The invention of the telescope at once extended the possibilities of accuracy in astronomical measurements. The planets were shown to have visible disks, and to be attended by satellites whose distance and position angle relative to the planet it was desirable to measure. It became, in fact, essential to invent a “micrometer” for measuring the small angles which were thus for the first time rendered sensible. There is now no doubt that William Gascoigne, a young gentleman of Yorkshire, was the first inventor of the micrometer. Crabtree, a friend of his, taking a journey to Yorkshire in 1639 to see Gascoigne, writes thus to his friend Horrocks. “The first thing Mr Gascoigne showed me was a large telescope amplified and adorned with inventions of his own, whereby he can take the diameters of the sun and moon, or any small angle in the heavens or upon the earth, most exactly through the glass, to a second.” The micrometer so mentioned fell into the possession of Mr Richard Townley of Lancashire, who exhibited it at the meeting of the Royal Society held on the 25th July 1667.

The principle of Gascoigne’s micrometer is that two pointers, having parallel edges at right angles to the measuring screw, are moved in opposite directions symmetrically with and at right angles to the axis of the telescope. The micrometer is at zero when the two edges are brought exactly together. The edges are then separated till they are tangent to the opposite limbs of the disk of the planet to be measured, or till they respectively bisect two stars, the angle between which is to be determined. The symmetrical separation of the edges is produced and measured by a single screw; the fractions of a revolution of the screw are obtained by an index attached to one end of the screw, reading on a dial divided into 100 equal parts. The whole arrangement is elegant and ingenious. A steel cylinder (about the thickness of a goose-quill), which forms the micrometer screw, has two threads cut upon it, one-half being cut with a thread double the pitch of the other. This screw is mounted on an oblong box which carries one of the measuring edges; the other edge is moved by the coarser part of the screw relatively to the edge attached to the box, whilst the box itself is moved relatively to the axis of the telescope by the finer screw. This produces an opening and closing of the edges symmetrically with respect to the telescope axis. Flamsteed, in the first volume of the Historia Coelestis, has inserted a series of measurements made by Gascoigne extending from 1638 to 1643. These include the mutual distances of some of the stars in the Pleiades, a few observations of the apparent diameter of the sun, others of the distance of the moon from neighbouring stars, and a great number of measurements of the diameter of the moon. Dr Bevis (Phil. Trans., 1773, p. 190) also gives results of measurements by Gascoigne of the diameters of the moon, Jupiter, Mars, and Venus with his micrometer.

Delambre gives 3 the following comparison between the results of Gascoigne’s measurements of the sun’s semi-diameter and the computed results from modern determinations :— [table]

Gascoigne, from his observations, deduces the greatest variation of the apparent diameter of the sun to be 35”; according to the Connaissance des Temps it amounts to 32" - 3. These results prove the enormous advance attained in accuracy by Gascoigne, and his indisputable title to the credit of inventing the micrometer.

Huygens, in his Systema Saturnium (1659), describes a micrometer with which he determined the apparent diameters of the principal planets. He inserted a slip of metal, of variable breadth, at the focus of the telescope, and observed at what part it exactly covered the object under examination; knowing the focal length of the telescope and the width of the slip at the point observed, he thence deduced the apparent angular breadth of the object. The Marquis Malvasia in his Ephemerides (Bologna, 1662) describes a micrometer of his own invention. At the focus of his telescope he placed fine silver wires at right angles to each other, which, by their intersection, formed a network of small squares. The mutual distances of the intersecting wires he determined by counting, with the aid of a pendulum clock, the number of seconds required by an equatorial star to pass from web to web, while the telescope was adjusted so that the star ran parallel to the wires at right angles to those under investigation. In the Phil. Trans., 1667, No. 21, p. 373, Auzout gives the results of some measures of the diameter of the sun and moon made by himself, and this communication led to the letters of Mr Townley and Dr Bevis above referred to. The micrometer of Auzout and Picard was provided with silk fibres or silver wires instead of the edges of Gascoigne, but one of the silk fibres remained fixed while the other was moved by a screw. It is beyond doubt that Huygens independently discovered that an object placed in the common focus of the two lenses of a Kepler telescope appears as distinct and well-defined as the image of a distant body; and the micrometers of Malvasia, Auzout, and Picard are the natural developments of this discovery. Gascoigne was killed at the battle of Marston Moor on the 2d July 1644, in the twenty-fourth year of his age, and his untimely death was doubtless the cause that delayed the publication of a discovery which anticipated, by twenty years, the combined work of Huygens, Malvaison, Auzout, and Picard in the same direction.

As the powers of the telescope were gradually developed, it was found that the finest hairs or filaments of silk, or the thinnest silver wires that could be drawn, were much too thick for the refined purposes of the astronomer, as they entirely obliterated the image of a star in the more powerful telescopes. To obviate this difficulty Professor Felice Fontana of Florence {Saggio del real gabinetto di fisica e di storia naturale, 1755) first proposed the use of spider webs in micrometers, but it was not till the attention of Troughton had been directed to the subject by Rittenhouse that the idea was carried into practice. In 1813 Wollaston proposed fine platinum wires, prepared by surrounding a platinum wire with a cylinder of silver, and drawing out the cylinder with its platinum axis into a fine wire. The surrounding silver was then dissolved by nitric acid, and a platinum wire of extreme fineness remained. But experience soon proved the superiority of the spider web; its perfection of shape, its lightness and elasticity, have led to its universal adoption.

