rest on its edge on any fixed support when in an inclined position, or be pressed against any ring in front of it, but should lie against its cushion, pendulum-fashion. This may be accomplished (see Results of Cape Observations, p. xii., 1847) by suspending it from above in a strap or band of leather, or, for very heavy mirrors, of steel strong enough to carry it, from a point in its own medial plane in the upper part of the tube. In the 6-feet speculum of Lord Rosse, the stickage caused by friction, when resting on the bottom of the tube, amounted to two tons, or would require the full force of six horses to overcome it; and its operation was totally to defeat the good effect of the equable back support till relieved by suspending the whole mass in a chain. Mr Lassell, also, has found it necessary to have recourse to a similar mode of suspension. The annexed figure (fig. 14) exhibits a simple and easily constructed suspending frame on this principle.

(65.) Another very material obstacle to the good performance of a telescope is the disturbing effect of currents of unequally heated air in the tube. In refracting telescopes, closed at both ends, there is little circulation. When the angle of elevation is suddenly altered, a temporary disturbance arises, but soon subsides. In reflectors, however,

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1 Lord Rosse found that a strong pressure of the hand, applied at the back of his 6-feet speculum, nearly 6 inches in thickness, produced flexure enough to distort the image of a star. In one of M. Foucault's silvered glass mirrors, the excess of central pressure of an air-cushion, slightly over inflated, destroyed all distinct vision, which was instantly restored on allowing the excess of air to escape.

2 From a drawing made about the year 1845. Telescope whose front aperture is necessarily open, as night advances

and the air cools, there is a constant current and counter-current of warmer and colder air ascending along the upper and descending along the lower part, or occasionally taking on spiral motions, which cause great and singular distortions and movements in the images of objects. The remedy is to dispense with a tube, and use only a light but stiff skeleton framework of iron to connect the large spectrum with the small one and the eye-piece. (Results of Cape Observations, p. xv., note.) Lord Rosse has recently mounted a 3-feet reflector on this principle, which has also been adopted by Mr Lassell in that of 4-feet aperture mentioned in art. 56.

(66.) The performance of an achromatic object-glass is often very materially improved by stopping out the central rays by a small circular disc (exactly centred), of from a twelfth to a tenth part of its diameter, which intercepts only \( \frac{1}{12} \)th to \( \frac{1}{10} \)th part of its light, the increased distinctness much more than compensating for this sacrifice. Limiting the aperture of the object-glass or speculum, also, to its inscribed equilateral triangle, is often useful in stellar observation, as it reduces the "spurious discs" of stars to very small points. (See Optics, ut supra.)

(67.) Of Telescopes with Glass Specula.—Newton was the first to suggest the idea of employing a concave glass, silvered on the back, for the larger reflector of his telescope (Opt. i., prop. viii.), on account of the alleged greater facility of polishing glass than metal, and its non-liability to tarnish. The unwieldy weight of large metallic specula (which in Newton's time could not be contemplated as ever likely to become a practical obstacle to their enlargement), has given importance to this line of construction, and induced several eminent persons to turn their attention to it, and in the first place, to obviate a material defect in that proposed by Newton, viz., the production of colour by oblique transmission through glass supposed of equal thickness throughout. The first construction of this kind we have to notice is that proposed by Caleb Smith in 1739 (Phil. Trans., 1740, p. 326). ABC (fig. 15) is a glass meniscus, silvered on the convex surface B. This will collect rays of red light incident on its concavity parallel to REB, the common axis of its surfaces, in a point Q in front of it, because the lens being a positive one, will give the rays in their first transmission through it a certain degree of convergence, which will be increased by reflexion on a concave surface, and still further increased by re-transmission through the lens. And it is evident, that as the reflexion tends to produce no separation of the coloured rays, the place of the violet focus P will be nearer to the Telescope lens H than Q, those rays being more refracted, i.e., made to converge more, in both their transmissions through AC.

Now, let the rays be incident on a concave glass surface GHI. Then, if its curvature be properly chosen, the red rays, instead of converging to Q, will, after refraction, converge to R, a point more distant. Suppose, then, a pencil of violet rays to be incident on H, converging to the same point Q, this would be brought to a focus at a point S more distant (as having their convergence more counteracted). And as the conjugate foci of a lens move in the same direction, if the focus of incident violet rays, first supposed to be at Q, be moved towards H up to P, its real place, their conjugate focus S will move in the same direction or towards R, and by assigning a proper concavity to the surface H, may be made to coincide with it. This condition, as the reader may easily satisfy himself, is equivalent to the following relation between \( \frac{1}{R} \), the radius of the convex silvered surface \( \frac{1}{\phi} \), the focal length of the meniscus regarded as a lens, \( \frac{1}{\delta} \), the distance EH, and \( \frac{1}{p} \) the radius of the concave surface H, viz.:

\[ \rho = \delta \left( 1 + \frac{\delta}{V} \right) + \frac{2\mu}{\mu - 1} \left( \frac{\delta}{V} \right)^2 \phi; \quad \ldots \quad (a) \]

where \( \mu \) is the refractive index of the glass used, and \( V = 2(R + \phi) - \delta \).

(68.) Thus, after refraction at the first surface H of the lens, all the coloured rays will converge to one point R beyond the lens; and if the second surface be worked to a spherical concavity, having R, so found, for its centre, this convergence will not be altered; so that an achromatic image will be formed at that point. The radius of concavity requisite for this being denoted by \( \frac{1}{p'} \), will be given by the equation:

\[ \rho' = -\delta \left( 1 + \frac{\delta}{V} \right) - 2\phi \left( \frac{\delta}{V} \right)^2; \quad \ldots \quad (b) \]

As an example, Smith takes the case of a meniscus worked to radii of 40 and 48 inches respectively, so that \( R = \frac{1}{40} \); from which, by assuming \( 1.56 = \mu \) for the refractive index of the glasses, its focal length as a lens comes out 428.45 in., and as a reflector, 18293 in. Taking, then, 15963 in. for the distance of the glasses EH, he assigns 28 in. for the radius of the surface GHI, and 67 in. for that of the surface KLM. We find, from the formulae given above, 2.695 and 7.062 for the exact values, the difference arising from a slight arbitrary alteration made by him in one part of his calculation, which destroys its numerical exactness.

(69.) If the silvered lens, instead of a meniscus, be convexo-convex, the refracting lens must be a meniscus. In either case, for the latter lens, it is obvious that in practice a prism of 45°, having its surfaces (ghi, hli) worked into Telescope concavities of the same radius as those of the lens, must be substituted to give the telescope a Newtonian form, and thus prevent the observer obstructing the light. There being two radii and a distance disposable, by assuming a proper relation between them, the spherical aberration may be also corrected; or, by leaving all the four radii arbitrary, and omitting Smith's condition that the second surface of the small lens shall be concentric with its focus, a greater latitude of choice will be afforded, and better curves, practically speaking, rendered available.

(70.) The next construction of this nature is that of Professor Airy, who proposes (Camb. Phil. Trans., ii. 105, 1822) to silver one side of each of the two glass lenses, so as to give the resulting reflector a Gregorian or Cassegrain form. In this construction, the large mirror is either a meniscus, or a double-convex lens, silvered at the back; and the smaller (supposing a Gregorian form contemplated), a negative lens of a concavo-convex form, silvered also on its convex or posterior surface, and placed, not as in Smith's construction, between the large reflector and its focus, but beyond it, as in fig. 16. (If the Cassegrain form be contemplated, the reverse must be the case, and the small lens must have its posterior silvered surface concave. The reasoning, mutatis mutandis, being similar in both cases, we shall suppose the form Gregorian.) In this case, the coloured red and violet pencils (as in Smith's construction) will be brought to foci Q and P; that of the red Q being nearer to the small reflector than that of the violet. Now, in this arrangement, the small lens being negative in character, both the transmissions through it act in opposition to, and partly counteract the convergency impressed on the rays by reflection at the internal concavity KLM. And it is by the excess of the latter action over the sum of the former, that the pencils are finally made to converge to a point at or near E. The convergent portion of the total effect is equal on rays of all colours, being produced by reflexion; but the divergent portion, arising from refraction, is greater for violet than for red, and, therefore, the excess, or the final convergence, greater for the red than the violet. If, then, both those coloured pencils, in their incidence on the small mirror, had diverged from one and the same point, the independent action of that mirror would bring the red rays to a shorter focus than the violet. But, in point of fact, the former rays (by what has been above shown) diverge on it from a point Q nearer to it; the effect of which, in the case of reflexion at a concave surface, is to lengthen the focus, i.e., to act in opposition to the independent action of the small mirror as above described, and so to correct the coloured aberration. By a proper adjustment, therefore, of the powers of the two lenses, regarded as such, the red and violet foci may be united at E, and therefore, if the lenses be of the same glass, all the intermediate rays; so that in this construction (and the same is true of Smith's) no secondary spectrum will be produced, and a perfect achromatism attained. This adjustment, as Mr Airy has demonstrated, will be effected by employing lenses for the two reflectors, whose powers, the one as a positive, the other as a negative lens, are to each other inversely as the squares of the distances of the first formed image from the two reflectors respectively.

(71.) Since there are four spherical surfaces, and therefore four radii of curvature disposable, this condition establishes only one relation among them. The length of the telescopes, and the distances of its two speculars from the first-formed image being assigned, this is equivalent to the establishment of two others. For the determination of all the radii, there remains yet one other relation among them which may be such as shall secure the destruction of the spherical aberration. The calculation is too complex for insertion here, but leads, as Mr Airy has shown, to a final cubic equation, which, having always a real root, such destruction is always possible.

