Fig. 84.

is the object, c the lens, and i the image formed with it. In this manner it has been employed for producing beautiful combinations of flowers, trees, animals, &c. When the lengths of the reflecting planes are less than the distance of distinct vision, a convex lens whose focus is the length of the plates should be attached to the eye-end of the tube. In this way polished speculums may be used, by which the brilliancy of the picture is increased, as less light will be lost by reflection. Dr. Brewster has found, that in order to produce perfectly beautiful and symmetrical forms, the following three conditions are necessary.

1. That the reflectors should be placed at an angle which is an even or an odd aliquot part of a circle, when the object was regular, and similarly situated with respect to both the mirrors, or an even aliquot part of a circle, when the object was irregular.

2. That out of an infinite number of positions for the object both within and without the reflectors, there was only one position where perfect symmetry could be obtained, namely, by placing the object in contact with the ends of the reflectors. 3. That out of an infinite number of positions for the situation of the eye there was only one where the symmetry was perfect; namely, as near as possible to the angular point, so that the whole of the circular field could be distinctly seen; and that this point was the only one out of an infinite number at which the uniformity of the reflected light was a maximum.

CHAPTER XVII.-Micrometers. (113.) THE micrometer is an instrument usually applied to telescopes and microscopes, for the purpose of measuring minute bodies or small angles subtended by bodies at a remote distance, by which their real magnitude is obtained. By the modern introduction of this instrument for the use of the astronomer, and the improvement of the telescope, may be attributed our accurate and extensive acquaintance with the universe of matter; while from the perfection to which the microscope has recently been brought, an equal acquaintance with the minute organization of bodies may be expected. By the application of the micrometer to this latter

sists of a brass rectangular box a a, the upper and lower plate having an opening in the centre, (but in the figure both are removed ;) this box is made to slide along an opening cut in the tube of the eye-piece of the telescope at right angles to its axis, so that the wires ce may be in the field of view; these wires are fixed to the forks in, moveable in each other by the screws i and n, connected to the micrometer heads hh: there is also another fixed wire at right angles to the two former from c to e. To measure any small angular distance with this instrument, as the diameter of a planet, the two parallel wires are made to approach or recede from each other by turning the screw-heads h h till the bodyto be measured is exactly enclosed by them, while the longitudinal wire crosses the centre of the body. Having thus accurately measured the planet by the two cross wires, we must next ascertain their distance asunder, in the manner following: suppose there are 50 threads of the screw to an inch, and that the heads are divided each into 100 equal parts; now one of the screws is to be turned till one of the wires is brought into accurate contact with the other, when the number of turns and divisions requisite to effect this purpose will give the diameter of the planet, each division being equal to 8th of an inch. But if we are desirous of determining in seconds, or parts of a degree, it is found by previously measuring a known base, or by ascertaining the time an equatorial star takes in passing from one wire to the other, and from thence deducing the seconds or parts of a second agreeing with each revolution of the screw-head.

The essential requisite in this micrometer is, that the wires be perfectly parallel, and that there be no shake in the forks that carry them.

(115.) The micrometrical telescope of Dr. Brewster, (§ 40) for measuring distances, may be employed for determining the diameters of bodies by having two parallel wires fixed across the field of view in the focus of the eye-glass; these wires being immoveable will not be liable to any inaccuracies in the screws, or from the uncertainty of obtaining a correct zero. The manner of using it is thus: suppose the inner moveable object-glass to be in the focal point of the principal one, and that the wires, by experiment, exactly take in an object of known magnitude, this will be the minimum angle capable of being measured with it. But when we have a larger object than can be enclosed within the wires, the inner object-glass must be brought nearer the principal one, thus reducing the power of the telescope by shortening its focus, so that the angle between the wire will be increased to admit the object to be measured; and as by the laws of optics it is known that when the two object-glasses are in contact the focus is shortest, so the angle between the wires will then be a maxımum. Hence, any angle between these two points ascertained by experiment, may be determined by divisions registered along the tube.

(116.) The preceding principle of a micrometer may be applied to the Gregorian or Cassagranian telescope, without any additional apparatus; for the magnifying powers of either of these instruments may be varied by altering the distance between the large metal and the eye-piece, and then adjusting for distinct vision by the little metal. In this way Dr. Brewster proposed to determine the angle subtended by any object, having experimentally formed the scale for adjustment.

