Micrometer

MICROMETER, an instrument generally applied to telescopes and microscopes for measuring small angular distances with the former or the dimensions of small objects with the latter.

Before the invention of the telescope the accuracy of astronomical observations was necessarily limited by the angle that could be distinguished by the naked eye. The angle between two objects, such as stars or the opposite limbs of the sun, was measured by directing an arm furnished with fine “sights” (in the sense of the “sights” of a rifle) first upon one of the objects and then upon the other, or by employing an instrument having two arms each furnished with a pair of sights, and directing one pair of sights upon one object and the second pair upon the other. The angle through which the arm was moved, or, in the latter case, the angle between the two arms, was read off upon a finely graduated arc. With such means no very high accuracy was possible. Archimedes concluded from his measurements that the sun’s diameter was greater than 27' and less than 32'; and even Tycho Brahe was so misled by his measures of the apparent diameters of the sun and moon as to conclude that a total eclipse of the sun was impossible. Maestlin in 1579 determined the relative positions of eleven stars in the Pleiades (Historia Coelestis Lucii Baretti, Augsburg, 1666), and Winnecke has shown (Monthly Notices R. Λ. S., vol. xxxix. p. 146) that the probable error of these measures amounted to about + 2'.

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 circle on the butt end of the telescope-tube in which, after the wear and tear of a few years, some looseness or shake could not be detected. This is a fatal fault, especially in those delicate observations of difference of declination which have latterly formed so prominent a feature in refined micrometric research. On the other hand, in some good old micrometers at the Royal Observatory, Cape of Good Hope, that are fitted with attached position circles, there is no trace of shake or wear after fifty years of work.

The micrometer of type B represented in fig. 9 is the original Merz micrometer of the Cape Observatory, made on Fraunhofer’s model. S is the head of the micrometer screw proper, s that of the screw moving the slide to which the so-called “fixed web” is attached, s' that of a screw which moves the eye-piece E. C is the clamp and Μ the slow motion in position angle. I., I. are tubes attached to a larger tube N; the latter fits loosely on a strong hollow cylinder which terminates in the screw V. By this screw the whole apparatus is attached to the telescope. The nozzles of small lamps are inserted in the tubes I., I., for illuminating the webs in a dark field; the light from these lamps is admitted through apertures in the strong hollow cylinder above mentioned (for illumination, see below). In this micrometer the three slides moved by S, s, and s' are simple dovetails. The lowest of these slides reposes upon a foundation-plate pp, into one end of which the screw s is tapped. In the middle of this slide a stiffly fitting brass disk is inserted, to which a small turn-table motion may be communicated by an attached arm, acted on by two fine opposing screws accessible to the astronomer; and by their means the “fixed wire” may be rendered strictly parallel with the movable wire.

The micrometer screw is mounted on the slide which carries the movable web. Fig. 10 shows a plan of this slide; the divi<led drum of the screw is omitted for sake of clearness. The screw S has a shoulder at κ, carefully fitted and ground to a bearing so as to work sweetly in a hole in the very strong spring σσ; the other extremity of the screw is formed into a pivot, which fits a hole in the brass piece ββ. The end of this pivot—hardened, polished, and slightly rounded—rests on the flat surface of an agate a, which is imbedded in the end of the slide, and kept firmly in its place by the brass piece ββ. By careful adjustment of the screws θ, θ sufficient pressure may be left upon κ to slightly bend the strong spring <r<r and thus eliminate all end-shake without preventing easy action of the screw. The screw passes at the same time through the bush B (shown in plan and elevation, fig. 10) attached to pp (fig. 9); and there is a fine saw cut, which can be narrowed by the small screw τ, to close the bush upon the micrometer screw with a view of preventing “loss of time.” The spider web ω is cemented on the further side of the thin plate vvv, the varnish being applied in the countersunk holes shown by the dotted circles μ, μ. The slide is countersunk to about half its thickness within the area indicated by oooo, in order to allow the adapter of the eye-piece to come sufficiently close to the webs. The eye-piece was originally moved by a pinion working in a rack r (fig. 9); but the screw s’ applied by Simms was found by Maclear to be more convenient for the purpose. Beyond this, and the graduation of the edge of the circle with more strongly cut divisions than those originally engraved on the face of the circle, the instrument remains and is figured in its original form. Pistor and Martius (Berlin) have also made excellent instruments of the above type. There is a celebrated micrometer of their make, with which, in the hands of Brunnow at Dunsink (Dublin), some of the most perfect and refined investigations ever made in practical astronomy have been executed. In this micrometer the screw s is mounted on its own slide and has a divided head precisely like the screw S (fig. 9). The plate pp is elongated towards s, and the corresponding bush B is attached to this elongation. The screw √ is shifted to another part of the eye-piece slide, so that it does not interfere with the increased diameter of the screw s. Fraunhofer’s micrometer in this form belongs to type A, but is quoted under type B for convenience of description.

It is not necessary to give a figure representing type C. Such micrometers have been generally constructed on Troughton’s type (figs. 1, 2, 3) with the omission of one of the screws, and with one or more of the modifications described in detail under type A. Some have also been made similar otherwise to the Fraunhofer construction, by omitting the screw s with its corresponding slide an<l attaching the fixed wire to a circular plate in pp.

Good instruments have been made on type C by Clark (Cambridge, Massachusetts), by Steinheil (Munich), and by the great French artists Secretan, Froment, Brunner, Eichens; and good work has been done with them. But it is necessary that the errors of the screw should be very carefully determined, since, in type C, such errors cannot be eliminated by employing different parts of the screw to measure the same angle. There is a noteworthy description of micrometer that forms a link between types C and D, of which the most famous example (by Clark) is attached to the great Washington telescope. It is essentially a micrometer of type C, with a slide (or fork) and a screw of the English form of construction. But the instrument is provided with a screw as at s (fig. 9), which, instead of changing the position of the fixed wire, moves the whole micrometer box in the direction of the axis of the measuring screw. Thus the fixed wire can be set exactly on one star by the screw s while the other star is immediately afterwards bisected by the movable wire, and that without disturbing the reading for coincidence of the wires. No one, unless he has previously worked without such an arrangement, can fully appreciate the advantage of bringing up a star to bisection by the fixed wire by moving the micrometer box with a delicate screw-motion, instead of having to change the direction of the axis of a huge telescope for the same purpose. When it is further remembered that the earlier telescopes were not provided with the modern slow motions in right ascension, and that the Struves, in their gigantic labours among the double stars, used to complete their bisections on the fixed wire by a pressure of the finger on the side of the tube, one is puzzled whether most to wonder at the poor adaptation of means to ends or the marvellous patience and skill which, with such means, led to such results. It should be added that Dawes practically adopted a modification of Clark’s micrometer by using a slipping piece, and bolting one of the heads of his micrometer {Mem. R. A. S., vol. xxxv. p. 139). His slipping piece gave motion to the micrometer by two slides, one in right ascension the other in declination, so that “either of the webs can be placed upon either of the components of a double star with ease and certainty.”

All micrometers used, in conjunction with a microscope, for reading the divisions of transit circles, heliometer scales, &c., are of the type C. The reading micrometer-is shown in fig. 11. C is the objective, D the micrometer box, E the graduated head of the screw, G the milled head by which the screw cc is turned, A an eyepiece sliding in a tube B, aa (fig. 12) the slide, and b, b the spiral springs. The focal length of the objective and the distance between the optical centre of the lens and the webs are so arranged that images of the divisions are formed in the plane of the webs, and the pitch of the screw is such that one division of the scale corresponds with some whole number of revolutions of the screw.

There is what is technically called a “comb” inserted in the micrometer box at d (fig. 12),—its upper surface being nearly in the plane of the wires. This comb does not move with reference to the box, and serves to indicate the whole revolution of which a fraction is read on the head. In fig. 12 a division is represented bisected by cross webs, and five revolutions of the screw correspond with one division of the scale. In all modern reading micrometers the cross webs of fig. 12 are replaced by parallel webs embracing the division (fig. 13). The means for changing the length of the tube and the distance of C from the scale are omitted in the figure. These appliances are required if the “run” has to be accurately adjusted. By “run” is meant the difference between the intended whole number of screw-revolutions and the actual measure of the space between two adjacent divisions of the scale in turns of the screw divided by the number of intended revolutions. In delicate researches two divisions of the scale should always be read, not merely for increased accuracy but to obtain the corrections for “run” from the observations themselves.

Fig. 14 represents an important type of reading micrometer by the Repsolds. Here the web-frame is mounted on the screw itself. The limiting plane of motion is at p, where the end of the micrometer screw bears upon the hardened, flattened end of the screw s, and is kept in bearing against this plane by the spiral spring q. Rotation of the wire-frame is prevented by the small stud m which passes through the web-frame and projects slightly on both sides of it, just barely touching the inner surfaces of the top and bottom of the micrometer box. The web-frame thus rests solely on the screw and on the point m, and therefore follows it absolutely and accurately.