(72.) Hitherto nothing has been said about the portions of light reflected from the first surfaces of the glass mirrors (in each reflection about 2½ per cent. of the incident light). No adjustment of the curvatures of the surfaces will unite these finally into a common focus with the transmitted portions. On the contrary, in any conceivable state of the data, they will ultimately converge to or diverge from points very remote from that common focus and from each other, and will therefore be so dispersed and enfeebled on reaching the eye-glass, and so small a percentage of them will reach it at all, as to create no perceptible haziness or confusion in the image.

(73.) A few years ago, a method was discovered by M. Glass Liebig, of coating glass, by an elegant chemical process, with a film of pure silver of perfect continuity, the highest possible reflective brilliancy, and exceeding thinness and evenness of substance, so much so as even to possess a certain very feeble transparency, the sun being visible through it, of a dull blue colour.¹ This has been taken advantage of, in the first instance (in March 24, 1856—Gazette Universelle d'Augsburg), by M. Steinheil, and somewhat later (Feb. 1857—see Comptes Rendus, vol. xlv., p. 330), without knowledge of M. Steinheil's results, by M. Leon Foucault, to produce silvered glass specula in the following manner:—A glass disc, of the requisite diameter, and thick enough to bear grinding and polishing without distortion (but which needs not to be optically pure), streaks and veins in its substance being of no moment), is worked and highly polished to a true concave parabolic figure on one of its surfaces, which is then coated with silver by Liebig's process. The thin metallic film thus formed is then polished by delicate friction, with a cotton pad covered with the finest glove leather, little or no polishing powder being needed. Its texture is so close, and its thickness so perfectly uniform, that it at once and with the utmost facility receives a perfect polish, and retains a true optical surface, identical with that of the glass paraboloid to which it adheres.²

(74.) The advantages offered by this construction (supposing the performance of large reflectors so executed to correspond to the reasonable expectations excited by the complete success of trials on a moderate scale) are immense. In the first place, glass, weight for weight, is incomparably stiffer than metal; so that a glass speculum, to be equally strong to resist change of figure by flexure, need weigh only one-fourth of a metallic one. Secondly, a glass disc of 6 or 8 feet in diameter may be cast, annealed, and wrought with infinitely less labour, hazard, and cost than one of speculum metal. Thirdly, supposing a slight tarnish to arise from sulphuration, the reproduction of the polish is

¹ Gold leaf in like manner transmits a feeble green light. ² The most successful process for silvering has been found by M. Delarue and Dr Miller to be that described by M. Liebig in the Annales der Chemie und Pharmacie, xviii., p. 132. It is also stated at length in the Notices of the Astronomical Society, xix., p. 171. An easier (possibly a better) process, is that of M. Petitjean, described in No. 57 of the Photographic News, iii., p. 49. Telescope, the work of a few minutes, and is performed without any chance of injuring the figure. Even if irretrievably spoiled, the silver coating can be instantly removed, and a fresh one laid on at a comparatively trifling cost; the parabolic figure once given to the glass being indestructible. Fourthly and lastly, the reflective power of pure silver (according to Steinheil's experiments) is, to that of the best speculum alloy, as 91 to 67, or as 1:36 to 1.

(75.) The largest reflector on this construction which we have heard of as being completed, is one by M. Foucault, of 0°-33 (= 13 in.) aperture, and the singularly small proportional focal length of 2m-25 (7 ft. 4½ in.), with which, under a magnifying power of 600, he has succeeded in separating the small double companion of γ Andromeda, well known to astronomers as a test of the performance of a good telescope. M. Foucault is said to be actually engaged on the construction of others of larger dimensions, one of 15 in. being so far completed as to give an excellent view of the moon; directing his attention, however, rather to giving extraordinary perfection to the parabolic form of the glass-surface than to increase of aperture; and that most judiciously, inasmuch as the perfect figure, once imparted, is permanent; whereas, in metallic specula, it is destroyed, and has to be reproduced at every repolishing. His processes for this purpose are quite peculiar, and will be noticed more particularly hereafter. M. Kaiser (Astron. Nachr., 1070) reports very favourably of the performance of a glass speculum by Steinheil, of 4 in. aperture and 8 ft. focus, which divides λ and τ ophiuchi, very difficult double stars; and he is understood to be engaged on one of 13 in. aperture, for M. De la Rue's equatorial.

(76.) Nothing prevents the adoption of Liebig's process set silvering to produce the internal reflective coating in Mr Airy's and Caleb Smith's constructions; and as the metallic film might then be preserved from sulphuration and abrasion by a coating of copal or mastic varnish, the reflectors would be indestructible.

(77.) The Helioscope.—There is yet another species of reflecting telescope to be noticed, the specula of which are made of unsilvered glass, employing only the portions of light reflected at their first surfaces. The object of this construction (first proposed by the author of this article in 1847—see Results of Astron. Obs. at the Cape of Good Hope, p. 436) is to obviate the necessity of employing darkening glasses in viewing the sun with telescopes of great power, which break by the heat and endanger the eye, besides other inconveniences. It might be imagined that this end would be effected by simply contracting the aperture of any good telescope, and so shutting out all superfluous rays. But this does not succeed in practice. Perfect distinctness is not attainable in telescopes with very small apertures and high magnifying powers, when directed to the sun, moon, or planets: a certain ratio of the aperture to the focal length (not less than one-twelfth or one-fifteenth as the minimum) is requisite; so that, if we would obtain the full advantage of a large aperture and high power, some means of suppressing, or otherwise getting rid of, a large percentage of the sun's rays, becomes necessary. This is done by the following arrangement:—The large speculum (A) of a Newtonian telescope is a double concave crown or plate-glass lens, the radius of curvature of whose anterior or reflecting surface is twice the proposed focal length. This surface must be worked to a true parabolic figure. The back requires only to be well polished, and worked (whether accurately or not is of no moment) to any moderately deep concavity. Neither is the quality of the glass, as to veins or streaks, of any consequence, provided it be colourless. When the sun's rays are incident on such a glass, about 2½ (2½) percent are reflected at the first surface, and converged towards a focus F. The rest falls on the second surface, and is for the most part transmitted and dispersed out at Telescope, the back of the telescope (which must be open, to permit their escape into the air, so as not to heat the glass and thereby distort its figure). The small percentage reflected internally is dispersed by the joint action of this reflection and a second refraction out into the air, forwards, and so rendered incapable of interfering with the image formed by the first surface. The rays from this are received and partially reflected at 45°, on (BC) the first surface of a crown-glass prism BCD, having a refracting angle C (turned towards the eye) of not less than 30 or 40 degrees. The intensity of the light finally reflected then will be about 0·026 × 0·030 = 0·00076, or about 1/337th part of the direct illumination; which, being further enfeebled by magnifying (art. 58), will allow the image to be viewed either without a darkening glass, or with a very feebly coloured one, and without any danger of fracture. The transmitted portion of the cone of rays converging to F, pursues the course indicated in the figure, and is entirely thrown out at the mouth of the telescope, the prism being set transparent for that purpose. Only the reflecting surface (BC) of the prism needs to be truly worked, and (as in the case of the large speculum) its perfect homogeneity is of no moment. M. Porro, an eminent French artist, has recently constructed an instrument (exhibited to the French Institute, Jan. 28, 1858) on a principle very similar to this, only that the second reflection, instead of being performed at an incidence of 45°, is performed at the polarizing angle for glass (incid =55°, obliquity =35°); so that the rays form an image completely polarized in the plane of reflection; and a Nicol prism being placed between the eye and the eye-piece, the light may be enfeebled to any extent we please without the use of any darkening glass.

(78.) Of Binocular Telescopes.—One of the first conditions which the States-General of the Hague imposed on telescopes, Lippersheim (the reputed Dutch inventor of the telescope), on his application to them for a patent (which they refused him, on the ground of the alleged prior publication of the invention, while agreeing to pay him a high price for a stipulated instrument), was, that it should be binocular. They had no idea of restricting the newly acquired faculty to one eye and keeping the other idle. It is no doubt more comfortable to use both eyes in looking through a telescope, as in natural vision; and the binocular principle has also this advantage (assuredly not contemplated as one of their motives for insisting on it), that when each eye looks through a separate telescope, the foci may be separately adjusted to perfect vision for each, and then a long and a short sighted eye (and few persons have both exactly alike in this respect) may be brought into precisely consensual action.

(79.) The usual form of the binocular telescope is that of two equal and equally magnifying refracting structure telescopes, mounted side by side at a fitting distance, to admit of each eye being applied to its corresponding eye-piece at the same time. Of course this restricts the aperture of either telescope not to exceed the interval between the centres of the two pupils. But this is no contemptible aperture, and although for the most part the use Telescope.

of this construction is confined to the small double opera- glasses, with which every one is familiar; it has also been employed (though without any very great practical advan- tage) to astronomical purposes, for viewing the sun, moon, and planets. When used for viewing near objects, the mounting must admit of a slight convergence being given to the axes of the telescopes, to direct them at once to the same object. If this be not done, the object is seen double; but so soon as the images are brought very near, they sud- denly spring together, even while some minute deviation still subsists, in a very singular and striking way; while the sensation changes at once, from that of contemplating a picture, to that of viewing a real object.

(80.) No particular description of an instrument of this kind can be needed. But a binocular construction, imag- ined by M. Vallack (Ast. Soc. Notices, viii. 139), is of a higher kind, and merits notice. He proposes to place two Newtonian reflectors, of any (equal) apertures and magni- fying powers, side by side as in fig. 18, with both their axes in the plane passing through the two pupils. The small mirror of the further telescope is placed closer to the large one than that of the nearer, by a distance equal to the whole aperture of the latter plus the thickness of tube, so that the two images shall be formed equi-distant from the two eyes. By this ingenious device the binocular principle is rendered available for telescopes of any aperture.