(117.) Fibres for micrometers.-After the contact of brass plates, employed by Huygens, for micrometers was discontinued, silver wire, hairs, and spiders' webs were introduced; the former, how ever, till latterly, could not be produced finer than tath of an inch diameter in this country, which, consequently, led to the choice of the other fibres. But, by the ingenuity of Dr. Wollaston, wire can now be obtained of only the both of an inch in diameter: this he effects by having a fine platina wire thickly coated with silver, which is drawn out as fine

as possible in the usual manner, through steel or jewelled holes, and then, by finally immersing this wire in an acid that will dissolve the silver and not the platina, he obtains a perfect wire of any fineness that may be required.

(118.) The spider's web was first successfully employed for micrometers by Mr. E. Troughton, who used the stretcher, or the long line which supports the web, for this purpose, ths others being too weak. He found thie thread to possess the valuable properties of fineness, opacity, and elasticity.* But the difficulty of procuring this particular thread has led to other contrivances in its stead.

(119.) The micrometer threads of Dr. Goring, which have been termed artificial cobwebs, were introduced by him to obviate the easy destruction of the natural ones when kept for any length of time, and from the difficulty of procuring those of the proper kind. These threads are formed from a thick solution of gum caoutchouc in oil of turpentine, and by not employing in their formation a heat greater than that of the human body; after the threads are drawn out, the essential oil evaporates, and leaves the Indian rubber in the same state as at first. The cobwebs made in this manner are not liable to injury by keeping, like the ordinary ones, while they possess the essential properties of opacity, fineness, parallelism, and elasticity, and are far superior to them in strength.

(120.) The divided object-glass micrometer is composed of two semilenses a, c, (fig. 86; these act as two distinct Fig. 86.

object-glasses, each producing an image of the same object, and in order that their foci shall be of the same length, they are made by dividing a circular

This quality is lost by keeping.

It should be observed, that the Indian rubber solution must not be kept in any vessel from which

the air is entirely excluded, whereby the slow evaporation of the essential oil is prevented, as this

consequence will decompose or change its nature, so

that when drawn out into threads it remains in a clammy state and will not dry. This remark equally

applies to all its solutions for making water-proof articles. The solution may be covered with a piece of wash leather,

their focal distance will be equal to the real angle subtended by the two objects at F, or at the place of the objectglasses, (the real distance, of a F or c F being very small in comparison to the distance of the objects OP from the objeet-glasses :) to find, therefore, the angle of the semilenses, we have the sides a c (i. e. the distance of the two centres) and e F their focal distance, which are all the data necessary to determine it trigonometrically. But as the angle in practice is usually very small, it may with little error be considered simply as the subtense a c, having experimentally determined the distance of the semilenses corresponding to two objects making a known angle with each other, when by simple proportion the angle for any other distance may be found.

(121.) The improvements that have been made on this divided object-glass micrometer by Dr. Brewster, consist in having the centres of the two semilenses at a fixed distance from each other, and by employing another object-glass in the ordinary manner: to produce the requisite variation of angle, the fixed semilenses are made to traverse along the axis of the telescope between the other object-glass and the eyepiece, thus producing a change in the magnifying power of the instrument; and by means of a divided scale along the tube, showing the distance of the semilenses from the principal objectglass, the angle is ascertained.

(122.) The principle of the divided object-glass micrometer has been applied to the microscope, for the purpose of measuring the diameters of various fibres, and from thence determining the quality and value of the material for the manufacture of different articles; its principal application has been in the measurement of wool, from which it is called an eriometer. The instrument

consists of a compound microscope, either refracting or reflecting, having two semi-concave lenses capable of adjustment by screws and a vernier's scale; this apparatus is fixed between the object and object-glass or metal, and the measurement of the fibre, by the contact of its two images, is effected in the same manner as in a telescope.

(123.) The mother-of-pearl micrometer, invented by Mr. T. Cavallo, and described by him in the Phil. Trans. for 1791, has, from its simplicity, been very extensively employed in practical astronomy, and is indeed admirably suited for measuring any small angle with expedition. The strip of pearl used for this purpose is minutely divided, and stretched across the diaphragm, or stop, usually placed in the anterior focus of the eyeglass, either of a telescope or compound microscope; so that the divisions may be distinctly seen by the eye at the same time as the object. When we are desirous to measure an object with the former instrument, any given number of equal divisions on the pearl corresponding to a known angle is first determined by experiment; then, on looking through the telescope at the object to be measured, and counting the number of divisions the diameter of the object occupies, the angle it subtends is determined from the proportion of that number to the number answering to the known angle. When this micrometer is applied to the compound microscope, in order to ascertain the magnitude of any minute object, the strip of pearl is stretched across the field-bar of the instrument; it is then brought in the direction of the length of the object to be measured, by turning the tube of the eye-piece till they coincide. Then, if we suppose the number of divisions on the pearl dynameter to be 100 in the space of an inch, and the

loss of time, besides the liability of disarranging the instrument for distinct vision. Having thus stated the defects of that micrometer, it is only necessary to mention that the circular micrometer is entirely free from these evils; for the central space being clear, the rays are not obstructed, while the divisions are all equally magnified, and the object can be measured with equal facility and accuracy in any direction: indeed, the advantage of employing this instrument is so great, that we need only mention that the orbits of three out of the four new minor planets were determined by a circular micrometer alone.

