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MICROMETER (from Gr. wcp6c, small, jA...

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Originally appearing in Volume V18, Page 390 of the 1911 Encyclopedia Britannica.
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MICROMETER (from Gr. wcp6c, small, jArpov, a measure), 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 (q.v.), 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.' Michael Maestlin in 1579 determined the relative positions of eleven stars in the Pleiades (Historia coelestis Lucii Baretti, Augsburg, 1666), and A. Winnecke has shown (Monthly Notices R.A.S., xxxix. 146) that the probable error of these measures amounted to about 21.2 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 ' Grant, History of Physical Astronomy, p. 449. 2 This is an astonishing accuracy when the difficulty of the objects is considered. Few persons can see with the naked eye—much less measure—more than six stars of the Pleiades, although all the stars measured by Maestlin have been seen with the naked eye by a few individuals of exceptional powers of eyesight.inventor of the micrometer. William Crabtree, a friend of his, taking a journey to Yorkshire in 1639 to see Gascoigne, writes thus to his friend Jeremiah 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 Richard Townley of Lancashire, who exhibited it at the meeting of the Royal Society held on the 25th of 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 loo 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 John 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 ' the following comparison between the results of Gascoigne's measurements of the sun's semi-diameter and the computed results from modern determinations: Gascoigne. Conn. d. temps. October 25 (o.s.) .. .. 16' II"or Io 16' Io"•o 31 .. 16' II" 16' II"•4 December 2 . . . . 16'24" 16' 16"•8 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".3.3 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 net-work 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.4 In the Phil. Trans. (1667), No. 21, p. 373, Adrien 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 Townley and 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 Delambre, Hist. ast. moderne, ii. 590. 4 Mem. acad. des sciences (17.17), pp. 78 seq. 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 2nd of 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 Felice Fontana of Florence (Saggio del real gabinetto di fisica e di storia naturale, 1755) first proposed the use of spider webs in micro-meters,' but it was not till the attention of Troughton had been directed to the subject by Rittenhouse that the idea was carried into practice .2 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 .3 The surrounding silver was then dissolved by nitric acid, and a platinum wire of extreme fineness remained. But experience small 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,4 Wren, Smeaton, Cassini, Bradley, Maskelyne, Herschel, Arago, Pearson, .Bessel, Struve, Dawes, &c., 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 pointed 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), lxxi, 50o. It was used by him in his earliest observations of double stars (1779–1783); but, even in his 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 ft. 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 to ft. 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 46o the scale was a quarter of an inch for every second. The Modern 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 ' In 1782 (Phil. Trans. lxxii. 163) Sir W. Herschel writes:—" I have in vain attempted to find lines sufficiently thin to extend them across the centres of the stars, so that their thickness might be neglected." It is a matter of regret that Fontana's suggestion was unknown to him. 2 J. T. Quekett in his Treatise on the Microscope ascribes to Ramsden the practical introduction of the spider web in micrometers. The evidence appears to be in favour of Troughton. 3 Phil. Trans. (1813), pp. 114–118. 4 Dr Hooke made the important improvement on Gascoigne's micrometer of substituting parallel hairs for the parallel edges of its original construction (Hooke's Posthumous Works, p. 497). ' Herschel and South (Phil. Trans., 1824, part iii. p. to) claim that 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 micrometer represented in figs. I, 2, 3 is due to Troughton. Fig. t is a horizontal section in the direction of the axis of the tele- scope. The eyepiece ab consists of two plano-convex 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 b. This is known as Ramsden's eye-piece, having been made originally by him. The eyepiece 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 1, 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, 1, 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 too equal parts on the drums u and v, so that, by estimation, the reading can easily be carried to rbth 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 (t) being cemented in a fine groove cut in the inner fork k, the other (s) in a similar groove cut in the outer fork 1. 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 it or the fixed wire, and without rubbing on any part of the brass-work. 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 micrometer by Troughton, fitted to their 5 ft. equatorial telescope, is the first position micrometer constructed capable of measuring position angles to t' of arc. 6 So far as we can ascertain, the first telescope of large size driven by clockwork was the 9-in. equatorial made for Struve at Dorpat by Fraunhofer; it was completed in 1825. The original idea appears to be due to Claude Simeon Passemant (Mem. Acad., Paris, 1746). In 1757 he presented a telescope to the king, so accurately driven by clockwork that it would follow a star all night long. Spider Web. S 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 communica- ting motion to the slides, by attaching the screws perman- ently 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. Troughton's form. Fraunhofer's Filar Micrometer.—The micrometer represented in fig. 5 I 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 M the slow motion in position angle. L, L 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 L, L, 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 p. 385). 