(81.) It is, however, only when used in combination with the principle of stereoscopic vision (as explained by Mr Wheatstone), in all its extent, that the full advantage of binocular vision through telescopes can be realized. When an object, at any considerable distance, is viewed through an ordinary binocular, the base afforded by the interval between the eyes is too small to bring them up to a high relief, or to define the relative situations of several objects seen together, in space. But, by artificially enlarging this base, the same advantage is gained which would arise from increasing the personal dimensions of the spectator to giant size. He will thus be enabled to view a distant complex object (as a town or a group of mountains), as a person of ordinary size would contemplate a model of it placed much nearer to him.

(82.) A very simple experiment will illustrate the way in which this takes place. On a horizontal board (ABCD fig. 19) place two looking-glasses (EF), with their planes vertical, and set on stands, so as to allow of their being turned round in any azimuth. In the middle of the board place two others (GH), smaller and similarly mounted, their centres being distant from each other by the interval between the two eyes (about 2½ inches), their planes being parallel to those of EF, and their reflecting surfaces turned towards the others respectively. All the glasses being placed at about 45° to the length of the board, their planes are to be adjusted by turning them a little in azimuth, until the two images of a distant object, seen by the two eyes, at IK, by double reflexion, are brought into exact coincidence. When this is the case, they will seem to spring into one, as described (art. 77), and the object so seen will appear nearer and smaller than when directly viewed. The in- creased apparent proximity is a consequence of the greater convergence of the visual pencils, by which the object is seen by the two eyes: the apparent diminution is a conse- quence of its being judged to be nearer, while subtending the same angle at the eye.

(83.) This diminution may be counteracted, and con- verted into an apparent augmentation, by interposing be- tween the two pairs of reflectors (EG and FH) refracting telescopes of equal apertures and magnifying powers.¹ Or two such telescopes may be fitted with reflectors at 45°, at the object and eye-end, and fastened on the arms of a jointed ruler, to allow of adjustment to objects at different distances. Or a single tube may be fitted with equal object-glasses at the two ends, and with their corresponding eye-pieces in the middle between them, each furnished with a reflector, directing the visual pencil out at right angles, into eye-tubes at 2½ in. apart. Reflectors, adjust- able by a screw motion, may be fitted into caps and applied externally beyond the object-glasses, giving the instrument the convenient and portable form represented in fig. 20;

¹ The arrangement here described, in this its most simple form, was suggested and tried successfully by Mr A. S. Herechel in 1855. A stereo-telescope has been described, and we presume constructed, by M. Helmholtz, but we are not aware (Oct. 2, 1859) of its pre- cise form or its date. Telescope, considerable nicety by turning the tool in a lathe, to fit a guage. The lens is then connected, or otherwise firmly attached, to the lower end of a vertical rod of wood or metal AB (fig. 21), the upper end of which terminates in a steel ball, working in a cup, to which it has been accurately fitted by smooth grinding, so that every point of the surface A of the lens, when made to oscillate or revolve conically, by a motion given to the rod by a hand grasping it at B (where it is enveloped in woollen cloth or felt, to prevent the communication of warmth), will move in a spherical surface, concentric with the ball C.

Below is fixed a small polisher D of pitch, spread on brass coated with some fine polishing powder, mixed with water, and brought up into delicate contact with the lens by a fine screw motion, and the rod being worked to and fro, and circularly, so as to bring every portion of the lens equally over the polisher, by degrees a perfect spherical and polished surface is acquired, the radius of which can be adjusted with any requisite precision by lengthening or shortening the radius-rod by a screw adjustment. Lenses may also be figured and polished to perfect spherical, and probably also to good parabolic or hyperbolic surfaces, by any of the processes which are found to succeed in the case of specula, and indeed with greater ease and certainty, the material being little, if at all, harder, the texture at least as close and equable, and the weight much less obnoxious. Mr Grubb, of Dublin, has constructed an apparatus equally applicable to both, which has produced very successful results.

(85.) The glass discs are either cut from blocks of glass, as practised by Fraunhofer and, we presume, by his successors, or moulded out of selected fragments of such blocks, softened by heating to redness, and carefully annealed; which, when once pure glass fit for the purpose is obtained, offers no peculiar difficulty of manipulation. With metal specula the case is very different, the material being much more intractable, so that with these the peculiar difficulties of construction commence with the formation of the disc itself to be operated on.

(86.) The raw material of metallic specula at present in use is an alloy of pure copper with pure tin. In the origin of this art various other metals were added in small proportion. Thus Hadley recommended an alloy of 24 copper, 12 brass (copper and zinc), 12 of tin, and 1 of silver; Painter, 32 copper, 13 tin, and 1 antimony; Edwards, 32 copper, 15 tin, 1 brass, 1 silver, and 1 arsenic; the latter of which alloys gives a beautiful metal, but excessively brittle. These small admixtures of other metals are now pretty generally abandoned, as it is by no means clear that they are productive of any advantage. Mr Lassell, however, adds still a portion of arsenic. Mudge (Phil. Trans., vol. lxvii., p. 298), who was the first to reject these additions, recommends the proportion of $64:29$, or $31:18$ per cent. of tin, approaching very nearly to an atomic composition of 4 atoms of copper to 1 of tin, which gives a percentage of $31:79$. The latter is the proportion found by Lord Rosse to give the most brilliantly reflective metal, and the least liable to tarnish; labouring, however, under the disadvantage of excessive brittleness, and of such extreme hardness, that a steel file will barely mark it. Sir William Herschel found it impracticable, by the methods then in use, to obtain durable castings of a speculum 36 inches in diameter, or even with certainty of 24, with so high a percentage as $29:41$; these metals, however slowly cooled, cracking in the mould; and for one of 48 inches he was obliged to lower the percentage to $25$ for the same reason. For smaller specula his usual composition was that of $29:41$, above mentioned, which, when well polished, he found to reflect $0:678$ of the incident light. In making the mixture it is indispensable to cast the metal first into ingots, and then to remelt it (which requires a much lower heat than that required for the first melting, which must be that of melting copper), adding a small quantity of tin to replace that destroyed by oxidation, and stirring the melted metal before pouring with a wooden pole (as in the "poling" of copper castings).

(87.) The destruction of the more brittle metal, by crack-moulding in a close mould, is owing to the violent tension induced casting in the internal portions of the mass by the simultaneous fixation of the whole external crust, while the interior remains fluid, and which cannot then contract in dimension without solution of continuity. Mr Potter (Brewster's Jour., N.S., iv. 18, 1831), by casting the metal into a mould, the lower surface of which consisted of a thick mass of steel, succeeded in determining the rapid fixation of the lower surface, and the subsequent abstraction of the heat by conduction through it in the same direction, and thus solidifying the mass in successive strata from below upwards, allowing each new stratum to accommodate itself in some degree to the already contracted state of the previous one. Dr Macculloch (Journ. of Science, June 1828) had previously recommended quick cooling to the fixing point, not to obviate fracture, but to prevent crystallization, but without a word as to the mode of accomplishing it. The same principle has been adopted by Lord Rosse in the casting of his large specula, with perfect success. An iron bed was prepared of strips of iron-plate, set edgewise, and forcibly held together by an iron ring. These were turned on a lathe to a convexity equal to the intended concavity of the mirror, and the metal being then poured into an open mould, formed by ramming sand round a pattern laid on this bed, assumes a close-grained and even surface, free from pores, by the escape of air or vapour between the iron-plates. The difficult and costly construction of such a bed is dispensed with in Mr Lassell's practice, by using a solid one of cast-iron, inclining it slightly, introducing the fluid metal at the lowest point, in a smooth, even flow, and gradually reducing the inclination to the horizon, as the mould fills, to an exact level.

(88.) The metal, when solidified, still requires long and most cautious annealing in a furnace or oven, at first red-hot, but gradually suffered to cool for many days, or even weeks, the walls and roof for this purpose being very massive, and every aperture carefully closed. Even when thus prepared, such is the brittleness of the material, that even the sudden affusion of moderately hot water occasions fracture.

(89.) The next process to be performed is the grinding, Grinding, to prepare it for which the disc must first be edged or brought to a clean, round circumference, by grinding it with emery on a concave iron tool or basin, so as to give its margin a gentle convex slope, inwards, which, in the subsequent operation on a convex tool, allows of its passage over the coarser grinding particles without splintering or tearing the edge. It is then ground on such a tool, turned by a gage as nearly as possible to a segment of a sphere of the intended radius, which should be of iron; and if for very large metals, divided into squares by grooves cut into its surface, to allow the free circulation of the grinding powder,

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1 In all other respects his paper is a wonderful example of what a multitude of words can do towards obliterating meaning. Telescope, and the water with which it is mixed. If the metal be of moderate size, not exceeding 20 inches in aperture, and strong enough to bear rather rough handling, this process is most easily performed by working it to and fro, with short strait strokes, and with a regular rotation on its centre, upon a solid and massive cast-iron tool of the same diameter as the metal, or only a very little larger, avoiding to go much over the edge. When this is done the tool must not be divided into squares, as the lodging of coarse particles in the grooves would be fatal to the operation. By this adjustment the abrasion takes place uniformly over the whole surface, and the curvature has no tendency to alter. If the tool be smaller than the mirror, it is obvious that, the central portions of the latter being always ground, while the circumferential alternately escape, the centre will be more abraded than the rest; and as the mirror and tool react on each other, and always tend to a common curvature, the curvature of both will increase, and the focus be shortened. On the other hand, if the tool be much larger than the mirror, and its edge be little or not at all overpassed at each stroke, its centre will be more abraded, the curvature of both flattened, and the focus lengthened. On this principle, by lengthening or shortening the stroke in grinding, on a tool but little larger than the mirror, a certain (though not a great) command over the focal length is obtained. Coarse emery is used at first; but so soon as the whole surface is found to be attacked, it must be changed to finer, and, as the scratches disappear, for still finer, obtained by washing and allowing the coarser particles to subside, till at length the smoothness is so perfect, and the fitting of the surfaces so equable, that it seems to float on the tool, and (however heavy) requires no more force to move it than if it literally did so. For very large and massive specula, however, both Lord Rosse and Mr Lassell have found it preferable to lay the metal down on its back, and grind it from above by a lighter and more manageable tool, divided into squares, as above described.