The comparative merits of the various micrometers are discussed by Lord Lindsay and Mr Gill (D unecht Pzιblications, vol. ii. pp. 53-55, 1877). If the screw of the Repsold micrometer is bent, so that, for example, the end of the frame next the screw-head is raised and that next the end p lowered, a twist will be given to the webframe, and the centre of the wire will be moved nearer to the micrometer head than it should be, while the reverse effect will follow when the head has been turned through 180°. The effect of a similar error on the other micrometers described would be of a much less amount. They are, however, liable to errors of another character. If, as in Troughton’s original micrometer, the shoulder is square, the hole in the end of the box may be left sufficiently wide to allow for a small error in the parallelism of the screw-matrix with the motion of the slide, but the smallest bend in the screw causes the shoulder no longer to bear flat, but to ride on its edge, thus introducing an extremely uncertain form of error. If the shoulder is spherical, fitting into a hollow cone on the end of the box, as in the micrometers of Simms, Cooke, and Grubb, an almost inconceivable accuracy of construction is implied in drilling the matrix of the screw in the slide so that its axis and that of the cone shall be in the same straight line, and both parallel to the motion of a point in the slide. Any departure from perfect accuracy in this respect has the effect of bringing different portions of the spherical shoulder to bear on different parts of the cone for different revolutions, and introduces errors of a character by no means easy to deal with. In addition to these objections there always is the greater objection of employing as a delicate contact-measuring surface one that is exposed where oil is used. Dust and oil will arrange themselves in layers of variable and uncertain thickness and defeat all attempts to secure absolutely consistent results. In Repsold’s micrometer the point d'appzιi is a small hardened and polished bearing, requiring little lubrication, and perfectly protected from dust; the errors of the screw (some of them exaggerated, certainly) are faithfully reproduced, and consequently determinable, and beyond this the work to be done by the screw is reduced to a minimum,—no slidefriction having to be overcome. If we are to regard as the most perfect instrument, “not that which has absolutely the smallest errors, but that which reproduces its errors with the most perfect consistency,” undoubtedly Repsold’s form of micrometer is best.

In order to avoid the exaggeration of the screw-errors produced by the non-symmetrical position of the screw in Repsold’s micrometer, Stone, in December 1879, exhibited at the Royal Astronomical Society, and described (Monthly Notices, p. 270), a modification of Repsold’s instrument. But, both in his statement of the comparative merits of the Troughton and Repsold micrometers and in the new form which he figures, Stone overlooks a strong point in the Repsold form, and in that proposed by Lord Lindsay and Gill three years previously, —namely, the avoidance of all friction of the slide, and the elimination of all error or strain that may occur from a want of parallelism in the axis of the matrix and the motion of the slide. The Lindsay-Gill micrometer will be better understood from the following description. In fig. 15 Ss is the micrometer screw; its cylindrical axis is nicely ground to fit a hole in the side of the box at a; the same axis, but ground to a somewhat smaller cylinder, fits neatly but smoothly a hole in the web-frame at b. A screw, cut on the same axis, is tapped into the webframe at s, and the axis terminates in a pivot which fits a hole in a brass plate cc. The end of the pivot—hardened and slightly rounded —rests on a flat agate bearing α, which is imbedded in the plate B, and securely held in sitze by pressure of the plate cc. The plate B is firmly attached to the bottom of the box. q, q are spiral springs mounted on pins. Both springs and pin pass freely through the web-frame at p, p, and the pins (but not the springs) pass freely through the frame at n, n. The parallel webs for observing the division (fig. 13) are mounted on the forked end of the frame at zcw.

The web-frame is narrower and thinner than the breadth and height of the interior of the box, and is only prevented from rotating by the delicate touch of the projecting ends of the pin m on the inner surfaces of the top and bottom of the box. It appears that a frame so mounted fulfils all theoretical conditions of accuracy. It is perfectly free to follow the motion of the screw and accurately to reproduce its errors, notwithstanding any reasonable faults of workmanship; and no permissible shake or fouling of the bearing at a can produce sensible error in the distance between the bearing surface of the agate plane and the spider webs. The motion is produced with the minimum of friction; and the “feel” of the screw is therefore as delicate and perfect as it is possible to make it.

The micrometer of type D shown in fig. 16 has recently been made by the Repsolds for the Cape Observatory. As this instrument combines all their most recent modifications, we describe it in detail.

Fig. 17 represents the same micrometer with the upper side of the box removed. The letters in the description refer to both figures.

S is the head of the micrometer screw, s that of the screw by which the micrometer box is moved relative to the plate /(fig. 16), s ’ that of the screw which moves the eyepiece slide. K is the clamp in position angle, P the slow motion screw in position angle; pp is the position circle, R, R its two readers. The latter are in fact little microscopes carrying a vernier etched on glass, in lieu of a filar micrometer. These verniers can be read to 1', and estimated to 0'∙2. D is the drum-head which gives the fraction of a revolution, d that which gives the whole number of revolutions, I is the index or pointer at which both drums are read. This index is shown in fig. 17, but only its mode of attachment (X, fig. 17) in fig. 16. The teeth of the pinion z, fig. 17, are cut on the axis of the micrometer screw. The drum.rf and its attached tooth wheel are ground to turn smoothly on the axis of the screw. Ί lie pinion z and the toothed wheel d are connected by an intermediate wheel and pinion Y; the numbers of teeth in the wheels and pinions are so proportioned that twenty-four revolutions of the micrometer screw produce one revolution of the drum and wheel d. (This is the description of Repsold’s counter referred to under type A. ) The divisions of both drums are conveniently read, simultaneously, by the lens c ; at night the lamp which illuminates the webs and the position circle also illuminates the drum-heads (see on illumination below), aaaa is the web-frame (fig. 17), 3γ is a single rod consisting of two cylinders accurately fitting in the ends of the micrometer box, the larger cylinder being at β. There is a hole in the webframe which smoothly fits the larger cyliudcr at β', and another which similarly fits the smaller cylinder at y. A spiral spring, coiled round the cylinder y, resting one end on the shoulder formed by the difference of the diameters of the cylinders β and y and the other on the inside of the web-frame, presses the latter continuously towards y. Contact of the web-frame of the micrometer with the side of the box at y would therefore take place, were it not for the micrometer screw. This screw fits neatly in the end of the box at «, passes loosely through the web-frame at is tapped into the frame at f', and its end rests on a flat hardened surface at £ Rotation of the web-frame about βy is prevented by the heads of the screws at m ; the head of the screw on the lower side of the frame reposes on the plane w, that on the upper side (fig. 17) touches lightly on the inner surface of the lid of the box. Such rotation can obviously be controlled within limits that need not be further considered. But freedom of rotation in the plane of the paper

(fig. 17) is only prevented by good fitting of the holes β', y'∙, and, since the weight of the slide is on one side of the screw, misfit here will have the effect of changing the reading for coincidence of the movable with the fixed web in reverse positions of the micrometer. With the Cape micrometer a systematic difference has been found in the coincidence point for head above and head below amounting to 0" ’ 14. This corresponds, in the Cape instrument, with an excess of the diameters of the holes over those of the cylinders of about τ ∙ 5 ⅛ πr th of an inch,—a quantity so small as to imply good workmanship, though it involves a systematic error which is very much larger than the probable error of a single determination of the coincidence point. The obvious remedy is to make all measures on opposite sides of the fixed web before reversing in position angle,—a precaution, however, which no careful observer λvould neglect. In measuring differences of declination, where the stars are brought up by the diurnal motion, this precaution cannot be adopted, because it is necessary always to bisect the preceding star with the fixed web. But in ∆δ measures index error can always be .eliminated by bisecting both stars with the same web (or different webs of known interval fixed on the same frame), and not employing the fixed web at all. Had the spring q been placed as in fig. 14, and the cylinders β and y been made to bear like the pivots of a transit on segmental bearings in the frame at β' and y', it is probable that the difference in coincidence points would not have existed. Such a modification appears advisable, unless this construction, by leaving the end m less free, should make the “feel” of the screw less sweet and perfect. The discordance in zero when known to exist is really of no consequence, because the observations can be so arranged as to eliminate it.

The box is mounted on a strong hollow steel cylinder CC (fig. 17) by holes η, θ in the ends of the box, which fit the cylinder closely and smoothly. The cylinder is rigidly fixed in the studs C, C, and these are attached to the foundation plate f. The cylinder contains towards η a sliding rod, and towards θ a compressed spiral spring. There is thus a thrust outwards of the spring upon the hollow cap W (attached outside the box), and a thrust of the rod upon the end of the screw s. The position of the box relative to the plate∕, in the direction of measurement, depends therefore on the distance between the end of the screw s and the fixed stud C. A screwing in of s thus causes the box to move to the left, and vice versa. Rotation of the box round CC is prevented by downward pressure of the spring Z on a projection attached to the side of the box. The amount of tlιis pressure is regulated by the screw z ’.

The short screw whose divided milled head is σ shifts the zero of the micrometer by pushing, without turning, the short sliding rod whose flat end forms the poinZ d'appui of the micrometer screw at (’. The pitch of the screw <r is the same as that of the measuring screw (50 threads to the inch), and its motion can be limited by a stop to half a revolution.

The five fixed webs are attached to the table ττ, which is secured to the bottom of the box by the screws ρ. The three movable webs are attached to the projections λλ on the frame αα. The plane surfaces ττ and λλ are composed of a bronze of very close texture, which appears capable of receiving a finish having almost the truth and polish of an optical surface. It seems also to take a very clean V cut, as the webs can be laid in their furrows with an astonishing ease and precision. These furrows have apparently been cut in situ with a very accurate engine; for not the slightest departure from parallelism can be detected in any of the movable webs relative to the fixed webs. Extraordinary care has evidently been bestowed in adjusting the parallelism and distance of the planes τ and λ, so that the movable wires shall almost, but not quite, touch the surface τ. The varnish to fix the webs is applied, not on the surface τ as is usual, but on a bevel for the purpose, the position of the webs depending on their tension to keep them in their furrows. The result is that no trace of “fiddling” exists, and the movable and fixed webs come sharply together in focus with the highest powers. Under such powers the webs can be brought into apparent contact with such precision and delicacy that the uncertainty of measurement seems to lie as much in the estimation of the fraction of the division of the head as in the accuracy of the contact. It is a convenient feature in Repsold’s micrometer that the webs are very near the inner surface of the top of the box, so that the eye is not brought inconveniently close to the plate when high powers are used.