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 web " may be rendered strictly parallel with the movable one. Another web is fixed parallel to the axis of the screw, as nearly as possible in the same plane with it and passing through the axis of rotation of the micro-meter. For the internal structural details of the micrometer the reader is referred to the article " Micrometer " in the 9th edition of the Encyclopaedia Britannica. To use the instrument, it is well first to adjust the web moved by the screw S, so that its point of intersection with the web (commonly called the " position-web "), which is parallel to the axis of the screw, shall be nearly coincident with the axis of rotation of the micrometer box. For this purpose it is only necessary to direct the telescope to some distant object, bisect that object with the movable wire, and read the number of revolutions and parts .of a revolution of the screw; now reverse the micrometer box 18o° and repeat the observation; the mean of the two readings will be the point required. Now direct the telescope to a star near the equator and so that the star's image in its diurnal motion shall pass across the intersection of the two webs which mark the axis of rotation of the micrometer box. Then, as the diurnal motion causes the star-image to travel away from the axis of rotation, the micrometer box is rotated till the image of the star when at a considerable distance from the axis is bisected by the position-web. The micrometer is now clamped in position-angle by the clamp C, the star again brought back to the axis, and delicate adjustment given in position-angle by the slow-motion screw M, till the star-image remains bisected whilst it traverses the whole length of the position-web by the diurnal motion only. This determines the reading of the position-circle corresponding to position-angle 90` or 2700.2 1 When it is remembered that the measurements of the Struves, Dembowski, Secchi, the Bonds, Maclear and of most modern European astronomers have been made with Fraunhofer or Merz micrometers it is not too much to say that fig. 5 represents the instrument with which a half of the astronomical measurements of the 19th century were made. 2 For the corrections applicable to measures of position-angle in different hour angles, on account of errors of the equatorial instrument and of refraction, see Chauvenet's Practical and Spherical Astronomy, ii. 392 and 450. The position-angles of double stars are reckoned from north through east, the brighter star being taken as origin. To observe the position-angle of a double star it is only necessary to turn the position-web so that it shall be parallel to the line joining the centres of the components of the double star. To test this parallelism the single web must be made to bisect the images of both components simultaneously, as in fig. 6, because it is evident that if the two components of the double star are not exactly equal in magnitude, there will be great tendency to systematic error if the web is 6. is placed on one side or other of the stars. To avoid such error Dawes used double wires, not spider webs, placing the image of the star symmetrically between these wires, as in fig. 7, and believed that by the use of wires, much thicker than spider webs, the eye could estimate more accurately the symmetry of the star-images with respect to the wires. Other astronomers use the two distance-measuring webs, placed at a convenient distance • apart, for position wires. This plan has the advantage of permitting easy adjustment of the webs to such a distance apart as may be found most suitable for the particular observation, but has the disadvantage that it does not permit the zero of the position-circle to be determined with FIG. the same accuracy; because, whilst by means of the screws 7 (fig. 5) the eyepiece can be made to follow the star for a considerable distance along a position-web parallel to the screw, the bisection of the web by a star moving by the diurnal motion at right angles to the micrometer screw can only be followed for a limited distance, viz. the field of the eyepiece. But, as the angle between the position-web and the distance-webs is a constant, the remedy is to determine that angle (always very nearly a right angle) by any independent method and employ the distance-webs as position-webs in the way described, using the position-web only to determine the instantaneous index error of the position-circle. To measure distances with the Fraunhofer micrometer, the position-circle is clamped at the true position-angle of the star, and the telescope is moved by its slow motions so that the component A of the star is bisected by the fixed wire; the other component B is then bisected by the web, which is moved by the graduated head S. Next the star B is bisected by the fixed web and A by the movable one. The difference between the two readings of S is then twice the distance between A and B. The great improvement now introduced into all the best micro-meters is to provide a screw s, which, not as in the Fraunhofer micro-meter, moves only one of the wires, but which moves the whole micrometer box, i.e. moves both webs together with respect to the star's image in the direction of the axis of the screw. Thus the fixed wire can be set exactly on star A by the screw s, while star B is simultaneously bisected by the movable wire, or vice versa, 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 moving a micrometer 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 extensive labours among the double e stars, used to complete their bisections of the fixed .p wire by a pressure of the finger on the side of the tube, one is puzzled whether more to wonder at such poor adaptation of means to ends or the patience and skill which, with such means, led to such results.' Dawes, who employed a micrometer of the English type (figs. 1,'2 and 3), used to bolt the head of one of the screws, and the instrument was provided with a slipping piece, giving motion to the micrometer by screws acting on two slides, one in right ascension, the other in declination, so that " either of the webs can be placed upon either component of a double star with ease and certainty " (Mem. R.A .S. xxxv. 1 9). The micrometer shown in fig. 8 was made by Repsolds for the Cape Observatory. Fig. 9 represents the same 3 Professor Watson used to say, " After all the most important part of a telescope is the man at the small end." 384 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 f (fig. 8), 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 I', 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. 