In order to find the angle subtended by any number of degrees we have only to multiply the constant part of the formula corresponding to that number in the table by A B, or the angle subtended by the whole field. Thus, if A B is 30', the angle subtended by 1o of the scale will be 30′ × 0087 = 154", and the angle subtended by 40o will be 30′ × 342 = 10′15′′.6; and by making the calculation it will be found that, as the angle to be measured increases, the accuracy of the scale also increases; for, when the arch is only 1o or 2o, a variation of 1o produces a variation of about 16" in the angle; whereas, when the arch is between 170° and 180°, the variation of a degree does not produce a change of much more than 1" in the angle.

The single-lens micrometer, contrived by Dr. Wollaston, must now be adverted to. Having had occasion to measure some very small wires, with a greater degree of accuracy than he was enabled to do by any instrument hitherto made use of for such purposes, he was led to contrive other means that might more effectually answer the end proposed. The instrument to which Dr. Wollaston had recourse is furnished with a sin

gle lens of about one-twelfth of an inch focal length. The aperture of such a lens is necessarily small; so that, when it is mounted in a plate of brass, a small perforation can be made by the side of it in the brass as near to its centre as one-twenty-fifth of an inch. When a lens thus mounted is placed before the eye, for the purpose of examining any small object, the pupil is of sufficient magnitude for seeing distant objects at the same time through the adjacent perforation; so that the apparent dimensions of the magnified image might be compared with a scale of inches, feet, or yards, according to the distance at which it might be convenient to place it. A scale of smaller dimensions attached to the instrument will, however, be found preferable on account of the steadiness with which the comparson may be made; and it may be seen with sufficient distinctness by the naked eye, without any effort of nice adaptation, by reason of the smallness of the hole through which it is viewed. The construction that Dr. Wollaston chose for the scale is represented in fig. 9. It is composed of smal wires, about one-fiftieth of an inch in diameter, placed side by side, so as to form a scale of

The sphere, or lens, a, fig. 12, is formed of rock crystal, and placed in half holes, from which is extended the axis bb, with an index attached; which index registers the motion of the sphere, the extent of that motion being shown upon the divided face C, fig. 13. The sphere is so placed in the half holes that, when its natural axis is parallel to the axis of the telescope, only one image mage of the object is seen. In the other direction, or that which is at right angles to the axis of motion, it must be so placed that when it is moved the separation of the images, viz. the ordinary and extraordinary, may be parallel to that motion. The method of acquiring this adjustment is, by turning the sphere in the half holes parallel to its own axis.

The field of view of the eye-tube is increased, and the magnifying power varied, by the introduction of the lens d, fig. 12, between the sphere and the primary image of the object-glass; and its distance from the sphere will be in proportion to the magnifying power required; the magnifying powers are engraved upon the eye-tube at e, and will vary in proportion to the focal length of the object-glass to which the eye-tube is applied. Those marked in the figure are for an object-glass of forty-four inches in focal length. The object of Mr. Babbage's new zenith micrometer is to supersede the necessity of extreme accuracy in the divisions. The principle on which this instrument depends may be readily comprehended by imagining a parallelogram, admitting of free motion about its four angles, to be placed with two of its sides in a horizontal position, and the whole in a vertical plane, and a telescope to be fixed at right angles to the lower horizontal bar of this parallelogram. Here every motion of one of the perpendicular bars of the instrument round its upper joint will not change the angle which the telescope makes with the meridian; but will merely remove it into a new position in which it will point to the same object in the heavens. But, if either of the horizontal bars of the instrument be lengthened by a very small quantity, this parallelism of the telescope will no longer be preserved; but any movement of the upright bars round their axes will not only remove the telescope from its position, but will cause it to form a very small angle with its former direction. The magnitude of that angle will depend on the alteration in the length of the arm of the parallelogram, and also on the angle which that arm makes with its first direction. The arc which is actually measured in the heavens, by means of this instrument, is determined by a formula in which the sum of three arcs is taken from the semicircumference, one of them resulting from the actual observation; the other two from a cosine and a tangent, ascertainable by computation from the theorem itself. In an extensive use of this micrometer tables may easily be formed to facilitate the computa

It may now be advisable to examine the fibres proper for micrometers, and on the method of adjusting them to the eye-piece.

