, is an instrument usually fitted to a telescope, in the focus of the object-glass, for measuring small angles or distances; as the apparent diameters of the planets, &c.

There are several sorts of these instruments, upon different principles; the origin of which has been disputed. The general principle is, that the instrument moves a sine wire parallel to itself, in the plane of the picture of an object, formed in the focus of a telescope, and so with great exactness to measure its perpendicular distance from a fixed wire in the same plane: and thus are measured small angles, subtended by remote objects at the naked eye.

For example, Let a planet be viewed through the telescope; and when the parallel wires are opened to such a distance as to appear exactly to touch two opposite points in the circumference of the planet, it is evident that the perpendicular distance between the wires is then equal to the diameter of the picture of the planet, formed in the focus of the object-glass. Let this distance, whose measure is given by the mechanism of the micrometer, be represented by the line pq; then, since the measure of the focal distance qL may be also known, the ratio of qL to qp, that is, of radius to the tangent of the angle qLp, will give the angle itself, by a table of sines and tangents; and this angle is equal to the opposite angle PLQ, which the real diameter of the planet subtends at L, or at the naked eye.

With respect to the invention of the Micrometer; Mess. Azout and Picard have the credit of it in common fame, as being the first who published it, in the year 1666; but Mr. Townley, in the Philos. Trans. reclaims it for one of our own countrymen, Mr. Gascoigne. He relates that, from some scattered papers and letters of this gentleman, he had learnt that before our civil wars he had invented a Micrometer, of as much effect as that since made by M. Azout, and had made use of it for some years, not only in taking the diameters of the planets, and distances upon land, but in determining other matters of nice importance in the heavens; as the moon's distance, &c. Mr. Gascoigne's instrument also fell into the hands of Mr. Townley, who says farther, that by the help of it he could make above 40,000 divisions in a foot. This instrument being shewn to Dr. Hook, he gave a drawing and description of it, and proposed several improvements in it; which may be seen in the Philos. Trans. vol. 1, pa. 63, and Abr. vol. 1, pa. 217. Mr. Gascoigne divided the image of an object, in the focus of the object-glass, by the approach of| two pieces of metal, ground to a very fine edge; instead of which, Dr. Hook would substitute two fine hairs, stretched parallel to each other: and two other methods of Dr. Hook, different from this, are described in his posthumous works, pa. 497 &c. An account of several curious observations which Mr. Gascoigne made by the help of his Micrometer, particularly in measuring the diameter of the moon and other planets, may be seen in the Philos. Trans. vol. 48, pa. 190; where Dr. Bevis refers to an original letter of Mr. Gascoigne, to Mr. Oughtred, written in 1641, for an account given by the author of his own invention, &c.

Mons. De la Hire, in a discourse on the æra of the inventions of the Micrometer, pendulum clock, and telescope, read before the Royal Academy of Sciences in 1717, makes M. Huygens the inventor of the Micrometer. That author, he observes, in his Observations on Saturn's Ring, &c, published in 1659, gives a method of finding the diameters of the planets by means of a telescope, viz, by putting an object, which he calls a virgula, of a size proper to take in the distance to be measured, in the focus of the convex object-glass: in this case, says he, the smallest object will be seen very distinctly in that place of the glass. By such means, he adds, he measured the diameter of the planets, as he there delivers them. See Huygens's System of Saturn.

This Micrometer, M. De la Hire observes, is so very little different from that published by the marquis De Malvasia, in his Ephemerides, three years after, that they ought to be esteemed the same: and the Micrometer of the marquis differed yet less from that published four years after his, by Azout and Picard. Hence, De la Hire concludes, that it is to Huygens the world is indebted for the invention of the Micrometer; without taking any notice of the claim of our countryman Gascoigne, which however is many years prior to any of them.

De la Hire says, that there is no method more simple or commodious for observing the digits of an eclipse, than a net in the focus of the telescope. These, he says, were usually made of silken threads; and for this particular purpose six concentric circles had also been used, drawn upon oiled paper; but he advises to draw the circles on very thin pieces of glass, with the point of a diamond. He also gives some particular directions to assist persons in using them. In another memoir, he shews a method of making use of the same net for all eclipses, by using a telescope with two object-glasses, and placing them at different distances from each other. Mem. 1701 and 1717.