(90.) When the metal is reduced by grinding to a perfectly true and even surface, free from the smallest perceptible scratch, it will be found reflective enough to afford an image of a star, or of a distant white object, sufficiently distinct to try whether its focal length is correct; and, if it be so, the process of polishing may be commenced, the object of which is not merely to communicate a brilliantly reflective surface, but at the same time a truly parabolic form. If the material of the tool on which this operation is performed were perfectly hard and non-elastic, it is evident that this would be impracticable, since none but a spherical form could arise from any amount of friction on such a material once supposed spherical; and even if parabolic, it could not communicate that form to a more yielding body worked upon it otherwise than by a rotary motion about a common axis, which, with the slightest inequality of hardness in the metal, would infallibly work it into rings of unequal polish. Happily, however, there exists a material which, with sufficient hardness to offer a considerable resistance to momentary pressure, is yet yielding enough to accommodate its form to that pressure when prolonged, and at the same time sufficiently elastic to recover it if quickly relieved; that substance is pitch, whose properties, in this respect, were at once taken advantage of by Newton, with that sagacity which distinguished all his proceedings, as the fitting material for a polisher. A coating of this substance, liquefied by heat, is spread over the surface of a convex tool of a radius equal to the concavity of the speculum. The tool which has served Telescope, for the grinding process will be well fitted for this use; but if the metal be a very large one, and it is intended to polish it face uppermost, a lighter tool will be preferable, and Mr Lassell even employs one of deal plank, crossed in two thicknesses, and glued together, to obviate warping (a glass or slate slab would perhaps be better). If the tool be of iron or brass, its weight will require to be partly counterpoised. On such a tool the pitch should form a coating, which need not be more than a quarter of an inch in thickness. For small specula, however, which are intended to be polished face downwards, the tool may be a heavy mass of lead or iron, covered to a depth of half an inch with the pitch. In either case, the pitch, when laid on and cooled, must be moulded to the exact form of the mirror, either by very gently warming the latter (by the affusion of tepid water), or by similarly warming the polisher itself, which is safer when very brittle metals are concerned. A first approximation to the exact form will be attained by interposing a sheet of fine muslin, wetted and strained over the surface. The pitch must then be cut into small squares, not exceeding 1½ inch, or 2 inches in the side, separated by angular grooves or gutters, whose office is to receive the liquid necessary to moisten the polishing powder, to allow of its circulation, and to suffer the atmospheric pressure to act on the lower surface, and thus prevent adhesion in the act of lifting off, or when the surfaces do not exactly fit. In Lord Rosse's practice the tool itself is cut into such squares, which are not filled up by the very thin coating of pitch he applies; what does get in being removed by a cutter. In Sir W. Herschel's (who almost always operated by laying the speculum on the polisher, and working it face downwards) the squares were cut with a peculiar oblique-edged chisel or cutter, kept from sticking by frequent wetting, to very clean and definite edges; and, to promote the even distribution of the polishing material, the surfaces of the squares themselves were scratched or scarified, so as to subdivide them into still smaller ones. Circular gutters, crossed by others radiating from the centre, are sometimes employed, but are objectionable, and, on the whole, a uniform system of squares is both easiest and most effectual. Their free communication, inter se, is however of the last importance.

(91.) The proper quality and consistency of the pitch, Quality also, is of great moment. Mr Lassell's test of hardness is and consistence of the impression left by a sovereign standing vertically on its pitch, edge upon it, which in one minute ought to leave three complete impressions, of three milled notches at the then temperature of the atmosphere. Sir W. Herschel used a "pitch gage," being a weight of about half a pound, resting at one end of a wooden lever, on a supporting blunt edge of a piece of brass, by the depth of whose impression, in one minute, he was enabled to judge of the hardness. If pitch be too soft, it may be hardened by remelting with heat enough to vaporize some of the essential oil of turpentine it always contains; if too hard, a little of this oil, or of a softer pitch, may be added. But, besides the hardness, pitch varies exceedingly in quality, some specimens being quite unfit to communicate a fine polish. The best in Sir W. Herschel's experience was a mixture of brown Swedish or Stockholm pitch and a darker coloured and less glutinous variety, formed by boiling down American tar to a hard consistency. It is almost needless to remark, that the pitch employed should be fresh, taken from the centre of the barrel in which it was imported, and quite free from gritty or fibrous particles.

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1 If this latitude be not sufficient, the tool may be rendered flatter by grinding upon it a much smaller mirror or a flat disc; or the mirror be rendered more concave by laying it face upwards, and grinding it for a time with a much smaller tool, after which the grinding must be repeated in the regular way on the proper tool.

2 An intermediate step is sometimes interposed—viz., that of figuring the metal so ground on a bed of bones, imbedded in hard pitch, and previously brought to a true figure. Messrs Nasmyth and Delarue lay great stress on this part of the process. In the practice of all previous artists, followed both by Sir W. Herschel and Mr Lassell, the operation of polishing was performed by the surface of the pitch itself. Lord Rosse, however, uses this substance as, strictly speaking, only an elastic and yielding cushion, coating it over with a layer of harder substance, consisting of resin, melted with dry wheat-flour, and a small quantity of turpentine. So far as the experience of the author of this article extends, he is disposed to believe this additional preparation unnecessary.

That the final operation of polishing and figuring a speculum is one of great delicacy may be concluded from what is said in art. 56, of the thickness of metal which, in one of the largest dimensions, makes the difference between a spherical and parabolic surface. How far the processes now to be described are commensurate in delicacy to such requirements, may be gathered from the following experiment.—A speculum, 18½ inches in diameter, was polished with sesquioxide of iron (rouge or colochoth of vitriol, in the language of the old chemistry). After 1000 strokes of reciprocating motion, each 4½ inches in length, the whole of the polishing material, with all the matter abraded, was very carefully washed off both from the mirror and polisher, collected by subsidence, digested with nitro-muriatic acid, precipitated, and the copper taken up by ammonia, and re-precipitated by sulphuretted hydrogen. The sulphuret obtained weighed 2·6 grs., corresponding to 1·75 grs. of copper, or to 2·33 of abraded metal. This quantity distributed uniformly over the surface would form a coating only 0·0000045, or less than a two hundred and twenty thousandth of an inch in thickness.

The "rouge" in question is sold for the use of jewellers, and is an exceedingly sharp and cutting material. Lord Rosse prepares it by precipitating the sesquioxide of iron from its solution by ammonia and igniting. We have found it easiest prepared by fusing together, in an earthen crucible, sulphate of iron, sulphate of soda, and nitre (first fritted together to drive off the water), in the proportions 1, 2, 3, and after half an hour's ignition, pouring the melted mass into water. The salts being thoroughly abstracted by copious edulcoration, the finer particles are washed over (adding a minute quantity of gum-arabic to the water), and subsided for use. When the polisher is duly guttered and scarred, a paste or cream of this sediment and water is laid on over the whole surface with a fine camel-hair brush, and the polisher moulded to exact fitting by suffering the metal to rest on it (or rice vered) for a few minutes, shifting its position, however, every five or six seconds, and then slowly and cautiously giving it a continuous motion over the whole surface.

The earlier artists who occupied themselves with the construction of specula, having to deal with metals of no great weight, were content to work them by hand, the back of the speculum being cemented to a wooden block for convenience of handling. The process is described with great minuteness by Mudge in the Memoir already cited. In the beginning of the operation, when fresh from the emery grinding, the metal is worked round and round upon the polisher, carrying the edge but little over that of the latter, and now and then interrupting the circular movement with a cross-stroke. The effect of this is to drive the pitch inwards and force it to accumulate towards the centre of the polisher, and in consequence he found that in this way of working the polish invariably commenced in the centre, and extended itself gradually to the circumference of the metal. The form being originally perfectly spherical, it is evident that the figure thus communicated must deviate from that form by a continual and regular increase of curvature towards the centre, or, in other words, in the direction of that of the paraboloid. This process, then, was continued until the polish nearly reached the edge, when the circular motion was exchanged for short strait strokes carried across the centre, the operator meanwhile walking round the table on which the polisher is firmly bedded. The polish thus is extended equally over the whole surface, the figure meanwhile reverting to the sphere. Finally, the polish being perfected, which is known by the perfect smoothness of the working, recourse is again had to the circular motion to restore the parabolic figure, which is accomplished in a few minutes, but if overpassed, can only be brought back by going again over the whole process of working out a spherical figure by cross-strokes, and finishing by circular ones as before. It does not appear how Short worked his admirable specula, but Mudge, with whom he was contemporary and in habits of communication, considers himself as having strong reasons for believing their processes identical.

Sir William Herschel commenced his labours in this department of practical optics, on small metals, by hand-working, but this proving impracticable for large specula, he was led to the adoption of machinery, not, however, merely for the advantageous application of power, but by reason of the regularity of movement so attainable. Our limits will not permit us to give any account of the innumerable contrivances and experiments, failures and successes, by which he was gradually led up to the form of machinery and course of procedure in which he finally rested, which we shall here briefly describe, and whose availability we have ourselves repeatedly tested by successful operations on three specula of 18½ inches in diameter, as well as on others of smaller dimensions.