Micrometers of the type E have been invented by Alvan Clark and Grubb. Clark’s micrometer was exhibited at the June meeting of the Royal Astronomical Society in 1859 {Monthly Notices R. A. S., vol. xix.). It is capable of measuring angles up to about one degree. It is “furnished with two eye-pieces, composed of small single lenses, mounted in separate frames, which slide in a groove and can be separated to the required distance. A frame carrying two parallel spider lines, each mounted separately with its own micrometer screw, slides in a dovetailed groove in front of the eye-pieces; and by a free motion in this frame each web can be brought opposite its own eye-lens. In using this micrometer, the first step is to set the position-vernier to the approximate position of the objects to be measured. Then the eye-lenses are separated till each is opposite its own object. The frame containing the webs and their micrometer screws is then slid into its place; and the webs, having been separated nearly to their proper distance by their free motion in the frame, are placed precisely on the objects by their fine screws, the observer’s eye being carried rapidly from one eye-lens to the other a few times, till he is satisfied of the bisection of each of the objects by its own web. The frame is then removed for reading off the measure by means of an achromatic microscope, on the stage of which it is placed.” The advantages which Clark claims are these :—

“1. Distances can be observed with great accuracy up to about one degree, and the angles of position also.

“2. The webs, being in the same plane, are perfectly free from parallax, and are both equally distinct, however high the magnifying power may be.

“3. The webs are also free from distortion and from colour.

“4. A different magnifying power may be used on each of the objects,—which may be advantageous in comparing a faint comet with a star.”

It appears to us that the method of removing a slide in order to measure the interval between the webs is liable to objection, not only because of the risk to the webs, but because the taking of measurements of such a different character with a different instrument is inconvenient and troublesome. It is true that the intervals between the webs could be measured by an assistant, and two or more different slides be employed to save time; but astronomers will probably generally prefer the method introduced by Grubb described below. It is understood that Clark has since improved this instrument by an ingenious arrangement of prisms, which permits both webs, even though separated one degree in a large telescope, to be seen in the same eye-piece. The arrangement is not described, and is said to be, as yet, somewhat troublesome to arrange previous to measurement, though when arranged it gives very good results.

Grubb {Scientific Proceedings of Royal Dublin Society) thus describes what he calls his ‘ ‘ duplex micrometer,” shown in perspective in fig. 18 :—“A plate of glass about 2⅜ inches square is ruled with twenty-one lines in one direction τ ⅛-th inch apart, and two lines in the other direction 2 inches apart. The extreme lines of the set therefore form a perfect square of 2 inches. These lines are ruled with exceeding accuracy and care, but provision is left for ascertaining any errors that remain either as to distance or want of perfect squareness. Along one side of the square is mounted a micrometer frame in the ordinary way, actuated by a screw of one hundred threads to the inch. This micrometer frame carries eleven lines corresponding exact ly to each alternat, line in the glas; reticule, so that when the first spider line is made coincident with the first diamond line on the glass the last spider line will be coincident with the last line on the glass, and each of the spider lines will be coincident with all the odd numbers of diamond lines, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21. Over this glass plate is placed a brass cap in which two eye-pieces are mounted, one sliding in a groove at right angles to the other,—so that, while one has its journey backwards and forwards on the horizontal line, the other has its journey on the vertical line, according to how the cap is placed, for this cap is capable of rotation to meet various circumstances.

“How to Use the Instrument. — 1. The two stars are brought on the horizontal line, and the distance measured from centre to centre along that line. This distance is measured by counting the number of spaces on the glass, adding the residue as measured by the micrometer screw. Thus the screw is never used for larger measures than τ⅛th inch, and therefore errors of screw and temperature errors are much reduced. In bisecting, one star is brought into the field of one eye-piece, and a bisection is made with one of the diamond lines by moving the micrometer by one or other of its slipping piece screws. Then the other eye-piece is moved till the second star is seen, and a bisection is made with the nearest spider line by moving the micrometer head. Then the eye can be moved back to the first eye-piece, and the bisection checked, and again back to the other eye-piece. When it is seen that both are satisfactory the measure can be read off. 2. The micrometer is turned round till the horizontal line becomes parallel to the path of apparent motion of the star. This is easily found by stopping the clock and allowing the star to run along the horizontal wire. Now the other star will be found to cross the vertical line somewhere, while the first star is on the horizontal line. This second star is then bisected on the vertical line, while the first star is bisected by one of the spider lines; thus the difference in right ascension is found. We then have two sides of a right-angled triangle and of course all the elements are known.

‘ ‘ To Ascertain the Errors {if any) of the Distance of the Lines. — Of course, the usual plan of taking transits can be adopted, and to ascertain if the lines be perfectly at right angles a special additional eye-piece is provided, so that transits can be taken across each diagonal of the square.”

This instrument has great advantage over Clark’s in ease of adjustment and use, and has done good work at the University Observatory, Oxford {Mem. R. A. S., vol. xlvii. pp. 5-12). Professor Pritchard claims too much when he estimates its work as equal in accuracy with that of the heliometer—at least the published results do not confirm such a view. But it is a very valuable instrument for measuring objects too faint for the limited aperture of most heliometers, and which at the same time are farther apart than the field of view of an ordinary eye-piece.

The accuracy of the duplex micrometer would be very greatly increased if Clark’s idea (above mentioned) of viewing both widely separated webs in one eye-piece of high power could be reduced to a convenient practical form.

Method of Webbing the Filar Micrometer.

The webbing of a micrometer is a process that should be familiar to all practical astronomers. English opticians usually proceed as follows. A spider (the variety is marked by a cross on the back, and is found in English gardens about decayed wood) is caught, and placed on a wire fork. The insect immediately attaches a web to the wire and begins to lower itself by a web to the ground. This web is wound up on the fork till ten or twelve turns, separated by a convenient space, have been secured. A brush with varnish is then passed along the prongs; the webs are thus securely fixed to the fork. The parallel prongs of the fork must be sufficiently far apart to allow the web-frame of the micrometer to pass between them. The frame to be webbed is placed on a flat dull black surface between the prongs of the fork, the latter being carefully arranged so that one of the webs lies nearly in the furrow ruled in the frame for its reception. As the web-frame is generally thicker than the fork, the web will now be stretched across the former, with a certain amount of tension, and is brought into the furrow with a finely pointed piece of soft wood. If the surface of the frame is well polished, and the furrows sharply cut, without “burr,” the web should leap sharply and decidedly into its place. Each end of the web is then secured by a drop of shellac varnish, which should be allowed to harden thoroughly before the frame is touched. The webs can be very readily so handled against a black background, with the aid of a hand lens of 2 or 3 inches focus. In experienced hands this method gives good results, but the following, which is generally followed on the Continent, is preferable.

A web, about 2 inches longer than the width of the frame, is unwound from a cocoon, and small pieces of lead are attached to its extremities by beeswax. One end of the web, with its attached lead, is laid on a piece of cork floating in a tumbler of water; the other end is allowed to hang down in the water, where it becomes thoroughly saturated and untwisted. It is then laid across the fork, and dropped into its furrows in the manner above described, the little lead weights exerting a definite tension. Varnish 2 is immediately applied to secure the webs, and the frame is not touched till it is dry.

The bevel-edge of the web-frame introduced by Repsold (type D) offers great facilities for accurate webbing, and should be employed in all future micrometers.

Illumination of Micrometers.

When micrometer observations are made by night it is necessary to have some mode of rendering the webs visible,—either by rays of light at right angles to the axis illuminating the webs, or by rays nearly coincident with the axis of the telescope. In the former case we get bright webs in a dark field, in the latter dark webs on a bright field.

In the older telescopes bright web illumination is produced by small lamps with nozzles that enter the tubes I., I. (fig. 9). The illumination is regulated in colour and intensity by wedges of coloured or darkened glass passing through slides in the nozzles. But it is inconvenient to have lamps so near the observer’s eye, and it is at least very difficult to obtain a perfectly dark field when the wires are illuminated in this way.

The Clarks, in their micrometer of the great Washington telescope, have made the end of box T (fig. 15) transparent, and light is thrown on the webs from a lamp held by an assistant. Holden has very recently applied a lamp ingeniously hung so as to preserve its verticality and the constant direction of its light in a similar way, adding a plain silvered mirror inside the box and opposite the lamp, so as to illuminate the webs symmetrically. In the Clarks’ and Holden’s methods it is only the webs at right angles to the screw that are illuminated.

For illumination of the field, in very old telescopes, light was thrown on a small ivory reflector fixed outside the object-glass in the axis of the telescope by an arm fitting on the cell of the lens. This involved the aid of an assistant to direct lamplight on the ivory reflector, or the very frequent change of a lamp support. Afterwards the light from an attached lamp was introduced through a hole in the telescope-tube and thrown upon an elliptical plane (generally dull-gilt) having its centre part cut away sufficiently to avoid interruption of the cone of rays from the object-glass. Many ingenious modes of suspending the lamp have been invented for the purpose of securing a constant direction of its light coupled with verticality of the lamp. One of the best of these, due to Cooke, is shown in fig. 19. I. is the lamp, P a prism to reflect its light into the tube, D a disk to regulate the quantity of light, B a disk with glasses to regulate the colour of the light, S a spring to clamp the disks, C the counterpoise of the lamp, G a poise to preserve the horizontally of the axis CL. But astronomers owe to the genius of Grubb the introduction of a more efficient and convenient system, viz., the performance of all necessary illumination of an astronomical telescope by a single lamp, and the perfect control of the illumination of the field or webs, and the regulation of these as to intensity or colour by simple motions from the eye-end. It is impossible to speak too highly of Grubb’s efforts in this direction; he has broken the ground in this department of astronomical engineering, and rendered the working of so huge an instrument as the Vienna telescope of 27 inches aperture not only convenient, but easier for a single observer than that of a very small telescope of the older constructions.