M. Cassini invented a very ingenious method of ascertaining the right ascensions and declinations of stars, by fixing four cross hairs in the focus of the telescope, and turning it about its axis, so as to make them move in a line parallel to one of them. But the later improved Micrometers will answer this purpose with greater exactness. Dr. Maskelyne has published directions for the use of it, extracted from Dr. Bradley's papers, in the Philos. Trans. vol. 62. See also Smith's Optics, vol. 2, pa. 343.

Wolfius describes a Micrometer of a very easy and simple structure, first contrived by Kirchius.

Dr. Derham tells us, that his Micrometer is not put into a tube, as is usual, but is contrived to measure the spectres of the sun on paper, of any radius, or to measure any part of them. By this means he can easily, and very exactly, with the help os a fine thread, take the declination of a solar spot at any time of the day; and, by his half-seconds watch, measure the distance of the spot from either limb of the sun.

J. And. Segner proposed to enlarge the field of view in these Micrometers, by making them of a considerable extent, and having a moveable eye-glass, or several eye-glasses, placed opposite to different parts of it. He thought however, that two would be quite sufficient, and he gives particular directions how to make use of such Micrometers in astronomical observations. See Comm. Gotting. vol. 1, pa. 27.

A considerable improvement in the Micrometer was communicated to the Royal Society, in 1743, by Mr. S. Savary; an account of which, extracted from the minutes by Mr. Short, was published in the Philos. Trans. for 1753. The first hint of such a Micrometer was suggested by M. Roemer, in 1675: and M. Bouguer proposed a construction similar to that of M. Savary, in 1748; for which see Heliometer. The late Mr. Dollond made a farther improvement in this kind of Micrometer, an account of which was given to the Royal Society by Mr. Short, and published in the Philos. Trans. vol. 48. Instead of two object-glasses, he used only one, which he neatly cut into two semicircles, and fitted each semicircle in a metal frame, so that their diameters sliding in one another, by means of a screw, may have their centres so brought together as to appear like one glass, and so form one image; or by their centres receding, may form two images of the same object: it being a property of such glasses, for any segment to exhibit a perfect image of an object, although not so bright as the whole glass would give it. If proper scales are fitted to this instrument, shewing how far the centres recede, relative to the focal length of the glass, they will also shew how far the two parts of the same object are asunder, relative to its distance from the object-glass; and consequently give the angle under which the distance of the parts of that object are seen. This divided object-glass Micrometer, which was applied by the late Mr. Dollond to the object end of a reflecting telescope, and has been with equal advantage adapted by his son to the end of an achromatic telescope, is of so easy use, and affords so large a scale, that it is generally looked upon by astronomers as the most convenient and exact instrument for measuring small distances in the heavens. However, the common Micrometer is peculiarly adapted for measuring differences of right ascension, and declination, of celestial objects, but less convenient and exact for measuring their absolute distances; whereas the object-glass Micrometer is peculiarly fitted for measuring distances, though generally supposed improper for the former purpose. But Dr. Maskelyne has found that this may be applied with very little trouble to that purpose also; and he has furnished the directions necessary to be followed when it is used in this manner. The addition requisite for this purpose, is a cell, containing two wires, intersecting each other at right angles, placed in the focus of the eye-glass of the telescope, and moveable round about, by the turning of a button. For the description of this apparatus, with the method of applying and using| it, see Dr. Maskelyne's paper on the subject, in the Philos. Trans. vol. 61, pa. 536 &c.