In the micrometer constructed by Huygens, the object whose angle was required was comprehended between the edges of two plates of brass. Silver wires, and sometimes hairs, were afterwards substituted instead of the plates, and continued in use till about the end of the last century. The finest silver wire ever made was drawn in France to the thickness of Ts of an inch. The plates used for this purpose, and the secret of making them, are said to have been lost amid the convulsions of the revolution. The smallest wire which is made in this country does not exceed th of an inch.

The impossibility of obtaining wire of a diameter sufficiently minute for micrometers induced Felix Fontana, in 1775, to recommend the spider's web as an excellent substitute for silver wire. This suggestion of Fontana, however, did not excite much notice, till the use of the spider's web was introduced by the late celebrated Mr. Troughton, who found this fibre to be so fine, opaque, and elastic, as to answer all the objects of practical astronomy. We are informed, however, by this distinguished artist, that it is only the stretcher, or the long line which supports the web, that possesses these valuable properties. The other parts of the web, though equally fine and elastic, are very transparent, and therefore completely unfit for micrometrical purposes. The difficulty of procuring the proper part of the spider's web has compelled many opticians and practical astronomers to employ the raw fibre of unwrought silk, or, what is much worse, the coarse silver wire which is manufactured in this country. But, whatever be the comparative advantages of these different substances, they are all liable to the error arising from the inflexion of light, which renders it impossible to ascertain the exact contact between the fibre and the luminous body. This disadvantage has been experienced by every astronomical observer, and has always been considered as inseparable from the wire micrometer. After numerous trials, Dr. Brewster succeeded in obtaining a delicate fibre, which appears to remove the error of inflexion while it possesses the requisite properties of opacity and elasticity. This fibre is glass, which is so exceedingly delicate that it can be drawn to any degree of fineness, and can always be procured and prepared with facility; a circumstance of no small importance to the practical astronomer, who is frequently obliged to send his micrometers to a great distance when they require to be repaired.

When the vitreous fibre is formed, and stretched across the diaphragm of the eye-piece of a telescope, it will appear perfectly opaque, with a delicate line of light extending along its axis. This central transparency arises from the refraction of the light which falls upon the edges of the cylindrical fibre, and therefore the diameter of the luminous streak must vary with that of the fibre itself. In a micrometer which Dr. Brewster fitted up in this way the glass fibres are about the 1200th part of an inch in diameter, and the fringe of light which stretches across their axis, is distinctly visible, though it does not exceed in diameter the 30th part of an inch. In using these fibres for measuring the angle subtended by two luminous points, whether they be two stars, or the opposite extremities of a luminous disc, we may, as has hitherto been done, separate the fibres till the luminous points are in contact with their interior surfaces; but, in order to avoid the error arising from inflexion, Dr. B. proposes that the separation should be continued till the rays of light issuing from the luminous points dart through the transparent axes of the fibres. The rays, thus transmitted, suffer no inflexion in passing through the fibre to the eye; and, besides this advantage, we have the benefit of a delicate line, about one-third of the diameter of the fibre itself.

On some occasions Dr. Brewster employed threads of melted sealing-wax, which may be made extremely fine, though not of such a regular diameter as silver wire, or the fibres of glass. It is a very singular fact, that one of these fibres of wax was exposed, without injury, to the heat of the sun, concentrated in the focus of an object-glass, with an aperture of 2.3 inches, and twenty-nine inches in focal length.

These fibres are placed in delicate parallel grooves formed upon the diaphragm of the first eye-glass, and may be fixed in their places for temporary purposes by a thin layer of bees-wax; but, when they are required to be kept at an invariable distance, it is safer to pinch them to the diaphragm by a small screw-nail near the extremity of each wire.