But in the illumination of the field wires and scales of a micrometer Grubb’s original method has recently been surpassed by one which is due to the Repsolds. We shall therefore describe the latter.

Fig. 20 represents the eye-end of a telescope. The reader will recognize the micrometer (figs. 16 and 17) previously described. I. is a paraffin lamp fitting by a bayonet joint into a copper cover c. This effectually defends its glass chimney against accident, and protects the lamp from wind. The simple means by which this lamp is made to preserve its verticali ty in all positions of the telescope is evident from the figure. By this lamp alone the bright wire or bright field illumination is given at pleasure, and with any desired intensity, simply by movement of the small pin p.

The position circle and the head of the micrometer are also illuminated, as well as the declination circle, by the same lamp. AB is a cylindrical box, ending in a truncated cone towards A. It is shown, mid-section, in a plane passing through the telescope axis, in fig. 21, where all details unnecessary to the explanation of the illumination are omitted, and proportion of parts is sacrificed to clearness. P is a prism (fig. 21) that rotates with the lamp and reflects its light into AB. The flame of the lamp is in the focus of the lens ll, so that the rays become parallel after passing through it. There is a sliding motion to perfect this adjustment. There is a well-polished flat annular reflector of speculum metal rr (fig. 21), which reflects light upon the double mirror Μ (fig. 20), whence it is diverted to the two opposite points on the declination circle that are read by micrometer microscopes from the eye-end (the latter are omitted for sake of clearness).

The little handle at p' and the dotted lines p ’ z represent an iris-diaphragm, very ingeniously constructed, mounted on a plate of transparent glass. There is a flat ring of brass, carrying four pins, which is turned by the handle p ’ , in a plane at right angles to Pn. These pins work in spiral slots cut in four slides. Thus rotation of the ring causes the four slides to approach or recede from a centre. When the handle p ’ is in the middle of its range, the slides together form a disk as large as the hole in the diaphragm dd, and thus prevent all light from entering the telescope tube. When p' is pushed to one side of its range the slides move outwards leaving a square opening in the centre so that the light falls on the prism n, whence it is diverted to a silvered reflector cemented on the middle of the inner surface of the object-glass, and is then reflected back along the axis of the telescope to illuminate the field at «. When p , is pushed to the other side of its range the slides approach and overlap at the centre, excluding light from n and allowing it to fall upon the reflector s instead. From s the light is thrown upon the webs ω, ω by reflexion from a white papier mache surface laid on the inside of a thin hollow brass truncated cone xx. The edge of this cone forms the circle seen within ττ in fig. 17. All stray light is prevented by the light-guard tube mm, which is attached to and moves with the rotating part of the micrometer. The result is to produce a symmetrical illumination of the whole system of webs in a perfectly dark field. It is also obvious that by placing p' at an intermediate position between the centre and the extremes of its range any desired modification of bright wire or bright field illumination can be obtained at pleasure.

The light falling on the papier mâché hollow cone is intercepted at three points by prisms, one of which μ is shown in section. These prisms are inserted in the cylinder which carries the foundation plate of the micrometer box and rotate with it. Two of them divert light upon the reflectors (seen from different points of view in figs. 16, 17, 20). The third prism after two reflexions (figs. 16, 20) illuminates the micrometer head. The whole arrangement is in the highest degree elegant, and we have found it most simple and convenient in practice. The screen C (figs. 20 and 21)—made of thin copper and attached to AB—effectually protects the observer’s eye from stray light from the lamp.

It has been found essential, in bright field illumination, when the highest accuracy is desired, to have the illuminating rays parallel with the telescope axis.

In the best telescopes of the future some plan like that of Repsold’s, above described, will doubtless be adopted. It is probable also that with the introduction of condensers, in conjunction with the incandescent carbon light in vacuum, electricity will ultimately supersede the oil or paraffin lamp in illuminating astronomical instruments. A small “Swan lamp” can be placed anywhere, is unaffected by wind, and gives off comparatively little heat. These are most valuable qualities for the purpose in question.

The astronomer-royal (Mr Christie) has recently used luminous paint to render the measuring pointer of the Greenwich spectroscope visible at night. This paint, after exposure during the day to sunlight, shines at night with a dull phosphorescence sufficient to make the micrometer pointer, to which it is applied, faintly visible, and, it is stated, with very satisfactory results.

On the use of the filar micrometer consult Struve, Mensurte Micrometricae, St Petersburg, 1837; Brunnow, Practical and Spherical Astronomy; Chauvenel, Practical and Spherical Astronomy; Brunnow, Astronom teal Observations and Researches made at bunsink, Dublin, 1870, 1873, 1879; Ball, ibid.; Kaiser, Leiden Observations; and the papers of Dembowski in the Astronomische Nachrichten. Double-Image Micrometers.

The discovery of the method of making measures by double images is stated to have been first suggested by Roemer about 1678. But no such suggestion occurs in the Basis Astronomiae of Horre-bow (Copenhagen, 1735), which contains the only works of Roemer that remain to us. It would appear that to Savary is due the first invention of a micrometer for measurement by double image. His heliometer (described in a paper communicated to the Royal Society in 1743, and printed, along with a letter from Short, in Phil. Trans., 1753,p. 156) was constructed by cutting from a complete lens abed the equal portions aghc and acfe (fig. 22). The segments gbh and efd so formed were then attached to the end of a tube having an internal diameter represented by the dotted circle (fig. 23). The width of each of the portions aghc and acfe cut away from the lens was made slightly greater than the focal length of lens × tangent of sun's greatest diameter. Thus at the focus two images of the sun were formed nearly in contact as in fig. 24. The small interval between the adjacent limbs was then measured with a wire micrometer.

Savary also describes another form of heliometer, on the same principle, in which the segments aghc and acfe are utilized by cementing their edges gh and ef together (fig. 25), and covering all except the portion indicated by the unshaded circle. Savary expresses preference for this second plan, and makes the pertinent remark that in both these models “the rays of red light in the two solar images will be next to each other, which will ∙<∙nder the sun’s disk more easy to be observed than the violet ones.” This he mentions “because the glasses in these two sorts are somewhat prismatical, but mostly those of the first model, which could therefore bear no great charge” (magnifying power).

A third model proposed by Savary consists of two complete lenses of equal focal length, mounted in cylinders side by side, and attached to a strong brass plate (fig. 26). Here, in order to fulfil the purposes of the previous models, the distance of the centres of the lenses from each other should only slightly exceed the tangent of sun’s diameter × focal length of lenses. Savary dwells on the difficulty both of procuring lenses sufficiently equal in focus and of accurately adjusting and centring them.

In the Mém. Acad, de Paris, 1748, Bouguer describes an instrument which he calls a heliometer. Lalande in his Astronomie (vol. ii. p. 639) mentions such a heliometer which had been in his possession from the year 1753, and of which he gives a representation on Plate XXVIII., fig. 186, of the same volume. Bouguer’s heliometer was in fact similar to that of Savary’s third model, with the important difference that, instead of both object-glasses being fixed, one of them is movable by a screw provided with a divided head. No auxiliary filar micrometer was required, as in Savary’s heliometer, to measure the interval between the limbs of two adjacent images of the sun, it being only necessary to turn the screw with the divided head to change the distance between the object-glasses till the two images of the sun are in contact as in fig. 27. The differences of the readings of the screw, when converted into arc, afford the means of measuring the variations of the sun’s apparent diameter.

On the 4th April 1754 Dollond communicated a paper to the Royal Society of London (Phil. Trans., vol. xlviii. p. 551) in which he shows that a micrometer can be much more easily constructed by dividing a single object-glass through its axis than by the employment of two object-glasses. He points out—(1) that a telescope with an objectglass so divided still produces a single image of any object to which it may be directed, provided that the optical centres of the segments are in coincidence (i.e., provided the segments retain the same relative positions to each other as before the glass was cut); (2) that if the segments are separated in any direction two images of the object viewed will be produced; (3) that the most convenient direction of separation for micrometric purposes is to slide these straight edges one along the other as the figure on the margin (fig. 28) represents them: “for thus they may be moved without suffering any false light to come in between them; and by this way of removing them the distance between their centres may be very conveniently measured, viz., by having a vernier’s division fixed to the brass work that holds one segment, so as to slide along a scale on the plate to which the other part of the glass is fitted.”

Dollond then points out three different types in which a glass so divided and mounted may be used as a micrometer :—

“1. It may be fixed at the end of a tube, of a suitable length to its focal distance, as an object-glass,— the other end of the tube having an eye-glass fitted as usual in astronomical telescopes.

“2. It may be applied to the end of a tube much shorter than its focal distance, by having another convex glass within the tube, to shorten the focal distance of that which is cut in two.

“3. It may be applied to the open end of a reflecting telescope, either of the Newtonian or the Cassegrain construction.”

Dollond adds his opinion that the third type is “much the best and most convenient of the three”; yet it is the first type that has survived the test of time and experience, and which is in fact the modern heliometer

Fig. 29 illustrates Dollond’s divided object-glass heliometer of the third type. A is the end of the reflecting telescope, upon which the adapter B is fitted. B carries a wheel (not seen in the figure) formed of a ring racked at the outer edge, and fixed to the brass plate CO, so that a pinion moved by the handle D may turn it into any position. Two plates F, G, with the attached semi-lenses, move in slides fixed to the plate CC, —simultaneous motion, in contrary directions, being communicated to them by turning the handle E, which drives a concealed pinion that works in the two racks seen in the highest part of the figure. The amount of separation of the semi-lenses is measured by a scale 5 inches long, subdivided to ⅛th of an inch, and read by a vernier on the plate F to ^⅞ιyth of an inch. In practical use this micrometer has never given satisfactory results (see Mosotti in the Efemeride of Milan for 1821). It must be remembered, however, that when Dollond gave preference to this type he had not invented the achromatic object-glass; his preference was fully justified under these circumstances. So far as we know no heliometer with a divided achromatic object-glass was ever made by the elder Dollond on the principle of his first type. His son, however, made what he called an object-glass micrometer, which was a great improvement on the elder Dollond’s second type.