9, but only its mode of attachment (X, fig. 9) in fig. 8. The teeth of the pinion z, fig. 9, are cut on the axis of the micrometer screw. The drum d and its attached tooth wheel are ground to turn smoothly on the axis of the screw. The 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. The divisions of both drums are conveniently read, simultaneously, by the lens e ; at night the lamp which illuminates the webs and the position-circle also illuminates the drum-heads (see on illumination p. 385). aaaa is the web-frame (fig. 9), fry is a single rod consisting of two cylinders accurately fitting in the ends of the micro-meter box, the larger cylinder being at #. There is a hole in the web-frame which smoothly fits the larger cylinder at 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. ft 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 s, passes loosely through the web-frame at s', is tapped into the frame at I'', and its end rests on a flat hardened surface at Rotation of the web-frame about fry 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 vv, that on the upper side (fig. 9) touches lightly on the inner surface of the lid of the box. Such rotation tan obviously be controlled within limits that need not be further considered. But freedom of rotation in the plane of the paper (fig. 9) is only prevented by good fitting of the holes fl' -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 O"•14. This corresponds, in the Cape instrument, with an excess of the diameters of the holes over those of the cylinders of about ;I*WSth of an inch—a quantity so small as to imply good workman-ship, 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 would 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 AO measures index error can 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. 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. 9) by holes n, 0 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 +t a sliding rod, and towards B 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 Lox relative to the plate f, 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 this pressure is regulated by the screw z'. The short screw whose divided milled head is v shifts the zero of the micrometer by pushing, without turning, the short sliding rod whose flat end forms the point d'appui of the micrometer screw at i'. The pitch of the screw a is the same as that of the measuring screw (5o 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 rr, which is secured to the bottom of the box by the screws p. The three movable webs are attached to the projections as on the frame aa. The plane surfaces TT and XX 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 T and X, so that the movable wires shall almost, but not quite, touch the surface r. The varnish to fix the webs is applied, not on the surface r 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 Repsolds' 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. Another excellent micrometer, originally based on a model by Clark of Cambridge, Massachusetts, has been largely used by Burn-ham and others in America. The form, as constructed by Warner and Swasey for the 4o-in. Yerkes telescope, is shown in figs. 10 and 11. The micrometer box, and of course with it the whole system of spider webs, is moved by the screw s, whilst the measuring web is independently moved by the screw S. The other parts of the instrument will be readily understood from the figure without further explanation. The method of counting the total number of revolutions gives more friction and is less convenient than Repsolds', and no provision seerps to he made for illuminating the micrometer head in the practical and convenient plan adopted by Repsolds. Repsolds' more recent form of the ppider-line micrometer (since ' The marks of varnish so applied will be seen in fig. 9. 1893) for large telescopes is shown in fig. 12. Quick motion in position-angle for rough setting or for the measurement of close double stars is given by the large ring R. The micrometer is clamped in position-angle by the screw K and slow motion in position-angle is given by the screw p. The small drum-head T opposite the micro-meter head S turns a screw which acts upon a short cylinder that cannot turn but can move only in the direction of the axis of the micrometer screw. The end-plane of this cylinder receives the pressure of the micrometer screw, so that by turning the small drum-head the coincidence-reading of the movable web with the fixed web can be changed, and thus any given angle can be measured with different parts of the micrometer screw in order to eliminate the effects of periodic error of the screw. The electric lamp a gives illumination of the webs in a dark field, nearly in the manner described for the Cape transit circle micrometer; the intensity of illumination is regulated by a carbon-resistance controlled by the screw b. The lamp c illuminates the drum-head and also, by reflection, the portions of the position-circle which come under the microscopes d and e. The head f is a switch which enables the observer to illuminate lamp a or c at pleasure. These lamps, although shown in the figure, are in reality covered so as not to shine upon the observer's eye. The illumination of the field is given by a lamp near the object glass, controlled by a switch near the micrometer. Repsolds in more recent micrometers under construction give a second motion to the eyepiece at right angles to the axis of the micrometer screw; this enables the observer to determine the zero Instruments have been invented by Alvan Clark and Sir Howard Grubb for measuring with the spider-line micrometer angles which are larger than the field of view of the eyepiece. In both cases two eyepieces are employed, one to view each separate web. One draw-back to this form of instrument is that the two webs cannot be viewed simultaneously, and therefore the observer must rely on the steadiness of rate of the clockwork and uniformity in the conditions of refraction whilst the eye is moved from one eyepiece to the other. Clark's micrometer was exhibited at the June meeting of the Royal Astronomical Society in 1859 (Monthly Notices, R.A.S., vol. xix.). Grubb's duplex micrometer is described in the 9th edition of the Encyclopaedia Britannica. Some examples of use of the latter are given by Professor Pritchard (Mem. R.A.S. xlvii. 