Beyond the introduction of the spider line it is unnecessary to mention the various steps by which the Gascoigne micrometer assumed the modern forms now in use, or to describe in detail the suggestions of Hooke, Wren, Smeaton, Cassini, Bradley, Maskelyne, Herschel, Arago,

Pearson, Bessel, Struve, Dawes, <fcc., or the successive productions of the great artists Ramsden, Troughton, Fraunhofer, Ertel, Simms, Cooke, Grubb, Clarke, and Repsold. It will be sufficient to describe those forms with which the most important work has been done, or which have survived the tests of time and experience.

Before astronomical telescopes were mounted parallactically, the measurement of position angles was seldom attempted. Indeed, in those days, the difficulties attached to such measures, and to the measurement of distances with the filar micrometer, were exceedingly great, and must have taxed to the utmost the skill and patience of the observer. For, on account of the diurnal motion, the direction of the axis of the telescope when directed to a star is always changing, so that, to follow a star with an altazimuth mounting, the observer requires to move continuously the two handles which give slow motion in altitude and azimuth.

Sir William Herschel was the first astronomer who measured position angles; the instrument he employed is described in Phil. Trans., 1781, vol. lxxi. p. 500. It was used by him in his earliest observations of double stars (1779-83); but, even in his matchless hands, the measurements were comparatively crude, because of the difficulties he had to encounter from the Want of a parallactic mounting. In the case of close double stars he estimated the distance in terms of the disk of the components. For the measurement of wider stars he invented his lamp-micrometer, in which the components of a double star observed with the right eye were made to coincide with two lucid points placed 10 feet from the left eye. The distance of the lucid points was the tangent of the magnified angles subtended by the stars to a radius of 10 feet. This angle, therefore, divided by the magnifying power of the telescope gives the real angular distance of the centres of a double star. With a power of 460 the scale was a quarter of an inch for every second.

The Modem Filar Micrometer.

When equatorial mountings for telescopes became more general, no filar micrometer was considered complete which was not fitted with a position circle. The use of the spider line or filar micrometer became universal; the methods of illumination were improved; and micrometers with screws of previously unheard-of fineness and accuracy were produced. These facilities, coupled with the wide and fascinating field of research opened up by Sir William Herschel’s discovery of the binary character of double stars, gave an impulse to micrometric research which has continued unabated to the present time. A still further facility was given to the use of the filar micrometer by the introduction of clockwork, which caused the telescope automatically to follow the diurnal motion of a star, and left the observer’s hands entirely at liberty.

The modern filar micrometer has now assumed forms of five types.

Type A.— Micrometers in which there are two webs, each movable by a fine screw with a divided head. This is the usual English form of filar micrometer.

Type B.— Micrometers in which one web is movable by means of a fine screw with a divided head, and the other by a screw without a divided head. The latter screw, in ordinary use, is only employed to change the coincidence-reading of the two webs, for eliminating the errors of the micrometer screw. This is the ordinary German form of micrometer as originally made by Fraunhofer and since by Merz, and employed by the Struves and other principal Continental astronomers down to the present day.

Type C.— A similar form of micrometer to B, except that the coincidence-point cannot be changed,—there being no second screw to alter the position of the fixed web.

Type D.— A micrometer somewhat similar in general construction to form B, except that, in addition to means of changing the zero point, there is a screw head by which a fine movement can be given to the whole micrometer box, in the direction of the axis of the micrometer screw. This is the modern form of micrometer as constructed by Repsold.

Type E.— Micrometers fitted with two eye-pieces for measuring angles larger than the field of view of an ordinary eye-piece.

The micrometer of type A is due to Troughton; it is represented in figs. 1, 2, 3. Fig. 1 is a horizontal section in the direction of the axis of the telescope. The eye-piece ab consists of two planoconvex lenses a, b, of nearly the same focal length, and with the two convex sides facing each other. They are placed at a distance apart less than the focal length of a, so that the wires of the micrometer, which must be distinctly seen, are beyond δ. The eye-piece slides into the tube cd, which screws into the brass ring ef, through two openings in which the oblong frame, containing the micrometer slides, passes. These slides are shown in fig. 2, and consist of brass forks k and I, into which the ends of the screws o and p are rigidly fitted. The slides are accurately fitted so as to have no sensible lateral shake, but yet so as to move easily in the direction of the greatest length of the micrometer box. Motion is communicated to the forks by female screws tapped in the heads m and n acting on the screws o and p respectively. Two pins q, r, with spiral springs coiled round them, pass loosely through holes in the forks k, I, and keep the bearings of the heads m and n firmly pressed against the ends of the micrometer box. Thus the smallest rotation of either head communicates to the corresponding slide motion, which, if the screws are accurate, is proportional to the amount through which the head is turned. Each head is graduated into 100 equal parts on the drums u and v, so that, by estimation, the reading can easily be carried to τ⅛<yth of a revolution. The total number of revolutions is read off by a scale attached to the side of the box, but not seen in the figure.