The diaphragm should be constructed so as to move along the axis of the eye-piece, in order that the fibres may be placed exactly in the anterior focus of the first eye-glass; and, before any observation is made, the eye of the observer ought to be fixed for a short time upon the fibres alone, till it is accommodated to that distance; and, while it is thus fixed, distinct vision should be produced by the motion of the eye-tube. By attending to this suggestion, which is of great practical importance, the rays that diverge from the fibres, and those that diverge from the distinct image, will unite on the same points of the retina. From the great facility which the eye possesses of adjusting itself to different distances, the adaptation of that organ, to the fibres and to the image, could not have been effected by looking at the image alone, while distinct vision was produced by the motion of the eye piece; for, as the eye has not any permanent focus like a lens, the image might appear distinct before the pencils of rays had actually converged to a point; and, when this does happen, the rays proceeding from the fibres cannot unite with those proceeding from the image on the same points of the retina.

When the micrometer is employed in terrestrial observations the end of the eye-tube, into which the observer looks, should be furnished with an aperture smaller than that which is used for common purposes, and this small aperture should be used when the sun shines, or when the light of the day is very great. If the fibres happen to be small, they will either cease to become visible in very strong light, or will appear to have a kind of vibratory motion which injures

VOL. XIV.

the eye of the observer, and prevents him from making the observation. Hence it becomes necessary to diminish the light by means of a small aperture.

1

Professor Wallace, of the Royal Military College, has suggested the employment of asbestos fibres in lieu of the fine wire or spider's web; and a filament about 3080 of an inch in diameter, having been applied to a telescope, was found to answer very perfectly the purpose for which it was intended.

The inventive genius of Dr. Wollaston has, however, far outstripped those who preceded him in the production of a micrometer fibre. The contrivance by which it is effected, is so ingenious, and promises to be productive of such valuable results, that it may be advisable to notice the account of the process employed by this philosopher:

The extremity of a platinum wire having been fused into a globule nearly one-fourth of an inch in diameter, was next hammered out into a square rod, and then drawn again into a wire

of an inch in diameter. One inch of this wire duly coated with silver, was drawn till its length was extended to 182 inches; consequently the proportional diminution of the diameter of the platina will be expressed by the square root of 182, so that its measure had become

1

3425

1

253 x 13.5

The specific gravity of the coated wire was assumed to be 10.5; and since the weight of 100 inches was 114 grains, its diameter was inferred to be th of an inch, or just eighty times that of the platina contained in it.

1

MICROPUS, bastard cudweed, a genus of the polygamia necessaria order, and, syngenesia class of plants; natural order forty-ninth, compositæ; receptacle paleaceous: CAL. calyculated; there is no radius of the corolla. The female florets are wrapped in the scales of the calyx. There are two species; viz.

1. M. erectus, and

2. M. supinus. The latter only is cultivated in gardens. It is an annual plant, growing naturally in Portugal, in places near the sea. The root sends out several trailing stalks, about six or eight inches long, which are garnished with small, oval, silvery leaves, whose bases embrace the stalks. The flowers come out in clusters from the wings of the stalks, and are very small, and of a white color. It flowers in June and

July; and is frequently preserved in gardens on account of its silvery leaves. It is easily propagated by seed sown in autumn, and requires no other culture but to be kept free from weeds.

MICROSCOPE. - This instrument has tended most materially to enlarge the boundaries of our knowledge in almost every branch of natural history. Its invention is attributed by the celebrated Dutch mathematician, Huygens, to a countryman of his, named Drebell (for it must be observed that it was entirely lost in the middle ages). He constructed them about the year 1621, or thirty-one years after the invention of the telescope.

According to Borelli, the microscope was invented by Jansen, the reputed contriver of the

2 K

telescope, who presented some instruments of his first construction to prince Maurice, and Albert archduke of Austria. These instruments were six feet in length, and consisted of a tube of gilt copper, one inch in diameter, supported by thin brass pillars, in the shape of dolphins, on a base of ebony which was adapted to hold the objects to be examined. Of the internal construction of this microscope we have no precise account; though there is reason to think that it was nothing more than a telescope converted into a compound microscope.