In this system of operations the speculum is worked (as already stated) face downwards, by strait, or nearly strait, strokes, on a polisher constructed as described in art. 90, of a diameter very little larger than the speculum, if circular, or, if oval, having the larger diameter in the direction of the stroke, and not exceeding that diameter by more than one-fifth. On an average of a great number of the most successful experiments with specula of all sizes, the proper diameter for a circular polisher may be taken at 1·06, and the larger and shorter diameter of an oval one at 1·12 and 0·97, that of the speculum being 1·1. When an oval polisher is used, and retained in a fixed position, the gutters must be cut at angles of 45° with the longer axis, so that the stroke shall always carry the metal across, and in no case along them.

The mechanism is adapted to give the following movements to the speculum and the polisher—viz., 1st, The stroke, being a reciprocating movement by which, acting alone, the centre of the speculum would describe a strait, or nearly strait, line, to and fro in a nearly invariable direction. 2dly, The side-motion, by which the track of the centre is shifted laterally at every stroke, or every alternate one, through a short interval, so as to carry it backwards and forwards by regular steps to a certain distance on either side of the centre of the polisher. 3dly, The round motion of the speculum, by which it is turned at each stroke, or alternate stroke, through a certain angle on its own centre, so as to vary the relative direction of the stroke in reference to the speculum all sorts of ways; and, 4thly, The round motion of the polisher (when a circular one is used), by which the gutters are presented successively at every angle of obliquity to the direction of the stroke.

The polisher being duly anointed with the creamy sediment, above described, the speculum (carefully cleaned) is laid down on it; and a "polishing ring," of a construction represented in fig. 22, is laid upon it. This apparatus consists of, 1st, A cylindrical outer ring AAA, whose depth is such that its lower rim shall not graze the polisher when moved across it. 2dly, A claw BCB, attached to the ring by two pivots BB, and having a hole C, to connect it by a pin to the lever which communicates the motion. 3dly, A flat interior ring of thin iron a a, not attached to the outer Telescope ring, but sustained in loose contact with it by three pins DDD above, and other three (not shown in the figure) below it, between which it can revolve freely in its own plane. This ring carries three cocks EEE, which rest upon the speculum, and so carry the whole apparatus, whose weight is small in comparison with that of the speculum, and, if necessary, may be counterpoised. By means of the flanges FFF projecting downwards, covered with felt, and adjustable by screw-pins, the speculum is held concentric, but not pinched or constrained, the felt being so adjusted as to touch the speculum a little below the middle of its thickness. Over the attachments of these cocks is screwed a ratchet-ring, by the action of an arm on whose notch the interior ring and the speculum with it can be carried round on its centre. e, e are two long springs, of the form shown in the margin e, whose office is to keep the arm, or arms, in question up to the ratched edge. Lastly, From the exterior ring projects a connecting-pin G, on which can be hooked a tail-piece for communicating the side motion.

(100.) The mode in which motion is communicated to this apparatus is shown in fig. 23. The loop C of the polishing claw is pinned on a fixed point of the lever AB, movable to and fro by a force applied at A, round a firm centre B. This would carry the centre of the speculum to and fro over the same space which C describes, which is the "length of the stroke," and can be measured on a scale by a traversing point projecting beneath the lever. To prevent the centre from wandering, a tail-piece GH is looped on to G, either working at the other end H, on a fixed centre F, or on a stud-joint in a lever HF, which gives the "side motion," in a manner presently to be described. By proper adjustment of the length of the arm GH, H being on the side of CG, opposite to B, it is evident that a very nearly rectilinear motion in any one stroke will be given to the centre of the speculum.

(101.) The round motion is given to the speculum by two arms DI and DK; the one a pushing, the other a pulling one, acting on the ratchet-wheel by claws at the ends, as represented in the margin atf, being lightly held against it by the springs cc (fig. 22). The other ends of these arms work on a pin D, attached to the lever at a distance from B, the centre of motion, less than BC, so that in the reciprocating motion of the lever, D traverses a less space than C, and the difference of motion causes the claws at K and L to work along the ratchet, and turn the mirror round, with the whole interior ring, on its centre, through an arc determined by the number of teeth of the ratchet brought into action at each stroke. The round motion of the polisher, when a rotating polisher is used, is similarly communicated by placing it on a bed, revolving horizontally on rollers on a solid metal ring, consisting of a flat circular iron plate, ratched at its circumference the contrary way of the speculum's round motion, and worked round by two claws attached at E to a pin at the under side of the lever, and pressed home by springs against the ratchet in the same manner. This is not shown in the figure, to avoid confusion. The angular amount of both these rotations can be varied within pretty extensive limits, by shifting the pins DE which attach the arms to the lever into one or other of a series of holes arranged along it.

(102.) A similar arm, attached to a pin at I, gives its impulse to the side motion, by acting on a ratchet-wheel N, carrying an arm OM; but as it is necessary that the tail-piece GH, and the lever arm BC, should be on contrary sides of the line of stroke, the revolving motion of the crank-arm OM is communicated by a rod MQ acting on the opposite arm of the lever FH, and thus gives a reciprocating motion to H, and therefore to G, at right-angles to the line of stroke. The extent of the side motion is varied ad libitum by altering either the length of the crank-arm OM, or of the lever-arm FH, or both.

(103.) All these movements, then, are completely under command, and adjustable in their relative extent. The stroke, too, or the side motion, if needed, may be made eccentric, or non-symmetrical, with respect to the polisher, by varying its situation, or that of the pin C, or the length of the arm GH. Every change in these dispositions is found, as a result of experience, to have its peculiar influence on the figure; and by a long induction from innumerable experiments (all minutely recorded), Sir W. Herschel was enabled to communicate at pleasure an elliptic, parabolic, or hyperbolic form to his specula, or to change any one of these forms into any other. The length of the stroke, and the extent of the side motion, would seem to be the most influential elements; and a similar average, from the record of the same experiments as those employed in deducing the averages of art. 97, assigns 0·47 for a good working length of stroke on a round polisher, without side motion, and 0·29 stroke, and 0·19 total amount of side motion (from for water, in which the speculum revolves, and which is maintained at a temperature of 55° Fahr., the hardness of the resinous coating of the polisher being adjusted to that temperature; G is another eccentric, adjustable, like the first, to any length of stroke, from 0 to 18 inches. The bar DG passes through a slit, and therefore the pin at G necessarily turns on its axis in the same time as the eccentric; HI is the speculum in its box, immersed in water to within an inch of its surface; and KL the polisher, which is of cast-iron, and weighs (for a 36-inch speculum, to which also the other dimensions above specified correspond) about 24 cwt.; M is a round disc of wood, connected with the polisher by strings hooked to it in six places, each two-thirds of the radius from the centre. At M there is a swivel and hook, to which a rope is attached, connecting the disc with a lever and counterpoise weight, so adjusted as to sustain the whole weight of the polisher, all but 10 lbs., which is therefore the amount of pressure upon seven square feet of surface, or 1·43 lb. on each square foot. The bar DG (seen here in section, but in fact opening into a ring) fits the polisher nicely, but without tightness, so that the polisher turns freely round, usually about once for every 15 or 20 revolutions of the speculum, and it is prevented by four guards from accidentally touching the speculum, and from pressing upon the polisher by the guides through which its extremities pass.

The wheel B makes, when polishing a three-feet speculum, 16 revolutions per minute; but for smaller sizes the velocity is increased by changing the pulley on the shaft A; for larger, diminished. For a six-feet speculum 8 strokes per minute was found to be a proper velocity. The length of the primary stroke, or that given by the crank-movement B, is one-third the diameter of the speculum, that of the eccentric G (or the side motion) one-fifth that diameter, from side to side, and variable according to the ratio of the diameter to the focal length. The period of rotation of G is once round in 15 strokes, while the speculum is made to revolve on its centre by means of the vertical axle N, which supports it, in 26 strokes. These adjustments have been found by Lord Rosse to command a good parabolic figure.

(105.) During the act of polishing, the speculum is supported in its box on the very same system of triangular plates and levers, which constitute its bed when in use. In fact, these supports are never removed, and the metal is transported on them in a horizontal position from the polishing apparatus to the telescope in the very same state of equilibration as when polishing. So sensitive has Lord Rosse found even the largest and most solidly constructed specula to any deviation in this respect, that the mere act of lifting them off their supports has produced a permanent alteration of figure, a result certainly which could not have been expected with so highly elastic a material.

(106.) The best and most satisfactory test of the perfect figure of a speculum, is its optical performance under favourable atmospheric conditions. When the spurious disc of a single star (or both those of a very close double one) is seen under a high magnifier, perfectly round and neatly defined, without rays or diffused light (other than the coloured rings due to diffraction, and which, when the apertures are very large, are much less offensively developed than in small telescopes); and when, too, on throwing the telescope out of focus, first one way and then the other, the area of the circle into which the image is dilated presents a similar distribution of light (proceeding from the centre outwards) on either side of the focus, the foci of all the annuli into which the speculum can be supposed divided cannot but coincide; and should any difference exist, the several annuli may be tested separately by covering the speculum, or the aperture of the telescope, by a circular screen, out of which is cut an annular opening corresponding to the area to be examined. If, on so dividing the area of the speculum into three or more annuli, and a central circle, the central, middle, and outer portions are found to agree in giving the same precise focal length under a high magnifier, the mirror may be pronounced perfect, so far as its figure is concerned. Another test, which can be applied without waiting for opportunities of weather, consists in the dial-plate of a watch, or a very white card, with clear small printed characters on it, fixed at a great distance, which should be seen with equal distinctness for all the annuli, without altering the focus, or rather, which should all give the same focus when thrown out of focus and restored. Mr. Foucault employs a peculiar method, different from either, which will be described presently.