(125.) The circular pearl micrometer was invented by Dr. Brewster, and consists of an annular portion of motherof-pearl, a, i, (fig. 88,) fixed on its

part to be measured is found to occupy two of these divisions, to determine its real size we must ascertain how much the object has been amplified by the object and field glasses. But if no field lens is employed, the power will be as the distance of the object-glass from the image, divided by the distance of the object from that glass. As inaccuracies are however liable to occur in these measures, the best practical manner (which is equally simple, let the number of glasses be soever numerous) is to determine the increase in magnitude by using another scale of very fine divisíons in place of an object; knowing how there are in an inch, and ascermany taining the number of divisions on the one employed as an object that are equal to any number of the equal divisions on the pearl dynameter across the fieldbar, by dividing the one number by the other, the amplifying power will be obtained. Example. Suppose the divisions on the scale (used as an object) be 1000 in the space of an inch, and one of such divisions is magnified so as exactly to cover one of the divisions on the pearl, which are th of an inch, it is evident the scale, or an object placed in its stead, is magnified 10 times. Hence we know that as the object we proposed to measure occupies two divisions, it is oths of an inch long; each division on the pearl being equal to the th of an inch on an object placed in the focus of the object-glass. In using the micrometer, the power of the eye-glass is not required to be known, as the divisions on the dynameter are magnified in the same ratio by it as the object.

outer edge to the diaphragm d, d, at the end of a piece of brass tube, which is capable of being adjusted exactly to the anterior focus of the eyeglass of the telescope or microscope; the inner circumference of the pearl is divided into 360 equal parts or degrees; and when this micrometer is thus adjusted for use, the maximum angle must be determined experimentally: this angle will be subtended by the inner diameter of the pearl a, c, i. Now, if we suppose this angle, by observation, to be two degrees, we shall be able to find the value of the angle any other object subtends in any direction less than 2°; thus, let the object be represented by the line e, which, by inspection, is found to occupy sixty divisions; bisect the angle the object e subtends, and it will be equal to the sine of half the angle a ci: or the angle which this object subtends is equal to twice the sine of half the angle, a c being the radius; so that the object e subtends half the maximum angle, or one degree. In this manner, trigonometrically, might be found the angle answering to every

(124.) Circular micrometers. The micrometer last described, as stretched across the field-bar for many astronomical purposes, is found objectionable from the three following circumstances. First, the central rays from the object are obstructed by the pearl, which likewise divides it into two portions. Secondly, the situation of the central portion of the pearl being nearer the eye-lens than the other parts, the various portions will be unequally magnified, although the pearl is really divided into equal parts; and therefore the measurements are inaccurate, unless taken from one particular part. Thirdly, the edge of the micrometer always requires to be in the direction of the parts to be measured: for this purpose, it is necessary always to turn the eye-piece to bring it in the proper direction; this, undoubtedly, is a

division, which should be formed into a table; and thus it would be given by inspection.

(126.) The circular suspended micrometer is an instrument, simple in its construction, and admitting of extreme accuracy in its execution; it is less subject to injury, while it possesses many advantages over others in its application to astronomical observations. This micrometer was invented by the late M. Fraunhofer, and consists of a circular disc of parallel plate glass a, (fig. 89,) having in its centre a small circular hole of about half an inch diameter, and turned very true in a lathe; to the inner edge of this circle a narrow ring of steel c is securely fastened, when its inner edge is turned Fig. 89.

a

perfectly circular, and reduced very thin. The glass plate, with its steel ring, is then mounted in a brass tube or setting d, d, by means of which it can be adjusted to the focus of the eye-glass, (similar to the last micrometer.) This micrometer, when viewed in the telescope, appears like a narrow ring suspended in the heavens, from whence it derives its name. The chief advantage in this instrument is the accuracy by which the moment of ingress and egress of a planet or star is determined; for the body being seen in the field of view through the glass plate, before it comes to the inner edge of the steel ring, allows the precise moment of contact to be very readily observed. The angle subtended by the ring must be found in the same manner as with the other micrometers; or by noting the time an equatorial star passes when near the meridian, and deducing therefrom the angle which the inner edge of the ring subtends. The velocity of a planet may be determined in the same manner while near the meridian; or the difference of the time occupied by a star and the planet passing together, would determine the motion of the latter, making proper allowance when crossing above or below the centre.