After all, the use of the object-glass Micrometer is attended with difficulties, arising from the alterations in the focus of the eye, which are apt to cause it to give different measures of the same angle at different times. To obviate these difficulties, Dr. Maskelyne, in 1776, contrived a prismatic Micrometer, or a Micrometer consisting of two achromatic prisms, or wedges, applied between the object-glass and eye-glass of an achromatic telescope, by moving of which wedges nearer to or farther from the object-glass, the two images of an object produced by them appeared to approach to, or recede from, each other, so that the focal length of the object-glass becomes a scale for measuring the angular distance of the two images. The rationale and use of this Micrometer are explained in the Philos. Trans. vol. 67, pa. 799, &c. And a similar invention by the abbé Rochon, and improved by the abbé Boscovich, was also communicated to the Royal Society, and published in the same volume of the Transactions, pa. 789 &c.

Mr. Ramsden has lately described two new Micrometers, which he has contrived for remedying the defects of the object-glass Micrometer. One of these is a catoptric Micrometer, which, besides the advantage it derives from the principle of reflection, of not being disturbed by the heterogeneity of light, avoids every defect of other Micrometers, and can have no aberration, nor any defect arising from the imperfection of materials, or of execution; as the great simplicity of its construction requires no additional mirrors or glasses, to those required for the telescope; and the separation of the image being effected by the inclination of the two specula, and not depending on the focus of lens or mirror, any alteration in the eye of an observer cannot affect the angle measured. It has peculiar to itself the advantages of an adjustment, to make the images coincide in a direction perpendicular to that of their motion; and also of measuring the diameter of a planet on both sides of the zero; which will appear no inconsiderable advantage to observers who know how much easier it is to ascertain the contact of the external edges of two images than their perfect coincidence.

The other Micrometer invented and described by Mr. Ramsden, is suited to the principle of refraction. This Micrometer is applied to the erect eye-tube of a refracting telescope, and is placed in the conjugate focus of the first eye-glass, as the image is considerably magnified before it comes to the Micrometer, any imperfection in its glass will be magnified only by the remaining eye-glasses, which in any telescope seldom exceeds 5 or 6 times; and besides, the size of the Micrometer glass will not be the 100th part of the area which would be required, if it were placed at the objectglass; and yet the same extent of scale is preserved, and the images are uniformly bright in every part of the field of the telescope. See the description and construction of these two Micrometers in the Philos. Trans. vol. 69, part 2, art. 27.

In vol. 72 of the Philos. Trans. for the year 1782, Dr. Herschel, after explaining the defects and imperfections of the parallel-wire Micrometer, especially for measuring the apparent diameter of stars, and the distances between double and multiple stars, describes one, for these purposes, which he calls a lamp Micrometer; one that is free from such defects, and has the advantage of a very enlarged scale. In speaking of the application of this instrument, he says, “It is well known to opticians and others, who have been in the habit of using optical instruments, that we can with one eye look into a microscope or telescope, and see an object much magnified, while the naked eye may see a scale upon which the magnified picture is thrown. In this manner I have generally determined the power of my telescopes; and any one who has acquired a facility of taking such observations, will very seldom mistake so much as one in 50 in determining the power of an instrument, and that degree of exactness is fully sussicient for the purpose.

“The Newtonian form is admirably adapted to the use of this Micrometer; for the observer stands always erect, and looks in a horizontal direction, notwithstanding the telescope should be elevated to the zenith. —The seale of the Mierometer at the convenient distance of 10 feet from the eye, with the power of 460, is above a quarter of an inch to a second; and by putting on my power of 932, I obtain a scale of more than half an inch to a second, without increasing the distance of the Micrometer; whereas the most perfect of my former Micrometers, with the same instrument, had a scale of less than the 2000th part of an inch to a second.

“The measures of this Micrometer are not confined to double stars only, but may be applied to any other objects that require the utmost accuracy, such as the diameters of the planets or their satellites, the mountains of the moon, the diameters of the fixed stars, &c.”