(107.) Mr Lassell's system of polishing depends entirely on circular movements, and the combination of such; in sell's process virtue of which, every point of the polisher (in this system, as in Lord Rosse's, lying on the speculum) would, if not allowed to rotate on its own axis, describe in reference ports (one of which is seen at B) in a cistern of water maintained at a proper temperature (of not sufficient depth to cover the surface). This cistern is not shown in the figure. It is carried (with the speculum) concentrically, on a wheel C, which revolves on a vertical axle D, being driven by a worm E acting on an oblique-toothed edge, and turned by a spindle F with adjustable grooves, and a cross-band G communicating with an upper similar spindle H, in immediate connection by a strap and gearing-wheel II with the moving power. Thus the speculum is maintained in slow and smooth rotation. On it rests the polisher J, of light material, as already described (art. ), to which motion is communicated by a pin at its centre, which, in Mr Lassell's original construction, is not fixed into the polisher, but merely enters loosely a hole or cup in its centre, so that the area of the polisher is carried bodily about over the surface by this pin, while it is thrown into rotation on its centre by the difference of friction on its different parts, arising from differences both of relative velocity and of adhesion. To this movement we shall presently have occasion to return. Meanwhile the Telescope, centre-pin is carried round in a hypocycloid by the following mechanism.

(108.) The spindle-head H turns a worm K, similar to E, and acting on the oblique-toothed wheel L, similar and equal to C, and having its axle M, in the prolongation, in a right line with the axle D, though not continuous with it. This axle passes down through the horizontal arm N, and through the centre of a toothed wheel O, fixed on and making a part of that arm. The prolongation of the axle below O carries, attached to, and revolving with it, 1st, a broad vertical iron arm PP, which is hollowed at its farther extremity, so as to allow the passage of another vertical axis, which it carries round with it, and which is itself thrown into more rapid rotation, in the same direction, by the pinion Q, at its upper extremity, which gears into the teeth of the fixed wheel O; 2dly, a sector S, a portion of a circle concentric with the moveable axle P, hollow and grooved internally, so as to allow a pinion T, projecting beneath it, to revolve on an axis adjustable to any place in the groove, and this pinion being kept always in gear with the wheel R, is thrown into yet more rapid rotation in a contrary direction. Finally, to the under side of this pinion is attached another hollow and grooved crank-arm V, in which the pin that works the polisher can be fixed at any distance from the axis of T within the limits of its length. By this mechanism it is evident that the pin will be carried circularly round a point which is itself maintained in circular motion. The polisher is fed from time to time with water, as it grows dry by evaporation, from the exposed edge of the speculum, through holes, as seen in the figure. The speculum can be made to revolve the same, or the opposite way, to the rotation of the polishing pin, by crossing or uncrossing the endless band G, and its relative angular velocity can be varied by shifting this band from groove to groove of the spindle-heads AH.

(109.) Such is Mr Lassell's mechanism in its original and simplest form. It needs little consideration to see the advantages it offers over the vibratory system. All the movements are continuous and perfectly smooth. The speculum and polisher are never allowed to come for a moment to relative rest, which, even with crank-movements, is unavoidable in the vibratory system, at the end of each stroke, by reason of the play of the parts, and thus not only shocks, but the unsettling of the particles of the polishing powder, and ruffling the surface of the pitch, are completely obviated. What may be the influence of these latter causes will be rendered apparent by a phenomenon which presented itself on one occasion to ourselves, in polishing by straight reciprocating strokes a speculum of 6 inches in diameter. On taking it off, the polish was brilliant, but however carefully wiped and cleaned, it seemed to have impressed upon it an image of all the grooves of the polisher, which, on minute microscopic inspection, was found to be owing to the existence of innumerable almost infinitesimally fine hair-lines, traceable to an abrupt termination in a little crook, at one end, but thinning off into nothing at the other. These evidently arose from polishing particles freshly brought into action, with a slight fluttering motion at the commencement of the stroke. But what was very singular, and not so easily accounted for, they seemed distributed over the surface quite casually, nor could the least tendency to a crossing linear arrangement of their terminations in any fixed situation be detected. In fact, the appearance of squares vanished on near inspection, and was only seen when the eye was withdrawn and the mirror inclined, when they appeared rather as an optical image in the air, at some undefined distance, than as if traced on the metal; and that this was really their character was

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1 From the Transactions of the Royal Astron. Soc., 1849. The radii of the first and second eccentric cranks (S and V), which have been found by Mr Lassell to give satisfactory results under this arrangement, for a speculum of 24 inches aperture and 20 feet focal length, are, for the first eccentric, S = 1'7 in., (= S); for the second, VS = 1'4 in. (= Q); in that of a 10-inch speculum of 80 in. focus, S = 1'4 in., Q = 0'9; and for the last-mentioned aperture, and 110 in. focus, S = 0'8 in., Q = 0'7 in. The diameter of the polisher to that of the metal may be taken as 92 to 100. The rapidity of movement may be such that the second eccentric shall make about thirty-four revolutions per minute.

(111.) The exact symmetry of the epicycloidal curves about the centre in this machinery was found by Mr Lassell to produce a tendency to bring on the polish, not uniformly over the whole surface, but in rings, gradually enlarging, till the polish became perfect in every part. This course must be attended with some corresponding irregularity of figure, and to obviate it, he was led to deviate in some measure from the rigorous application of circular movement, so far as to displace the centre of the speculum under the polisher backwards and forwards, through a certain interval, and thus, by varying continually the incidence of this tendency, to destroy its effect on the polish and figure. The mechanism by which he succeeded in accomplishing this (and which in principle is the same as the introduction of a side-motion in the vibratory system) is as follows:—The speculum, instead of resting immediately on the upper surface of the vertical axle (D, fig. 25), reposes on an iron-plate a (fig. 26), as seen in section and in plan, which, by three holes c c c, drops on three studs screwed into the upper surface of the wheel C. On this rests the plate b, fitting so as to slide easily between the raised sides of a, and carrying the triangular lever supports on which the speculum lies. d is a roller in a frame projecting from the wall plate W (fig. 25), which, as the axle D revolves, comes in contact with the obliquely-curved ends of the plate b, each once in a revolution, and forces it (the roller being itself immovable) to slide between the flanges smoothly and regularly, producing the effect of a correcting cross-stroke amid all the circular ones, and annihilating all ringlike tendency. An inch and a half, or two inches, of lateral thrust, so produced, suffices for a two-feet speculum. The improvement of figure, and the certainty of success in the operation, resulting from this contrivance, is described by Mr Lassell as very striking.

(112.) Mr Delarue, observing that in this arrangement Mr Delarue's rectilinear motion given to the speculum takes place rue's fur always along the same diameter of its area, with an effect their injurious to distinctness, has recourse to a mode of obviating this inconvenience, which may be easily understood without an additional figure, by conceiving the mirror not to rest directly on the movable plate b (fig. 26), but on a circular iron-plate interposed, capable of revolving on the pivot d in its centre, and carrying on its upper surface the three triangular lever supports. The edge of this plate is grooved, to admit an endless catgut band, passing over two pulleys connected together, attached to a vertical jointed arm, so as to allow them to move to and fro in the direction of the central displacement, thus retaining always the same distance from the circumference of the wheel. The band is led over these pulleys, and two other fixed pulleys below them, to a small grooved wheel fixed on the spindle D below, and is kept tight by a heavy weight applied to pull outwards the arm carrying the pulleys. Thus, a very slow relative motion of rotation is given to the speculum round the pivot d, in the contrary direction to that in which the plate b itself is carried round, and the diameter, which is parallel to its sides, or in the direction of the arrow, is constantly shifted.

(113.) Another and final improvement introduced by Mr Delarue is destined to obviate the irregularity of rotation of the polisher on its centre-pin, which, it will be recollected (art. 107), is produced in Mr Lassell's apparatus by the mutual reaction of the speculum and polisher, and is therefore apt to vary much in speed, or even to go by starts. In Mr Delarue's mechanism, the pin which drives the polisher, though loosely fitting (not to constrain its even bearing), is not round but hexagonal, so that the polisher quoad rotation is commanded by the pin. But this, were the pin merely that marked V in fig. 25, would oblige the polisher to rotate in precise conformity with the angular velocity of V on its axis, which would be much too swift. Mr Delarue, therefore, substitutes for Mr Lassell's lowermost crank V, which carries the polishing pin, another crank of a more complex construction, carrying a train of wheels very similar in their arrangement, and set in motion on the same principle as the upper train OQRT. The axle of the pinion T is hollow, and is penetrated by an internal spindle, not partaking of its motion, but held firm by the clamp which fixes the place of the pinion in the sector S. To the lower end of this spindle is keyed fast a wheel of fifty-two teeth, which performs as a (relatively) fixed wheel the same office as the upper fixed wheel O. On this spindle revolves the crank which supplies the place of V, and which goes along with the pinion T. This crank consists of a triangular iron frame, composed of two parallel plates, kept asunder by pins, which serves to carry the axles of a train of wheels, whose action will be best understood by the diagram, fig. 27, a, where T is the pinion carrying round the framework and its wheels around the fixed wheel a, which gears into another b of an equal number of teeth, and which carries on the same axle another similar c gearing again into another similar d, which carries the polishing pin Z. By this mechanism the wheels b c, which

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1 This strange phenomenon has only once presented itself in the course of our experience. Mr Delarue informs us that a similar one has also occurred in his own. Telescope may be considered as one, being carried round the fixed wheel \(a\), revolve in the same direction as that rotation (see fig. 27, b), while the third \(d\) revolves relatively in the opposite; the ultimate effect being that the wheel \(d\) absolutely does not revolve at all relatively to the wheel \(a\), but keeps one of its diameters (as marked by the arrow) always parallel to the corresponding diameter of \(a\). If the reader find this difficult to conceive, let him lay down three shillings on a table, working together by their milled edges, and holding one \((a)\) tight down, carry the other \((d)\) lightly round by the gentle pressure of the finger. If the heads on \(a\) \(d\) be placed parallel at first, they will always remain so, while that on \(b\) revolves twice round for each rotation of \(b\) round \(a\).