In the older construction the brass mountings of the semi-lenses obstructed the light entering the telescope in proportion to their separation, and the images were so coloured as to prevent the use of any but very low powers. In the later construction the movable segments are formed from a negative achromatic lens of much larger aperture than the object-glass of the telescope with which the micrometer is employed; and, for convenience in mounting, the segments gbh and edf (fig. 22) are removed. In the fine example of this instrument at the Royal Observatory, Cape of Good Hope, the movable lenses consist of segments of the shape gach and eacf (fig. 22) cut from a complete negative achromatic combination of 8∣ inches aperture and about 41- feet focal length, composed of a double concave flint lens and a double convex crown. This is applied to an excellent achromatic telescope of 3⅜ inches aperture and 42 inches focal length. The instrument is represented in fig. 30; the same letters indicate the analogous parts of fig. 29. The frame CO, moved by teeth on its outer edge, carries one of the halves G of the lens, and a similar frame with teeth carries the other half F. A scale 8⅛ inches long is fastened like an edge-bar to the frame of the segment G, and each inch is subdivided into twenty parts, which are read off by a vernier to τ √ cτ th of an inch, and, by estimation, this can easily be carried to ^∏∏rth or ^⅛⅛ τ th of an inch. The two movable frames are imbedded in a fixed plate HH, screwed to the adapter B, having a circular hole in its middle equal to the diameter of the object-glass. The slide of the segment G is moved by turning the milled head to the right of A, and the other segment F by means of a rack and pinion on the opposite side, the latter being turned from the eye-end by a handle not seen in the figure. A screw is provided for clamping the slide of the segment G, as it is intended that only the segment F shall be moved in making the final bisection. There is an index attached to the slide of G, reading on a rough scale engraved on the plate H, which is obviously intended for setting the optical centre of the segment G approximately as far from the optical axis of the telescope on one side as the optical centre of the segment F will be on the other side during the intended measurement. This arrangement not only permits the measurement of angles twice as great as would be possible if one segment were fixed, but is also important in increasing the symmetry of the measures. The vernier is placed at one end of the scale when the optical centres of the segments are in coincidence, and is provided with screws at I, which are intended for adjusting the zero of the scale. The younger Dollond has in this model retrograded, in some respects, from the admirable example of his father, who, as shown in fig. 29, not only gave the lenses automatic opposite motion symmetrically with respect to the axis of the telescope, but seems also to have provided for entire elimination of index error by making it possible to observe all angles on opposite sides of zero—a precaution possible in the later form only when very small angles are measured. Rotation of the micrometer in position angle is provided for as in the earlier form, but the instrument is not furnished with a position circle.

With one of these instruments of somewhat smaller dimensions (telescope 2⅜ inches aperture and 3⅜ feet focus) Triesnecker made a series of measurements at the observatory of Vienna which has been recently reduced by Dr Schur of Strasburg (Nova Acta der Ksl. Leap.-Carol. Deutschen Akademie der Natursforschcr, xlv. No. 3). The angle between the stars ζ and g Ursae maj. (708" , 55) was measured on four nights; the probable error of a measure on one night was ± 0"∙44. Jupiter was measured on eleven nights in the months of June and July 1794; from these measures Schur derives the values 35" - 39 and 37"‘94 for the polar and equatorial diameter respectively, at mean distance, corresponding with a compression 1/14’44. These agree satisfactorily with the corresponding values 35"'21, 37"'60, 1/15'69 afterwards obtained by Bessel {Königsberger Beobachtungen, xix. 102). From a series of measures of the angle between Jupiter’s satellites and the planet, made in June and July 1794 and in August and September 1795, Schur finds the mass of Jupiter — 1fua .A ∣ ∙ ∣ u ⅛ > a result which accords perfectly with the received value of the mass derived from modern researches. The probable errors for the measures of one night are ±O"'577, ±0"'889, ±0"∙542, ±1"O96, for Satellites I., II., III., and IV. respectively. It is probable that Triesnecker deduced the index error from his measures of the diameter of Jupiter, as, in 1794, the measures of diameter are made on the same nights with those of the measures of distance of the satellites, and it is possible that measures of diameter may have been made in 1795 but not published.

Considering the accuracy of these measures (an accuracy far surpassing that of any contemporary observations), it is somewhat surprising that this form of micrometer was never systematically used in any sustained or important astronomical researches, although a number of instruments of the kind were made by Dollond. Probably the last example of its employment is an observation of the transit of Mercury (November 4, 1868) by Mr Mann, at the Royal Observatory, Cape of Good Hope {Monthly Notices R. A. S., vol. xxix. p. 197-209). The most important part, however, which this type of instrument seems to have played in the history of astronomy arises from the fact that one of them was in the possession of Bessel at Königsberg during the time when his new observatory there was being built. In 1812 Bessel measured with it the angle between the components of the double star 61 Cygni and observed the great comet of 1811. He also observed the eclipse of the sun on May 4, 1818. In the discussion of these observations {Königsberger Beobacht., Abth. 5, p. iv) he found that the index error of the scale changed systematically in different position angles by quantities which were independent of the direction of gravity relative to the position angle under measurement, but which depended solely on the direction of the measured position angle relative to a fixed radius of the object-glass. Bessel attributed this to non-homogeneity in the object-glass, and determined with great care the necessary corrections. But he was so delighted with the general performance of the instrument, with the sharpness of the images, and the possibilities which a kindred construction offered for the measurement of considerable angles with micrometric accuracy, that he resolved, when he should have the choice of a new telescope for the observatory, to secure some form of heliometer.

Nor is it difficult to imagine the probable course of reasoning which led Bessel to select the model of his new heliometer. Why, he might ask, should he not select the simple form of Dollond’s first type? Given the achromatic object-glass, why should not it be divided? This construction would give all the advantage of the younger Dollond’s object-glass micrometer and more than its sharpness of definition, without liability to the systematic errors which may be due to want of homogeneity of the object-glass; for the lenses will not be turned with respect to each other, but, in measurement, will always have the same relation in position angle to the line joining the objects under observation. It is true that the scale will require to be capable of being read with much greater accuracy than τ √< rσ th of an inch—for that, even in a telescope of 10 feet focus, would correspond with 2" of arc. But, after all, this is no practical difficulty,—for screws can be used to separate the lenses, and, by these screws, as in a Gascoigne micrometer, the separation of the lenses can be measured; or we can have scales for this purpose, read by microscopes, like the Troughton circles of Piazzi or Pond, or those of the Carey circle, with almost any required accuracy.

Whether Bessel communicated such a course of reasoning to Fraunhofer, or whether that great artist arrived independently at like conclusions, we have been unable to ascertain with certainty. The fact remains that before 1820 Fraunhofer had completed one or more of the five heliometers (3 inches aperture and 39 inches focus) which have since become historical instruments. In 1824 the great Königsberg heliometer was commenced, and it was completed in 1829.

To sum up briefly the history of the heliometer. The first application of the divided object-glass and the employment of double images in astronomical measures is due to Savary in 1743. To Bouguer in 1748 is due the true conception of measurement by double image without the auxiliary aid of a filar micrometer, viz., by changing the distance between two object-glasses of equal focus. To Dollond in 1754 we owe the combination of Savary’s idea of the divided object-glass with Bouguer’s method of measurement, and the construction of the first really practical heliometers. To Fraunhofer, some time not long previous to 1820, is due, so far as we can ascertain, the construction of the first heliometer with an achromatic divided object-glass, i.c., the first heliometer of the modern type.

Double-Image Micrometers with Divided Lenses.

Various micrometers have been invented besides the heliometer for measuring by double image. Ramsden’s dioptric micrometer consists of a divided lens placed in the conjugate focus of the innermost lens of the erecting eye-tube of a terrestrial telescope. The inventor claimed that it would supersede the heliometer, but it has never done anything for astronomy. Dollond claims the independent invention and first construction of asimilar instrument(Pearson's Practical Astronomy, vol. ii. p. 182). Of these and kindred instruments only two types have proved of practical value. Amici of Modena {Mem. Soc. Ital., xvii. (1815) pp. 344-359) describes a micrometer in which a negative lens is introduced between the eye-piece and the object-glass. This lens is divided and mounted like a heliometer object-glass; the separation of the lenses produces the required double image, and is measured by a screw. Dawes has very successfully used this micrometer in conjunction with a filar micrometer, and finds that the precision of the measures is in this way greatly increased {Monthly Notices, vol. xviii. p. 58, and Mem. R. A. S., vol. xxxv. p. 147).

In the improved form of Airy’s divided eye-glass micrometer {Mem. R. A. S., vol. xv. pp. 199-209), the rays from the objectglass pass successively through lenses as follows. [table]

The lens b is divided, and one of the segments is moved by a micrometer screw. The magnifying power is varied by changing the lens a for another in which p has a different value. The magnifying power of the eye-piece is that of a single lens of focus -^p.

In 1850 Valz pointed out that the other optical conditions could be equally satisfied if the divided lens were made concave instead of convex, with the advantage of giving a larger field of view {Monthly Notices, vol. x. p. 160).