Opties in general. Euclid's Optics, Paris, 1557. -Kepler's Dioptrics, Augsburg, 1611.-Descartes's Dioptrics, in his works, vol. ii.; published also in Baron Maseres's Scriptores Optici, London, 1823.Huygens's Dioptrics, in his posthumous works.James Gregory's Optica Promota, London, 1663; pub. lished also in Baron Maseres's Scriptores Optici, David Gregory's Elements of Catoptrics and Diop trics, Oxford, 1695.-Newton's Optics, London, 1701. -Newton's Lectiones Optica, 1728.-Smith's Optics, 2 vols. 4to., Cambridge, 1738.-Martin's New and Compendious System of Optics, London. - Le Caille's Lectiones Optica, Vienna, 1757.-Harris's Optics, 4to., London, 1775.-Priestley's History of Vision, Light, and Colour, 2 vols. 4to., London, 1772. -Emerson's Elements of Optics, London, 1768.-En ler's Dioptrics, 3 vols. 4to., Petersburg, 1769, 1770, 1771.-Hauy's Treatise on Natural Philosophy, translated by Dr Olinthus Gregory, 2 vols., London, 1807. -Wood's Elements of Optics, Cambridge, 1811.Biot's Traité de Physique, tom. iii. and iv.-Robison's Works, vol. iii., Edinburgh, 1823. The article Telescope in this volume is very excellent.-Euler's Letters to a German Princess, 2 vols., Edinburgh, 1823. Dr. Brewster's edition. This work contains a very full treatise on Optics, in which the various branches are illustrated in a most popular manner.-Ferguson's Lectures on Select Subjects in Mechanics, Optics, &c. 2 vols. 4to., Edinburgh, 1823. Dr. Brewster's edition, This work contains a very popular treatise on Optics. -Coddington's Elementary Treatise on Optics, Cambridge, 1823.-Optics, in Dr. Brewster's Encyclopæ dia, vol. xv. This article contains a very copious treatise on the various branches of Optics, historical, theoretical, physical, and practical, with minute re

ferences to all the works and memoirs.-Dr. Thomas Young's Elements of Natural Philosophy, 2 vols. 4to. This work is one of our most valuable books of reference.

Achromatic Telescope.-Boscovich's Opera Pertinentia ad Opticam et Achronomiam, 5 vols., Bassano, 1785.-Achromatic Telescope, in Dr. Brewster's Encyclopædia, vol. i.-Biot's Traité de Physique, vol. iii.-Dr. Blair, on the Inequal Refrangibility of Light, in the Edinburgh Transactions, vol. iii. p. 1.Dr. Brewster's Treatise on New Philosophical Instruments, Edinburgh, 1813.-Clairant, Mém. Acad. Par. 1756, 1757, and 1761.-D'Alembert, Opuscules Mathématiques, 3rd, 4th, 5th, 6th, and 7th vols., and Mém. Acad. Par. 1761.-Mr. J. F. W. Herschel, Phil. Trans., 1821.-Fraunhofer, in the Memoirs of the Bavarian Academy, 1814, 1815.-Professor Barlow, on his New Achromatic Telescope, in the Edinburgh Journal of Science, No. 15, 1828.

Physical Optics.-Grimaldi, Physico-Mathesis de Lumine, Bologna, 1665.-Dutour, Mém. Sav. Etrang. vols. iv., v., vi., and Rozier's Journal, vols. i.,ii., v., vi., vii.-Comparetti, de Luce Inflexa, Padua, 1787. -Mr. Brougham, Phil. Trans. 1796, 1797.-Mr. Jordan's Observations on Light and Colours, London, 1797.-Dr. Thomas Young, Phil. Trans. 1800, 1803, 1808 and Sup. Encyclopædia Brit., Art. Chromatics. -Dr. Young, on Medical Literature, London, 1813.MM. Biot and Pouillet in Biot's Traité de Physique, tom.iv. App.-M. Fraunhofer's Neue Modifikation des Lichtes.-M. Fresnel, Ann.de Chimie et de Physique. Photometry-Bouguer's Traité d'Optique.-Lambert's Photometria, Augsburg, 1760.-Prof. Leslie, on Heat, London, 1804.-Mr. W. Ritchie, Phil, Trans. 1825.