(114.) The polisher then carried by \(d\) will therefore, under this arrangement, rotate only so fast as the wheel \(a\) rotates by the motion of the crank-arm, PP. If the wheels \(a\) \((b c)\) \(d\), instead of having the same, have different numbers of teeth, thus \((a, 52; b, 52; c, 54; d, 50)\), even this rotation will be modified and made to approximate to that which the polisher takes up on an average when left uncontrolled. And when the numbers are 52, 52, 51, 53 (which are the numbers found most advantageous by Mr Delarue), the result is a movement of the point in the periphery of the polisher, in an epicycloid of thirty-four loops for seven rotations.

(115.) There is only one particularity in this contrivance yet unnoticed. The situation of the centres of the wheels \(a\) \((b c)\) \(d\) need not be in a right line. The axle of \(d\) is therefore made movable round \(b\) by fixing it in an arm (part of the crank frame), movable on the axis of \(b c\), as its centre, so as to vary the interval between the centres of \(a\) and \(d\) from nil up to a certain maximum, and thus to make the centre of the polisher revolve in a circle of any size from nil up to that maximum. It is fixed in any desired position by a clamping-screw, pinning it in a slot or narrow circular guiding slit in the upper plate \(e\) (fig. 27, a) of the crank-frame.

(116.) Such is Mr Delarue's mechanism, which has afforded very admirable results in the production of specula 13 inches in aperture and 10 feet focal length, the perfection of which is enhanced by his practice of bestowing the same care and precision on every step of the figuring of the speculum, from the grinding, the smoothing on a bed of bones, or rather a slab of slate cut into squares, carefully brought to the same figure; and to the figuring of the polisher itself, which, being thus previously rendered almost perfect, the speculum is saved the rough work of having to figure the polisher for itself on every occasion of repolishing. For this part of his system of working he acknowledges his obligations to Mr Nassyth, who has also engaged with much success in these delicate operations.

(117.) The combination of the epicycloidal movement of the polisher specified in art. 112, with the movements of the speculum itself, described in arts. 109, 110, gives rise to a relative epicycloidal movement of much complexity, and of which the general character is that of a near approach to rectilinearity in the circumferential regions of the speculum, over a considerable part of each stroke, with a short and highly curved loop at each extremity. Thus the general character of this system of polishing may be described as a blending of the rectilinear and circulating form of stroke, regulated to perfect smoothness and evenness of distribution, according to a regular law over the whole surface. Nor does there seem the slightest ground for doubting its applicability to specula of any size.

(118.) These improvements, or their equivalents, have been adopted by Mr Lassell, who, however, limits the rotation of the polisher to a slow uniform movement round its axis, at the rate (for a 24-inch speculum of 20 feet focus) of one revolution to every thirty revolutions of the pinion T (fig. 25), corresponding to which he assigns for the eccentricity of that pinion upon the sector S, \(S = 1:50\) in.; for that of the polishing pin upon the crank V, \(Q = 1:00\) in.; for the semi-thrust of the speculum itself, \(1:52\); for the diameter of the polisher, \(23\frac{1}{2}\) to 24 inches, and for its weight 16 or 18 lb.; the working speed being such that the pinion T makes seventeen revolutions per minute. With these adjustments he considers success in giving a true parabolic form certain, and the efficacy of a change in any of them so distinctly ascertained, and the whole process so entirely under control, that taking nine-inch specula A, B, C, D, all sensibly perfect even in the opinion of a competent judge, he would engage to take A, B, and C successively to the machine, and communicate to A a sensibly elliptical figure (having the focus for central rays shorter than for marginal ones), to B a figure sensibly hyperbolic (affected with the opposite error), while C should come off apparently unaltered, as compared with the untouched one D, and all should give round images of stars when in focus, and the penumbra when out round and symmetrical.

(119.) Mr Grubb, of Dublin, has also devised a very ingenious mechanism for figuring and polishing reflectors, which equally secures the regular rotation of the polisher on its axis, and which the reader will find described and figured in Nichol's Physical Sciences, art. Speculum, from the learned pen of Dr Robinson.

(120.) M. Foucault, in working the parabolic surfaces of M. Foucault's glass reflectors for silvering (art. 76), after attaining a faultless good spherical figure in the first instance by grinding to a fine and considerably reflective surface, discards all further mechanical appliances for its conversion to a parabolic curve by a system of regulated movement, and works by hand-abrading; by gradually polishing off, with tools and polishing materials of fitting delicacy, the difference in substance between a spherical and parabolic segment of equal focus (which, as we have seen, art. 56, amounts in a 4-feet speculum of 48-feet focus, to less than a 21,000th part of an inch in thickness, even at the extreme edge). To enable him to execute such a manipulation with certainty, it is necessary to have at every instant a test of the state of the surface infinitely more delicate than can be afforded by any mechanical means of measurement; and this he finds in the following optical processes, by which every, even the smallest, irregularity of level in the surface, and every, the minutest, deviation from its proper inclination to the axis, is made glaringly conspicuous. [As to the process of hand-abrasion, it is analogous to that by which a truly plane form is given to extensive steel surfaces in engine work, where the prominences are reduced, not by grinding the whole of one plane surface against another, but by a series of local abrasions, tested from instant to instant by contact with a fiducial plane.]

(121.) M. Foucault's first procedure for the detection of Detection irregularities of figure is to place very near to the centre of irregularity a minute object, as the point of a pin. The image of this will be formed of the same size, and very near to the object itself—side by side, for instance, and can thus be compared microscopically with the object, and thus an approximate judgment of the figure can be formed. As a still nicer test, he places an object, having parallel sides (such as the edge of a thin piece of steel, about \(1/8\)th of an inch thick), near the centre of curvature, being enlightened from the side opposite the mirror. Its image then is seen dark on a bright ground, and if viewed with Telescope. the naked eye at the distance of distinct vision, each of its parts is seen by rays converging only from a small portion of the surface of the mirror, the others passing beside the pupil. If, then, the curvature be not uniform, or offer irregular gradations, the edge will appear distorted; contractions and dilatations will appear—each indicative of a corresponding more or less abrupt change of curvature. Finally, and still more delicately, a thin piece of metal, pierced with a small hole of above \( \frac{1}{4} \)th of an inch in diameter, illuminated with artificial light, is placed within the centre of curvature, the rays diverging through which come back and form an image situated a little beyond that centre. By placing the eye in the cone of rays which, having formed this image, diverge anew, and bringing it gradually almost close to the image, the whole pencil is received, and the whole surface of the metal is seen illuminated. If, now, an opaque, rectilinear edge be brought near the image of the hole, and be made to infringe on it by degrees, the mirror will also by degrees lose its brilliancy, and when all the light is about disappearing, the whole of the irregularities of the surface of the metal will be plainly seen. Suppose, for instance, the surface a perfect sphere, then the very last indivisible point of the image will be formed by rays coming from the whole surface of the metal, and this, though feebly, will appear uniformly illuminated. Quite otherwise, if irregular. Some portions will send rays which ought to go to form this point aside of it. These will not enter the eye, and those portions of the surface will appear dark; vice versa, other portions will appear unduly illuminated, as sending to the eye rays which do not properly belong to them, and which emanate from other parts of the hole. The missing rays will leave on their corresponding places on the speculum a deficiency of light, and the accumulated ones will produce an increased intensity in others, and the result is to produce the appearance of valleys and hills, by a kind of chiaro-oscuro effect, in which all the inequalities of surface become enormously exaggerated, and are seen as real elevations and depressions. Thus a surface can be judged of in a few seconds, and, when defective, the faults are known immediately with great precision.

(122.) M. Foucault sets out from a good spherical surface, and, by polishing off the exterior zones in a ratio increasing from the centre, renders it elliptic. The regularity of this ellipse (if we rightly understand his process) is then tested, just as that of a spherical surface would be, the illuminated object or minute hole being placed in the farther focus of the ellipse, and its image being formed in the nearer, all the other steps in the process remaining the same. Thus the more distant focus is by degrees carried farther and farther away, till so near an approximation to the parabolic form is certainly attained, that a very slight continuation of a similar process in the same direction finishes the work.

(123.) It is no small recommendation of this mode of optical examination of the surface, that by it the real defects of configuration can perfectly well be distinguished from those accidents which temporarily divert the rays from their strict geometrical paths, from flexure in the mirror itself, and even from undulations in the air above it, or in the tube of a telescope, which seem to pass like waves over the surface. Whoever has viewed the coloured fringes seen when a prism is pressed against a plane glass within the coloured arc, fixing the limit of total reflection, and seen them undulate under a trifling pressure, disfiguring the surface, will easily appreciate the delicacy thus attainable.

(124.) Our limits will allow us to say little as to the Telescope modes of mounting telescopes. For astronomical purposes of precision, where the object is to determine the places of celestial objects with exactness, or for geodetical uses, the tube of the telescope is part and parcel of the graduated apparatus, and strictly limited as to its connection with it. Portable stands for merely viewing objects, are either tripod stands, in which a vertical axis revolves within the upright shaft, and carries the telescope on an elbow-joint, allowing a movement in a vertical plane, thus constituting a movable "alt-azimuth" mounting; or frameworks of wood, on which one or both ends of the tube can be elevated or depressed, and a certain limited horizontal movement given by a screw. Such are usually provided with a "finder," or small telescope, with a large field of view, and low magnifying power, provided with a cross-wire in the focus of the eye-glass, by whose aid an object, first seen by the naked eye, or otherwise found by a "sweeping motion," and brought by the movements of the telescope (to which it is fixed) to coincidence with the cross, shall then be found (by previous adjustment to parallelism) in the centre of the field of view.