Two spider webs are stretched across the forks, one (Z) being cemented in a fine groove cut in the inner fork k, the other (s) in a similar groove cut in the outer fork I. These grooves are simultaneously cut in situ by the maker, with the aid of an engine capable of ruling fine straight lines, so that the webs when accurately laid in the grooves are perfectly parallel. A wire st is stretched across the centre of the field, perpendicular to the parallel wires. Each movable web must pass the other without coming in contact with .t or the fixed wire, and without rubbing on any part of the brasswork. Should either fault occur (technically called “fiddling”) it is fatal to accurate measurement. One of the most essential points in a good micrometer is that all the webs shall be so nearly in the same plane as to be well in focus together under the highest powers used, and at the same time absolutely free from “fiddling.” For measuring position angles a brass circle gh (fig. 3), fixed to the telescope by the screw i, has rack teeth on its circumference that receive the teeth of an endless screw w, which, being fixed by the arms xx to the oblong box mn, gives the latter a motion of rotation round the axis of the telescope; an index upon this box points out on the graduated circle gh the angular rotation of the instrument.

The English micrometer still retains the essential features of Troughton’s original construction above described. The later English artists have somewhat changed the mode of communicating motion to the slides, by attaching the screws permanently to the micrometer head and tapping each micrometer screw into its slide. Instead of making the shoulder of the screw a flat bearing surface, they have given the screw a spherical bearing resting in a hollow cone (fig. 4) attached to the end of the box. The French artists still retain Troughton’s form. Simms (Troughton’s successor) and Cooke (of York), for symmetry and more effectual elimination of “the loss of time” (called by the Germans “todter Gang,” and sometimes in English “back-lash”), have provided two pins with spiral springs, like q and r (fig. 2), one on each side of the screw which moves each slide.

Grubb of Dublin, with the intention of avoiding the variation of pressure exerted by the spiral springs when the slide is at different distances from the head of the screw, has adopted the following plan. Where the screw enters the slide he has a nut n attached to a strong spring pp (fig. 5), the pressure of which exerts a constant tension in the axis of the screw, tending to bring the threads into close contact, in opposite directions, with their bearings in the nut n and the slide q. The pressure of this spring is regulated by the screws s, s, tapped into the thickened ends of the springs. For maintaining the spherical shoulder of the screw in close and constant pressure on its conical bearing he has attached a conical bearing to the spring p'p' (fig. 6). The pressure of this on the upper part of the spherical shoulder is regulated by the screws s', s', passing through elongated holes in the spring p'p', and tapped into the end of the box.

The screws of micrometers are generally made with 50 or 100 threads to the inch. Troughton’s method of reading the number of whole revolutions by a silver scale is inconvenient, because r ⅜^th or even 7 ⅛th of an inch is too small a quantity to read easily with the naked, eye, especially with the faint illumination that it is desirable to use when measuring faint objects. Different methods, including the “comb” (see below) and various kinds of “counters,” have been introduced with more or less success; but recently the Repsolds of Hamburg have contrived a plan at once so simple and so efficient that it will be unnecessary to describe those methods which this plan is certain to supersede (see below, type D). Grubb has introduced a modification in the form of the slides with a view to avoid the friction of one slide against the other. On the inner side of the brass plate which forms the bottom of the box (i.e., the side opposite to the eye-piece) four V-shaped furrows are placed (fig. 7); and at each end of the slides are projections (fig. 8, end view) which fit into these furrows. The slides are kept down in their places by springs attached to them, which press upon the inner side of the lid of the box.

Troughton’s mode of giving rotation to the position circle is now abandoned. A much quicker motion in position angle than can be obtained without slow motion is often desirable, since, in observing very close double stars, the uncertainty of each pointing may amount to several degrees in the most accurate measurements. The plan of a pinion working in a toothed wheel is often employed, but that also is too slow. Most modern micrometers are now fitted with a clamp and slow motion screw (see fig. 9, type B). This permits observation of position angles of veιy close objects by simple rotation of the box with the hand; while the slow motion, after clamping, permits the more delicate movements that are required in measuring the position angle of objects farther apart.

The Cookes and Grubb have for years almost invariably transferred the position circle from the micrometer to the telescope tube. The whole eye-end with its focussing arrangements rotates, and its rotation can be measured by a circle attached to the butt end of the tube. There is considerable convenience in this arrangement. One position circle only is required for all the micrometers that may be employed with the instrument; and the orientation of reticulated diaphragms, or the adjustment of the direction of the slit of a spectroscope, may also be accomplished by the same means. But, after a very extended experience of all the various types of existing mountings, the present writer does not hesitate to express a decided preference for a position circle attached to the micrometer and a rigid attachment of the eye-end to the telescope tube,—having never seen an eye-end attached to a position...