The last improvement on this instrument is mentioned in the Report of the R. A. S. council, February 1865. It consists in the introduction by Simms of a fifth lens, but no satisfactory description has ever appeared. There is only one practical published investigation of Airy’s micrometer that is worthy of mention, viz., that of Kaiser {Annalen der Sternwarte in Leiden, iii. pp. 111-274). The reader is referred to that paper for an exhaustive history and discussion of the instrument. It is somewhat surprising that, after Kaiser’s investigations, observers should continue, as many have done, to discuss their observations with this instrument as if the screw-value were constant for all angles.

Steinheil {Journal Savant de Munich, 28th February 1843) describes a “heliomètre-oculaire” which he made for the great Pulkowa refractor, the result of consultations between himself and the elder Struve. It is essentially the same in principle as Amici’s micrometer, except that the divided lens is an achromatic positive instead of a negative lens. Struve {Description de Γ Observatoire Central de Pulkowa, pp. 196, 197) adds a few remarks to SteinheiΓs description, in which he states that the images have not all desirable precision,—a fault perhaps inevitable in all micrometers with divided lenses, and which is probably in this case aggravated by the fact that the rays falling upon the divided lens have considerable convergence. He, however, successfully employed the instrument in measuring double stars, so close as 1" or 2", and using a power of 300 diameters, with results that agreed satisfactorily amongst themselves and with those obtained with the filar micrometer. If Struve had employed a properly proportioned double circular diaphragm, fixed symmetrically with the axis of the telescope in front of the divided lens and turning with the micrometer, it is probable that his report on the instrument would have been still more favourable. This particular instrument has historical interest, having led Struve to some of those criticisms of the Pulkowa heliometer which ultimately bore such valuable fruit (see below).

Ramsden (Phil. Trans., vol. xix. p. 419) has suggested the division of the small speculum of a Cassegrain telescope and the production of double image by micrometric rotation of the semispecula in the plane passing through their axis. Brewster (Ency. Brit., 8th ed., vol. xiv. p. 749) proposes a plan on a like principle, by dividing the plane mirror of a Newtonian telescope. Again, in an ocular heliometer by Steinheil double image is similarly produced by a divided prism of total reflexion placed in parallel rays. But practically these last three methods are failures. In the last the field is full of false light, and it is not possible to give sufficiently minute and steady separation to the images; and there are of necessity a collimator, two prisms of total reflexion, and a small telescope through which the rays must pass; consequently there is great loss of light.

Micrometers Depending on Double Refraction.

To the Abbé Rochon (Jour, de Phys., liii., 1801, pp. 169-198) is due the happy idea of applying the two images formed by double refraction to the construction of a micrometer. He fell upon a most ingenious plan of doubling the amount of double refraction of a prism by using two prisms of rock-crystal, so cut out of the solid as to give each the same quantity of double refraction, and yet to double the quantity in the effect produced. The combination so formed is known as Rochon’s prism. Such a prism he placed between the object-glass and eye-piece of a telescope. The separation of the images increases as the prism is approached to the objectglass, and diminishes as it is approached towards the eye-piece.

Arago (Comptes Rendus, xxiv., 1847, pp. 400-402) found that in Rochon’s micrometer, when the prism was approached close to the eye-piece for the measurement of very small angles, the smallest imperfections in the crystal or its surfaces were inconveniently magnified. He therefore selected for any particular measurement such a Rochon prism as when fixed between the eye and the eye-piece (i.e., where a sunshade is usually placed) would, combined with the normal eye-piece employed, bring the images about to be measured nearly in contact. He then altered the magnifying power by sliding the field lens of the eye-piece (which was fitted with a slipping tube for the purpose) along the eye-tube, till the images were brought into contact. By a scale attached to the sliding tube the magnifying power of the eye-piece was deduced, and this combined with the angle of the prism employed gave the angle measured. If p" is the refracting angle of the prism, and n the magnifying power of the eye-piece, then p"∕n will be the distance observed. Arago made many measures of the diameters of the planets with such a micrometer.

Dollond (Phil. Trans., 1821, pp. 101-103) describes a doubleimage micrometer of his own invention in which a sphere of rock-crystal is substituted for the eye-lens of an ordinary eye-piece. 1 n this installment (figs. 31, 32) a is the sphere, placed in half-holes on the axis bb, so that when its principal axis is parallel to the axis of the telescope it gives only one image of the object. Ina direction perpendicular to that axis it must be so placed that when it is moved by rotation of the axis bb the separation of the images shall be parallel to that motion. The angle of rotation is measured on the graduated circle C. The angle between the objects measured is = r sin 20, where r is a constant to be determined for each magnifying power employed, and θ the angle through which the sphere has been turned from zero (i.e. , from coincidence of its principal axis with that of the telescope). The maximum separation is consequently at 45° from zero. The measures can be made on both sides of zero for eliminating index error. There are considerable difficulties of construction, but these have been successfully overcome by Dollond; and in the hands of Dawes (Mem. R. A. S., xxxv. p. 144 sq.) such instruments have done valuable service. They are liable to the objection that their employment is limited to the measurement of very small angles, viz., 13" or 14" when the magnifying power is 100, and varying inversely as the power. Yet the beautiful images which these micrometers give permit the measurement of very difficult objects as a check on measures with the parallel-wire micrometer.

The Modem Heliometer.

The Königsberg heliometer is represented in fig. 33. No part of the equatorial mounting is shown in the figure, as it resembles in every respect the usual Fraunhofer mounting. An adapter h is fixed on a telescopetube, made of wood, in Fraunhofer’s usual fashion. To this adapter is attached a flat circular flange h. The slides carrying the segments of the divided object-glass are mounted on a plate, which is fitted and ground to rotate smoothly on the flange h. Rotation is communicated by a pinion, turned by the handle c (concealed in the figure), which works in teeth cut on the edge of the flange h. The counterpoise w balances the head about its axis of rotation. The slides are moved by the screws a and b, the divided heads of which serve to measure the separation of the segments. These screws are turned from the eye-end by bevelled wheels and pinions, the latter connected with the handles a', b'. The reading micrometers e, /also serve to measure, independently, the separation of the segments, by scales attached to the slides; such measurements can be employed as a check on those made by the screws. The measurement of position angles is provided for by a graduated circle attached to the head. There is also a position circle, attached at m to the eye-end, provided with a slide to move the eye-piece radially from the axis of the telescope, and with a micrometer to measure the distance of an object from that axis. The ring which carries the supports of the handles a', b', c is capable of a certain amount of rotation on the tube. The weight of the handles and their supports is balanced by the counterpoise z. This ring is necessary in order to allow the rods to follow the micrometer heads when the position angle is changed. Complete rotation of the head is obviously impossible because of the interference of the declination axis with the rods, and therefore, in some angles, objects cannot be measured in two positions of the circle. The object-glass has an aperture of 6⅛ inches, and 102 inches focal length.

There are three methods in which this heliometer can be used.

First Method.— One of the segments is fixed in the axis of the telescope, and the eye-piece is also placed in the axis. Measures are made with the moving segment displaced alternately on opposite sides of the fixed segment.

Second Method.— One segment is fixed, and the measures are made as in the first method, excepting that the eye-piece is placed symmetrically with respect to the images under measurement. For this purpose the position angle of the eye-piece micrometer is set to that of the head, and the eye-piece is displaced from the axis of the tube (in the direction of the movable segment) by an amount equal to half the angle under measurement.

Third Method.— The eye-piece is fixed in the axis, and the segments are symmetrically displaced from the axis each by an amount equal to half the angle measured.

Of these methods Bessel generally employed the first because of its simplicity, notwithstanding that it involved a resetting of the right ascension and declination of the axis of the tube with each reversal of the segments. The chief objections to the method are that, as one star is in the axis of the telescope and the other displaced from it, the images are not both in focus of the eye-piece, and the rays from the two stars do not make the same angle with the optical axis of each segment. Thus the two images under measurement are not defined with equal sharpness and symmetry. The second method is free from the objection of non-coincidence in focus of the images, but is more troublesome in practice from the necessity for frequent readjustment of the position of the eye-piece. The third method is the most symmetrical of all, both in observation and reduction; but it was not employed by Bessel, on the ground that it involved the determination of the errors of two screws instead of one. On the other hand it is not necessary to reset the telescope after each reversal of the segments.

When Bessel ordered the Königsberg heliometer, he was anxious to have the segments made to move in cylindrical slides, of which the radius should be equal to the focal length of the object-glass. Fraunhofer, however, did not execute this wish, on the ground that the mechanical difficulties were too great.

Wichmann states (Konigsb. Beobach., xxx. p. 4) that Bessel had indicated, by notes in his handbooks, the following points which should be kept in mind in the construction of future heliometers:— (1) The segments should move in cylindrical slides; x (2) the screw should be protected from dust; (3) the zero of the position circle should not be so liable to change; (4) the distance of the optical centres of the segments should not change in different position angles or otherwise; (5) the points of the micrometer screws should rest on ivory plates; (6) there should be an apparatus for changing the screen.

The elder Struve, in describing the Pulkowa heliometer, made by Merz in 1839 on the model of Bessel’s heliometer, submits the following suggestions for its improvement: —(1) to give automatically to the two segments simultaneous equal and opposite movement; and (2) to make the tube of brass instead of wood; to attach the heliometer head firmly to this tube; to place the eye-piece permanently in the axis of the telescope; and to fix a strong cradle on the end of the declination axis, in which the tube, with the attached head and eye-piece, could rotate on its axis.

Both suggestions are important. The first is originally the idea of Dollond (fig. 29); its advantages were overlooked by his son (description of fig. 30), and it seems to have been quite forgotten till resuggested by Struve. But the method is not available if the separation is to be measured by screws; it is found, in that case, that the direction of the final motion of turning of the screw must always be such as to produce motion of the segment against gravity, otherwise the ‘ ‘ loss of time” is apt to be variable. Thus the simple connexion of the two screws by cog-wheels to give them automatic opposite motion is not an available method unless the separation of the segments is independently measured by scales.