(125.) Large reflectors are often (as in Sir William Herschel's constructions) mounted alt-azimuthally on wooden masts, scaffoldings or frameworks, formed by an octagonal foundation frame, with strong beams in front and behind, braced together and connected with radii running up to a central pin, on which the whole revolves on rollers, on a ring or railway, firmly based on brickwork or timber. The front and back beams carry two pairs of ladders, one at each end, inclined to and resting against each other, and carrying between them, at their summits, a strong suspension-beam, from which, by a tackle of pulleys, the upper end of the tube is suspended. The lower rests on rollers, running to and fro on a rail, bedded on the radii of the foundation-frame, and can be advanced or driven back by appropriate mechanism. The rope which passes through the pulleys has one of its ends connected with a large barrel, by which (the other end remaining fixed) the tube can be elevated or depressed through great differences of altitude; the other, with a smaller barrel, worked by a finer and slower mechanism, to command lesser differences. [And we will here pause to notice the exceeding steadiness and absence of tremor (even in windy weather in the open air) which is secured by this mode of suspension, the several rope-lengths intermediate between the pulley-blocks (four, six, eight or more of each) being not all of equal length, and (from the effect of friction and stickage) far from having equal tensions, so that their vibrations, not being isochronous, contradict and annihilate each other.] The two ends of the upper suspension-beam are held firm in their places by stays springing from the lateral angles of the revolving foundation-frame, and the whole structure is studiously so designed in the disposition of its parts as to avoid rectangular and rhombic frame-work, and constitute an assemblage of triangles, so as to secure the maximum of stiffness by the avoidance of any play of parts, being, in fact, so far an anticipation of Seppings' principle of diagonal bracing; as the form given to the strengthening rings (of sheet-iron bent to an angle), applied within the sheet-iron tube of the largest of these structures, was of the principle of corrugated iron-plates, since adopted so largely in roofing.

(126.) Reflectors of the very largest size, however, are chiefly used as meridian instruments, and this dispenses with the necessity of much of the above-described mechanism. Lord Rosse's 6-feet reflector is suspended between

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1 If, in this account, we have done injustice to any part of M. Foucault's mode of procedure, we can only urge in excuse that his account of it (Nat. Hist. Soc., xix. 284) is in some parts quite unintelligible, p. 286, lines 9, 10, 11, for instance. 2 These are wanting in stands of Mr Ramsay's construction, to the great detriment of stability. 3 This refers chiefly to the mounting of Sir W. Herschel's telescopes of 20 and 25 feet focus. In the foundation-frame of the 40-feet reflector this could not be carried out in all the upper works. Telescope, two lofty meridional walls of solid masonry, between which its upper end is allowed a considerable amount of lateral motion, so as to admit of taking up the view of a celestial object considerably before its arrival on the meridian, and following it considerably after without displacing the lower end. One of the most elegant of Lord Ross's mechanical contrivances, is his mode of counter-balancing the weight of the tube of a telescope, which is seized by its centre of gravity and all but swung, so as to press lightly both on its lower end, where it rests on the supporting bed, and on its upper suspension, thus allowing the greatest freedom and facility of vertical movement, and that equally in whatever position it may happen to be placed.

(127.) The equatorial form of mounting telescopes, however, for general astronomical purposes, is gradually superseding every other. Previous to the vast improvements which modern engineering has effected in every description of iron machinery on a great scale, this mode of mounting was considered applicable only to light telescopes, such as refractors, of what would now be considered trifling dimensions. The general principle of this mode of mounting is easily understood. An axis parallel to that of the earth, or pointing to the sidereal pole, and therefore, at any particular place, having a fixed situation, is traversed by another axis at right angles to it, which carries the telescope. In whatever position the telescope may be placed by its rotation on the latter axis, if this position be maintained while the polar axis is made to revolve, the direction of the telescope will sweep out on the sphere of the heavens a circle parallel to the equinoctial, or a "parallel of declination." On the other hand, if the polar axis be prevented from revolving, and the telescope be turned round on the axis perpendicular to it, it will sweep along a meridian circle, or a "declination circle," i.e., one at right angles to the equinoctial. Therefore, if once set on a celestial object, which is carried round by the earth's diurnal motion, in order to follow it, it will suffice (if the small effect of refraction be left out of consideration) to turn the whole instrument round uniformly on the polar axis—that is to say, by a single movement; whereas, in every other construction two movements, in two planes, at right angles to each other, are requisite. This movement may be given either by hand, by means of a handle and Hook's joint moving a tangent screw, working into an oblique-toothed circle, fixed on the polar axis, or (according to a method first introduced by the German opticians, Fraunhofer and Utzschneider) by a clock-work movement, regulated so as exactly to keep pace with the apparent diurnal movement of the heavens. (Of this more presently.) The advantages of this construction, as adapted to finding, viewing, measuring, or photographing celestial objects, are immense. For, 1st, by means of two graduated circles fixed, the one on the lower end of the polar axis, the other on the "declination axis," perpendicular to and carried round with it, the telescope may be "set" (or adjusted in direction), by the aid of a clock showing sidereal time, upon any star or other object whose right ascension and declination are known, with the certainty of finding it in the middle of the field of view at any instant; and, 2dly (the clock movement being then thrown into gear), it may be kept there, without any personal aid on the observer's part, thus leaving both his hands and his whole attention at liberty to execute any micrometrical measurements he may have occasion to make, the object appearing all the while at rest relatively to the system of wires, &c., to which he may be referring it.

(128.) Two systems of equatorial mounting are in use, one, which may be called the English system, having been practised by the English opticians (while the optician's art might be considered almost exclusively an English one), in which the polar axis was supported at its two extreme ends, the telescope, with the whole weight of the declination circle, &c., being supported on it between them; the other, if not first introduced, at all events almost generally adopted by the German artists, and which may therefore not improperly be termed the German mounting, in which a short polar axis, revolving between two strong sustaining collars, but projecting at its upper extremity beyond them, carries, on the portion so projecting, and supported only by its stiffness, the telescope and its appendages. Both constructions have their advantages and disadvantages. Beautiful examples of the English construction, as adapted to large achromatic telescopes, are those of the 5-feet equatorial of Sir James South, constructed of tin plate by the late Captain Huddart, and which the reader will find fully described and figured in Phil. Tran., 182; of the equatorial of the Liverpool Observatory; of the "Northumberland" equatorial of the Cambridge Observatory; and lastly (and the most perfect of all), of that recently erected at the Royal Observatory of Greenwich, carrying the 12-inch achromatic noticed in our list, art. 31,—all three constructed on principles combining the requisites of extreme stiffness to resist both flexure and twist, and lightness, devised by the present astronomer-royal, Mr Airy.

(129.) Of the German system of equatorial mounting, so far as achromatic refractors are concerned, abundant examples are extant at the observatories enumerated in our list, as furnished with such instruments by the continental opticians, and the reader will find them minutely described in the annals of those observations, and (to specify one or two) in Prof. Strese's "Beschreibung des Grossen Refracters in der K. K. Sternwarte zu Dorpat," and his "Description de l'obs. Imp. de Poulikova." But more recently it has been found that this system of mounting, by the aid of the immense strength and stability which can now be combined with the utmost delicacy and smoothness of movement in great machinery of cast-iron, is peculiarly well adapted for the support of large and ponderous reflecting telescopes on the Newtonian or Herschelian construction. Thus Mr Delarue has adopted this system for the mounting of his reflector of 13 inches aperture and 10 feet focal length; Mr Lassell for his equatorial reflector of 2 feet aperture and 20 feet focus, and ultimately for the magnificent reflector of 4 feet aperture, and 39 feet focus, noticed in art. 57, and of which we can only regret that our limits will not allow of our entering into any details of description, photographed as we have it before us by the kindness of its distinguished constructor.

(130.) The clock movement, by which the polar axis in Application of these instruments is driven, has this peculiarity, that it cannot be regulated by the ordinary pendulum and escapement system of clock-work, which, of necessity, goes by jerks or fellow at each second. It is essential that the movement should be uniform, so as to keep even pace, under the highest rotation, magnifying power, with the diurnal rotation of the heavens. This Fraunhofer and his successors accomplish, or aim at accomplishing, by a movement not very unlike that of the governor of a steam-engine, only that the balls, instead of opening and closing a valve, rub against a brass hollow conoid, and so, in diverging, generate an increased friction, which destroys the excess of power, and keeps velocity from increasing beyond a definite limit. For this Mr Airy has substituted a far more elaborate and theoretically perfect system of equalization, by employing a regulated descent of water through a centrifugal wheel as the moving power, using a conical pendulum as the primary regulator of speed, and equalizing the amplitude of its circuit by the resistance of the fluid on vanes caused to dip deeper into it by an increased velocity, and at the same time to contract the supply through the intervention of a throttle-valve, and vice versed, the effect being to produce the nearest approach to a mathematical uniformity of rotation which has yet been accomplished. In addition to the works already cited in various parts of this article, the reader is referred for further or more detailed information to the following, viz.:

Bosovich, Opera pertinentia ad Opticam et Astronomicam, 1785. Kluge, Analytische Dioptrik; Prechtl, Praktische Dioptrik, Wien, 1822. Hopkins on the Equatorial Mounting of Telescopes, Notices of Ast. Soc., xiv., 41; Rothwell, ditto, ditto, xiv., 3, 85; Airy, ditto, xiii., 6, 186; Simms, ditto, ditto, xiii., 8, 290; Steinheil's ditto, ditto, xix., 2, 59. "Littrow on Barlow's Fluid Ob-