The construction both of single and compound microscopes has, within the last fifty years, been brought to a degree of perfection; and for all the purposes of amusement, and general observation, these instruments may be considered as sufficiently perfect. But when we employ the microscope as an instrument of discovery, to examine those phenomena of the natural world which are beyond the reach of unassisted vision, and when we use it in ascertaining the anatomical and physiological structure of plants, insects, and animalcula, we soon find that a limit, apparently insuperable, is set to the progress of discovery, and that it is only some of the ruder and more palpable functions of these evanescent animals that we are able to bring under observa tion. Naturalists, indeed, are less acquainted with the organisation of the microscopic world, and the beings by which it is peopled, than astronomers are with those remote systems of the universe which appear in the form of nebulæ and double stars. It was the improvement of the telescope alone which enabled Dr. Herschel to fix the views of astronomers upon those regions of space, to which, at a former period, their imaginations could scarcely extend; and, when the microscope shall have received a similar improvement, we may look for discoveries equally interesting, though less stupendous, even in those portions of space which are daily trampled under the foot of man.

It is both important and interesting to enquire into the cause of this limitation of microscopical discovery. The construction of single lenses, for the simplest form of the instrument, has been brought to great perfection. Dr. Brewster has in his possession glasses, executed by Mr. Shuttleworth, of the focal length of one-thirtieth, one-fortieth, and one-fiftieth of an inch, which are ground with great accuracy; and the performance of single lenses has been recently improved by Dr. Wollaston, who separates two hemispherical segments by means of a small plate of brass perforated in the centre. We cannot, therefore, expect any essential improvement in the single microscope, unless from the discovery of some transparent substance, which, like the diamond, combines a high refractive power with a low power of dispersion.

It is usual to say that the microscope magnifies objects seen through it; but this is true only with regard to the apparent, not the real magnitude of objects; they indeed appear to be larger with, than without the microscope, but in truth they are not; and the reason why they appear to be magnified will be easy to apprehend, by any person who understands the nature of the optic

angle. The apparent magnitude of objects is measured by the angle which they are seen under by the eye; and those angles are reciprocally as the distances from the eye. If, therefore, at the distance of six inches, we can but just discern an object, and then, by interposing a lens, or other body, we can view that very object at a nearer distance, the object will appear to be as much larger through the lens than before, to the naked eye, as its distance from the lens is less than its distance from the eye.

That this is the case, is evident from fig. 1, plate MICROSCOPE, where A is a point in an object not clearly visible to the naked eye, at a less distance than AB, because the rays which proceed from it are too divergent to admit of distinct vision till they have passed that distance; but if the same object be placed in the focus C of the lens D, fig. 2, the rays which proceed. from it will become parallel, by passing through the said lens, and therefore the object is distinctly visible to the eye E, placed any where before the lens D. Consequently it will appear as much larger through the lens than to the naked eye, as CD is less than A В.

If an object, AB, fig. 3, be placed in one focus C, of a lens DE, and the eye in the other focus F, the eye will see just so much of the object as is equal to the diameter of the lens; for the rays AD and BE, which go from the object to the extremities of the lens D and E, and are united at the focus F, must necessarily proceed from the object to the lens parallel to the axis FC, and therefore parallel to each other; consequently the part of the object A B, seen by the rays DF, EF, will be equal to the diameter DE of the said lens.

If only the part de of the lens be open, then only so much of the object ab as is equal thereto will be perceived by the eye. Now, since AB is equal to DE, or ab to de, therefore the angle DFE, ordFe, is the optic angle under which the part of the object A B, or a b, appears to the eye at F; and, since GF is but one-half FC, therefore the angle DFE, or dFe, is double to that under which the part AB, or a b, would appear to the naked eye at the distance FC; that is, the eye sees the object, situate as above, twice as large with the lens as it would do without it.

If you would see a portion of an object larger than the lens, your eye must be placed nearer the lens than its focus. Let the lens be DE, fig. 4, its two foci F and C; in the focus C, let there be an object, A B, larger than the lens; suppose the rays AD, BE, proceed from the extremities of the object to those of the lens; it is evident from the figure they will be convergent, and therefore will, by the lens, be united in a point K, between the lens DE and its focus F: if then the eye be placed at K, it will take into its view an object greater than the lens DE.

Again, let GH be a portion of an object, A B, less than the lens DE; draw GD, HE, which will be diverging rays, and therefore will be united at a point I, farther distant from the lens than the focus F; hence, if an eye be placed farther from the lens than its focal distance, it can never see any object, or part of an object, at one view, so large as the lens, but always smaller.