Struve’s second suggestion has been adopted in nearly all succeeding heliometers. It permits complete rotation of the tube and measurement of all angles in reversed positions of the circle; the handles that move the slides can be brought down to the eye-end, inside the tube, and consequently made to rotate with it; and the position circle may be placed at the end of the cradle next the eyeend where it is convenient of access. Struve also points out that by attaching a fine scale to the focussing slide of the eye-piece, and knowing the coefficient of expansion of the brass tube, the means would be provided for determining the absolute change of the focal length of the object-glass at any time by the simple process of focussing on a double star. This, with a knowledge of the temperature of the screw or scale and its coefficient of expansion, would enable the change of screw value to be determined at any instant. Or, if we suppose the temperature of the instrument to be the same in all its parts, the changed scale value becomes simply a function of the reading of the focal scale.

It is probable that the Bonn heliometer was in course of construction before these suggestions of Struve were published or discussed, since its construction resembles that of the Königsberg and Pulkowa instruments. Its dimensions are similar to those of the former instrument. Bessel, having been consulted by the celebrated statesman Sir Robert Peel, on behalf of the Radcliffe trustees, as to what instrument, added to the Radcliffe Observatory, would probably most promote the advancement of astronomy, strongly advised the selection of a heliometer. The order for the instrument was given to the Repsolds in 1840, but “various circumstances, for which the makers are not responsible, contributed to delay the completion of the instrument, which was not delivered before the winter of 1848.” The building to receive it was commenced in March 1849 and completed in the end of the same year. This splendid instrument has a superb object-glass of 7⅜ inches aperture and 126 inches focal length. The makers availed themselves of Bessel’s suggestion to make the segments move in cylindrical slides, and of Struve’s to have the head attached to a brass tube; the eye-piece is set permanently in the axis, and the whole rotates in a cradle attached to the declination axis. They provided a splendid, rigidly mounted, equatorial stand, fitted with every luxury in the way of slow motion, and scales for measuring the displacement of the segments were read by powerful micrometers from the eye-end. It is somewhat curious that, though Struve’s second suggestion was adopted, his first was overlooked by the makers. But it is still more curious that it was not afterwards carried out, for the communication of automatic symmetrical motion to both segments only involves a simple alteration previously described. But, as it came from the hands of the makers in 1849, the Oxford heliometer was incomparably the most powerful and perfect instrument in the world for the highest order of micrometric research. It so remained, unrivalled in every respect, till 1873; it remains still, optically, the most powerful heliometer in the world; and, with a few alterations, it might almost rival the most recent instruments in practical convenience and accuracy. These alterations, all of which could be made without great difficulty, are the following :—

(a) Beyond the automatic symmetrical motion above-described, the instrument should be fitted with means for adjusting the screens from the eye-end (see footnote 6 in last column).

(δ) The arrangement of the scales should be changed. At present both scales are read separately by separate micrometers, each relative to a separate fiducial line. What the observer requires is the difference of the readings of the two scales, and this can obviously be most quickly and accurately obtained if the edges of the two scales are brought together, and both are read, relatively to each other, by the same micrometer.

(c) The unsatisfactory motion in position angle should be replaced by the action of a pinion (attached to the cradle) in the teeth of a λvheel (attached to the tube). (d) The position circle should be read by telescopes or microscopes attached to the cradle, and accessible from the eye-end.

(e) It would add greatly to the rapidity of work and the ease of the observer if a small declination circle were attached to the crosshead, capable of being read from the eye-end.

As the transit of Venus of 1874 approached, preparations were set on foot by the German Government in good time; a commission of the most celebrated astronomers was appointed, and it was resolved that the heliometer should be the instrument chiefly relied on. The four long-neglected small heliometers made by Fraunhofer were brought into requisition. Fundamental alterations were made upon them:—their wooden tubes were replaced by tubes of metal; means of measuring the focal point were provided; symmetrical motion was given to the slides; scales on each slide were provided instead of screws for measuring the separation of the segments, and both scales were read by the same micrometer microscope; a metallic thermometer was added to determine the temperature of the scales. These small instruments have since done admirable work in the hands of Schur, Hartwig, Kustner, and Elkin.

The Russian Government ordered three new heliometers (each of 4 inches aperture and 5 feet focal length) from the Repsolds, and the design for their construction was superintended by Struve, Auwers, and Winnecke, the last-named making the necessary experiments at Carlsruhe. Fig. 34 represents the type of instrument which re-

reading the screws or even the heads from the eye-end. Bessel’s practice was to unclamp in declination, lower and read off the head, and then restore the telescope to its former declination reading, the clockwork meanwhile following the stars in right ascension. The setting of both lenses symmetrically would, under such circumstances, be very tedious.

suited from their labours. The brass tube, strengthened at the bearing points by strong truly-turned collars, rotates in the castiron cradle q attached to the declination axis, a is the eye-piece fixed iu that axis, b the micrometer for reading both scales.

c, d are telescopes for reading the position circle p, e the handle for quick motion in position angle, f the slow motion in position angle, g the handle for changing the separation of the segments by acting on the bevel-wheel çf (fig. 35). h is a milled head connected by a rod with h' (fig. 35), for the purpose of interposing at pleasure the prism τr in the axis of the reading micrometer; this enables the observer to view the graduations on the face of the metallic thermometer ττ (composed of a rod of brass and a rod of zinc), i is a milled head connected with the wheel i'i' (fig. 35), and affords the means of placing the screen s (fig. 34), counterpoised by w over either half of the object-glass, k clamps the telescope in declination, n clamps it in right ascension, and the handles m and I provide slow motion in declination and right ascension respectively.

The details of the interior mechanism of the “head” will be almost evident from fig. 35 without description. The screw, turned by the wheels at g', acts in a toothed arc, whence, as shown in the figure, equal and opposite motion is communicated to the slides by the jointed rods V, V. The slides are kept firmly down to their bearings by the rollers r, r, r, τ, attached to axes which are, in the middle, very strong springs. Sideshake is prevented by the screws and pieces k, k, k, k. The scales are at η, n; they are fastened only at the middle, and are kept down by the brass pieces t, t.

A similar heliometer was made by the Repsolds to the order of Lord Lindsay for his Mauritius expedition in 1874. It differed only from the three Russian instruments in having a mounting by the Cookes in which the declination circle reads from the eye-end. This instrument was afterwards most generously lent by Lord Lindsay to Gill for his expedition to Ascension in 1877.

These four Repsold heliometers proved to be excellent instruments, easy and convenient in use, and yielding results of very high accuracy in measuring distances. Their slow motion in position angle, however, was not all that could be desired. When small movements were communicated to the handle e (fig. 34) by the tangent screw f, acting on a small toothed wheel clamped to the rod connected with the driving pinion, there was apt to be a torsion of the rod rather than an immediate action. Thus the slow motion would take place by jerks instead of with the necessary smoothness and certainty. When the heliometer part of Lord Lindsay’s heliometer was ac quired by Gill in 1879, he changed the manner of imparting the motion in question. A square toothed racked wheel was applied to the tube at τ (fig. 34). This wheel is acted on by a tangent screw whose bearings are attached to the cradle; the screw is turned by means of a handle supported by bearings attached to the cradle, and coming within convenient reach of the observer’s hand. The tube turns smoothly in the racked wheel, or can be clamped to it at the will of the observer. This alteration and the new equatorial mounting have been admirably made by Grubb; the result is completely successful. The instrument so altered has been in constant use at the Cape Observatory since March 1881 in determining the parallax of the more interesting southern stars.

Still more recently the Repsolds have completed a new heliometer for Yale College, New Haven, United States. The object-glass is of 6 inches aperture and 98 inches focal length. The mounting, the tube, objectivecell, slides, &c., are all of steel. The instrument is shown in fig. 36. The circles for position angle and declination are read by micrometer microscopes illuminated by the lamp I.; the scales are illuminated by the lamp I. T is part of the tube proper, and turns with the head. The tube V, on the contrary, is attached to the cradle, and merely forms a support for the finder Q, the handles at f and p, and the moving ring P. The latter gives quick motion in position angle; the handles at p clamp and give slow motion in position angle, those at f clamp and give slow motion in right ascension and declination. a is the eye-piece, b the handle for moving the segments, c the micrometer microscope for reading the scales and scale micrometer, d the micrometer readers of the position and declination circles, e the handle for rotating the large wheel E which carries the screens. The hour circle is also read by microscopes, and the instrument can be used in both positions (tube preceding and following) for the elimination of the effect of flexure on the position angles.

There is very little left to criticize in this instrument. It embraces the results of all knowledge and experience on the subject to the present time. In one point, however, modern heliometers have a disadvantage compared with the older forms. A great advance in accuracy was, no doubt, made when the screw was abandoned as a means both of moving and measuring the displacement of the slides. But it is obviously much quicker to read and record the indication of one screw-head than to bisect two or four scale-divisions and enter the corresponding readings. Auwers, in his researches on the parallax of 61 Cygni, was able, with the Königsberg heliometer, to make forty pointings in about an hour; it is quick work to make sixteen pointings (reading two divisions on each scale at each pointing) with the modern heliometer in the same time, when attention is paid to the desirable reversals of the segments and of the position circle and the resettings in right ascension and declination. Now time during opportunities of good definition (or otherwise) is too precious to be sacrificed, if it can be saved even by ten-fold labour afterwards. Carrington has suggested the possible use of photography to record the readings of astronomical circles, and since his day “Swan lights” and “sensitive dry plates” seems to have brought his suggestion within the range of practice. A special microscope, fitted with an aplanatic photographic objective and a well-contrived carrier, might be made automatically to expose a different part of a narrow dry plate, by mere pressure or turning of a button after each bisection. Each plate might easily record the sixteen bisections which constitute a complete measure of two pairs of stars (as in a parallax determination). As it is only necessary to photograph two divisions of each scale, the photographic enlargement of these divisions need only be limited by the sensitiveness of the plates and the power of the illumination to produce a picture in a conveniently short space of time. Tire plates employed at night could be conveniently developed the following day and measured with a special apparatus at any convenient time and with almost any desired accuracy. Were such a system reduced to practice it would at least double, perhaps treble, an observer’s possible output of work.