The Micrometer has not only been applied to telescopes, and employed for astronomical purposes; but there have been various contrivances for adapting it to microscopical observations. Mr. Leeuwenhoek's method of estimating the size of small objects, was by comparing them with grains of sand, of which 100 in a line took up an inch. These grains he laid upon the same plate with his objects, and viewed them at the same time. Dr. Jurin's method was similar to this; for he found the diameter of a piece of fine silver wire, by wrapping it very close upon a pin, and observing how many rings made an inch: and he used this wire in the same manner as Leeuwenhoek used his sand. Dr. Hook used to look upon the magnified object with one eye, while at the same time he viewed other objects, placed at the same distance, with the other eye. In this manner he was able, by the help of a ruler, divided into inches and small parts, and laid on the pedestal of the microscope, as it were to cast the magnified appearance of the object upon the ruler, and thus exactly to measure the diameter which it appeared to have through the glass; which being compared with the diameter as it appeared to the naked eye, easily shewed the degree in which it was magnified. A little practice, says Mr. Baker, will render this method exceedingly easy and pleasant.

Mr. Martin, in his Optics, recommends such a Micrometer for a microscope as had been applied to telescopes; for he advises to draw a number of parallel lines on a piece of glass, with the fine point of a diamond, at the distance of one 40th of an inch from one another, and to place it in the focus of the eye-glass. | By this method, Dr. Smith contrived to take the exact draught of objects viewed by a double microscope; for he advises to get a lattice, made with small silver wires or squares, drawn upon a plain glass by the strokes of a diamond, and to put it into the place of the image formed by the object-glass. Then, by transferring the parts of the object, seen in the squares of the glass or lattice, upon similar corresponding squares drawn on paper, the picture may be exactly taken. Mr. Martin also introduced into compound microscopes another Micrometer, consisting of a screw. See both these methods described in his Optics, pa. 277.

A very accurate division of a scale is performed by Mr. Coventry, of Southwark. The Micrometers of his construction are parallel lines drawn on glass, ivory, or metal, from the 10th to the 10,000th part of an inch. These may be applied to microscopes, for measuring the size of minute objects, and the magnifying power of the glasses; and to telescopes, for measuring the size and distance of objects, and the magnifying power of the instrument. To measure the size of an object in a single microscope; lay it on a Micrometer, whose lines are seen magnified in the same proportion with it, and they give at one view the real size of the object. For measuring the magnifying power of the compound microscope, the best and readiest method is the following: On the stage in the focus of the objectglass, lay a Micrometer, consisting of an inch divided into 100 equal parts; count how many divisions of the Micrometer are taken into the field of view; then lay a two-foot rule parallel to the Micrometer: fix one eye on the edge of the field of light, and the other eye on the end of the rule, which move, till the edge of the field of light and the end of the rule correspond; then the distance from the end of the rule to the middle of the stage, will be half the diameter of the field: ex. gr. If the distance be 10 inches, the whole diameter will be 20, and the number of the divisions of the Micrometer contained in the diameter of the field, is the magnifying power of the microscope. For measuring the height and distance of objects by a Micrometer in the telescope, see Telescope.

Mr. Adams has applied a Micrometer, that instantly shews the magnifying power of any telescope.

In the Philos. Trans. for 1791, a very simple scale Micrometer for measuring small angles with the telescope is described by Mr. Cavallo. This Micrometer consists of a thin and narrow slip of mother-of-pearl finely divided, and placed in the focus of the eye-glass of a telescope, just where the image of the object is formed; whether the telescope is a reflector or a refractor, provided the eye-glass be a convex lens. This substance Mr. Cavallo, after many trials, found much more convenient than either glass, ivory, horn, or wood, as it is a very steady substance, the divisions very easy marked upon it, and when made as thin as common writing paper it has a very useful degree of transparency.

Upon this subject, see M. Azout's Tract on it, contained in Divers Ouvrages de Mathematique & de Phisique; par Messieurs de l'Academie Royal des Sciences; M. de la Hire's Astronomicæ Tabulæ; Mr. Townley, in the Philos. Trans. n°. 21; Wolfius, in his Elem. Astron. § 508; Dr. Hook, and many others, in the Philos. Trans. n°. 29 &c; Hevelius, in the Acta Eruditorum, ann. 1708; Mr. Balsbaser, in his Micrometria; also several volumes of the Paris Memoirs, &c.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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