Gill has introduced a powerful auxiliary to the accuracy of heliometer measures in the shape of a reversing prism placed in front of the eye-piece, between the latter and the observer’s eye. If measures are made by placing the image of a star in the centre of the disk of a planet, the observer may have a tendency to do so systematically in error from some acquired habit or from natural astigmatism of the eye. But by rotating the prism 90° the image is presented entirely reversed to the eye, so that in the mean of measures made in two such positions personal error is eliminated. Similarly the prism may be used for the study and elimination of personal errors depending on the angle made by a double star with the vertical. The best plan of mounting such a prism has been found to be the following. Z', Z 2 (fig. 37) are the eye lens and field lens respectively of a Merz positive eye-piece. In this construction the lenses are much closer together and the diaphragm for the eye is much farther from the lenses than in Ramsden’s eye-piece. The prism p is fitted accurately into brass slides (care has to be taken in the construction to place the prism so that an object in the centre of the field will so remain when the eye-piece is rotated in its adapter). There is a collar, clamped by the screw at S, which is so adjusted that the eye-piece is in focus when pushed home, in its adapter, to this collar. The prism and eye-piece are then rotated together in the adapter.

On the theory of the heliometer and its use consult Besseι, Astronomische Untersuchungen, vol. i.; Hansen, Ausführliche Methode mit dem Fraunhoferschen Heliometer anzustellen, Gotha, 1827; Chauvenet, Spherical and Practical Astronomy, vol. ii. pp. 403-436, Philadelphia and London, 1876; Seeiiger, Theorie des Heliometers, Leipsic, 1877; Lindsay and Gill, Dunechi Publications, vol. ii., Dunecht (for private circulation), 1877; Gill, Memoirs of the Royal Astronomical Society, vol. xlvi. pp. 1-172.

Micrometers which Involve the Employment of the Diurnal Motion.

Advantage is often taken of the diurnal motion to measure the relative positions of stars. The varieties of reticules and scales that have been employed are far too numerous even for mention in detail. The following are the means and methods by which most work has been done, and they are typical of all the others. In the focus of his meridian telescope Lacaille had a brass diaphragm in which was cut a hole, having parallel, sharp, straight edges of the shape shown in fig. 38. The longer diagonal of the rhomboid so formed was at right angles, and the shorter parallel, to the diurnal motion. The method of observation consisted in noting the instant of ingress and egress of each star which presented itself. The mean of the times thus noted for each star gave the time of its transit over the imaginary line ab, whilst the difference between the instant of ingress and that of egress (converted into arc by the known approximate declination) gave the length of the chord traversed by the star parallel to the imaginary line cd. Hence (the dimensions of the rhomboid being known) the difference of the star’s declination from the line cd became known (the observer was of course careful to note whether the star passed to north or south of cd). Thus every star that crossed the field was observed, all their right ascensions were referred to the clock-time of passing ab, and all their declinations to that of cd; hence their mutual differences of right ascension and declination were known. In this way, in the short space of ten months, Lacaille observed nearly ten thousand stars at the Cape of Good Hope in the years 1751-52. s Fraunhofer’s ring micrometer consists of a ring of steel, very truly turned, mounted in a hole cut in a circular disk of glass. The ring is placed in the focus of a telescope, and viewed by a positive eye-piece. The observer notes the instants when the two objects enter and emerge from each side of the ring. The only data required for computing the difference of right ascension and declination of the two objects are the times above mentioned, the diameter of the ring, and the approximate declination of one of the objects. The latter is always known. The methods of determining the former and of reducing the observations are to be found in every work on practical astronomy. The ring micrometer has been largely used in observing comets.

Argelander, in making his famous survey of the northern heavens, ® employed a semicircle of glass, the straight edge of which (truly ground) crosses the centre of the field of view at right angles to the diurnal motion of the stars. Differences of right ascension were directly observed at this edge, whilst differences of declination were noted by strong dark lines drawn at right angles to the edge at each 10' of arc. A telescope of 3 inches aperture with a magnifying power of 10 diameters commanded a field of 3° 20' in declination. One observer was placed at the telescope, another at the clock. The telescope observer marked the instant when the star touched the glass edge, by calling sharply the word “eight” or “nine,” &c., which also indicated the magnitude; the same observer also noted and recorded the reading of the declination scale (where the star crossed it), without removing his eye from the telescope. The clock observer wrote down the magnitude called out by the telescope observer, and the instant by the clock when the word was given. The two records were then compared after the observations of the night were over. In this way Schönfeld and Krueger (Argelander’s assistants) observed and catalogued about three hundred thousand stars. The probable error of an observation is about ±0 ’ 7 sec. in right ascension and ±0' ’ 4 in declination.

Bond employed a very similar arrangement, differing only from Argelander’s in having the scale cut on a sheet of transparent mica τo ⅛ τ th of an inch in thickness. Very oblique illumination was employed, and the divisions and figures were seen bright upon a dark background. The range of declination was limited to 10', the scale was divided to 10", the right ascensions were observed by chronographic registration, and the great refractor of the Cambridge U. S. Observatory (with an aperture of 15 inches and power of 140) was employed. The probable errors in right ascension and declination were found to be ±0 , 06 sec. in right ascension and ±0" - 6 in declination—results of marvellous accuracy considering the amount of work accomplished in a short time and the faintness (eleven to twelve magnitudes) of the stars observed.

We were on the point of criticizing Bond’s programme as somewhat too ambitious for realization without cooperation (it would take about twenty-six thousand hours of observing to carry out the scheme for the northern hemisphere alone) when we received from Peters of Clinton, U. S., the first twenty maps of a series which will include the whole of the sky between declination + 30° and - 30°. If we consider that all the stars in these maps of the eleventh magnitude or brighter have been observed by a method similar to Bond’s, that the enormous additional labour of frequent revision has been undertaken, and all stars visible with a power of 80 in a telescope of 13 inches aperture (about fourteenth magnitude) have been filled in by alignment, and that all this results from the unaided labour of a single observer, we find that our ideas of the possible have to be modified, when such a man undertakes a work with persistent unity of purpose for more than twenty years (1860-83).

There is an ingenious mode of registering differences of declination that has been in use at the Berlin Observatory since 1879, and is described by Dr Knarre in the Zeitschrift für Instrumentenkunde for July 1881. The instrument is called a declinograph. It has a web moved in declination by a quick-acting screw; the same screw carries a travelling pricker or point. The observer having bisected a star by the wire has simply to compress an india-rubber ball connected by a flexible tube with a thin metal box made on the principle of the vacuum chamber of an aneroid barometer. The expansion of this box so produced brings a sheet of paper in contact with two prickers, one the movable pricker before mentioned, the other a fixed pricker. The action of the vacuum box also automatically shifts the paper (a long roll) by a small quantity at each observation, so that successive observations are recorded in regular order. To obtain the observed differences of declination it is then only necessary to measure with a glass scale (divided for the special telescope to 10") the distance of each record of the moving pricker from the fixed pricker. It is found, with this declinograph on the Berlin equatorial, that the observed declinations have only a probable error of ±0" - 9. It is obvious that by using a chronograph in conjunction with this instrument both right ascensions and declinations could be recorded with great accuracy and rapidity.

Miscellaneous Micrometers.

Clausen in 1841 (Ast. Nach., No. 414) proposed a form of micrometer consisting of a divided plate of parallel glass placed within the cone of rays from the object-glass at right angles to the telescope axis. One half of this plane remains fixed, the other half is movable. When the inclination of the movable half with respect to the axis of the telescope is changed by rotation about an axis at right angles to the plane of division, two images are produced. The amount of separation is very small, and depends on the thickness of the glass, the index of refraction, and the focal length of the telescope. Secchi (Comptes Rendus, xli., 1855, p. 906) gives an account of some experiments with a similar micrometer; and Porro (Comptes Rendus, xli. p. 1058) claims the original invention and construction of such a micrometer in 1842. Clausen, however, has undoubted priority. Helmholtz in his “Ophthalmometer” has employed Clausen’s principle, but arranges the plates so that both move symmetrically in opposite directions with respect to the telescope axis. Should Clausen’s micrometer be employed as an astronomical instrument it would be well to adopt the improvement of Helmholtz.

Burton and Grubb (Monthly Notices, vol. xli. p. 59), after calling attention to Lamont’s paper (Jahrbuch der K. S. b. München, p. 187) and Littrow’s paper (Proc, of Vienna Acad, of Sciences, vol. xx. p. 253) on a like subject, proceed to describe a most ingenious form of “Ghost Micrometer,” in which the image of a fine line or lines ruled in (or rather cut through) a silver film deposited on glass is formed at the common focus of an object-glass and eye-piece of a telescope. A faint light being thrown on the outside of the silvered plate, there appear bright lines in the field of view. We have not had an opportunity of testing this, nor Grubb’s more recent models; but, should it be found possible to produce such images satisfactorily, without distortion and with an apparatus convenient and rigid in form, such micrometers will probably supersede the filar micrometer. Their absolute freedom from diffraction, the perfect control of the illumination and thickness of the lines, and the accuracy with which it will be possible to construct scales for zone observations will be important features of the new method.

For the use of micrometers in connexion with the microscope, see p. 277 of the present volume.