4-12), who estimates the accuracy attainable with the duplex micrometer as equal to that of the heliometer; but as few measures of permanent value have been made with the instrument, and those made exhibit an accuracy far inferior to that of the heliometer, it is unnecessary to describe the instrument here in greater detail. The Reading Micrometer-Microscope.—Micrometers used for sub-dividing the spaces on graduated circles and scales have, in general, only a siisgle pair of cross-webs or parallel webs moved by a single screw. The normal form of the apparatus is shown in figs. 13 and 14. A C is the objective, D the micrometer box, E the graduated head of the screw, G the milled i head by which the screw cc is turned, A an t eyepiece sliding in a tube B, as (fig. 14) 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. 14)—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. 14 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. 14 are replaced by parallel webs embracing the division (fig. 15). 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 measures of the space between two adjacent divisions of the scale in turns of the screw FIG. 15. 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. Repsolds employ for the micrometers of their reading microscopes the form of construction shown in fig. 9, omitting, of course, the motion of the whole micrometer box given by the screw s for those cases in which the axis of the micrometer is supposed to remain constant in position, as, for example, in the case of the reading microscopes of transit circles (see TRANSIT CIRCLE). But when the relative positions of two adjacent objects or scale-divisions have to be determined (as, for example, in the case of heliometer scales), much time is saved by retaining the motion of the micrometer box. One double web, fixed in the box, is pointed symmetrically, as in fig. 15, on one of the scales, by moving the whole micrometer box by means of the screw s; the pair of webs, mcved by the screw S, is then pointed upon an adjacent division on the other scale. If the reading for coincidence of the movable with the fixed webs is known, we then obtain from the single reading of S the difference from coincidence of the divisions of the two scales. T It is generally possible so to arrange the method of observation as to eliminate the effect of an error in " the reading for coincidence of the webs" from the results. This excellent time-saving contrivance has also been used in Gill's apparatus for measuring astrographic plates (see below). Ghost Micrometer.—C. E. Burton and Sir Howard Grubb (Monthly Notices, xli. 59), after calling attention to J. von Lamont's paper (Jahrbuch der K. S. b. Munchen, p. 187) and K. L. von Littrow's paper (Prot. of Vienna Acad. of Sciences, xx. 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 eyepiece 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 may possibly 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. The Astrographic 'Micrometer or Measuring Machine.—The application of photography to exact astronomy has created the necessity for new forms of apparatus to measure the relative positions of stellar and planetary images on photographic plates, and the relative positions of lines in photographic spectra. Especially important has been the problem of measuring the " catalogue plates " of the international Carte du ciel—a work that implies the determination of the positions of some millions of stars—that is to say, of all stars to the 11th or 12th magnitude. The problem has been how to accomplish this work with the minimum of labour consistent with the desired accuracy. The adoption of a reseau photographed upon the plate has greatly facilitated the procedure. A plate of parallel-surfaced glass has a film of silver deposited upon it. On this film is ruled a system of lines 5 mm. apart, and another similar system of lines at right angles to the first, thus dividing the silvered surface of the plate into squares 5 mm. on the side. The cutter employed to rule these lines removes the silver in fine lines from the surface of the glass, Thus, if a photographic plate, before it is exposed in the telescope, is placed with its sensitive surface nearly in contact with the silvered surface of this reseau, and if parallel light, normal to the surface of the plate, is allowed to fall on the silvered film through the glass on which the film has been deposited, that light will pass through the fine lines in the silver film where the silver has been removed by the cutter, but will other-wise be intercepted by the silver film. Thus a latent image of the " reseau-lines " will be formed on the sensitive plate, and, when the latter has been exposed to the sky in the telescope, we obtain, on development, a negative of the images both of the stars and of the reseau-lines. If the errors of the rectangular co-ordinates of these lines are known, the problem of determining the co-ordinates of any star-image on the plate becomes reduced to the comparatively simple one of interpolating the co-ordinates of the star relative to the sides of the 5 mm. square within which that image is included. This interpolation can, of course, be accomplished with the aid of a micrometer-microscope whose optical axis is normal to the plate, provided that the plate is mounted on slides which enable the observer to bring the reseau-squares successively, under the microscope. This system has an additional advantage beyond its convenience, viz. that if any distortion of the film takes place during development the same distortion will be communicated both to the star-images and to the reseau-lines, and consequently its effect will be eliminated from the resulting star co-ordinates, except in so far as the distortion within the 5 mm. square is of an irregular character; this exception is hardly worth consideration. An originally unanticipated difficulty has arisen from the fact that the reseau-lines have not been ruled on plates of optical glass with optical surfaces, and that, in consequence of irregular refraction in the glass plate, the rays do not always pass through the silver film-lines in a direction strictly normal to the silvered surface; therefore, if the sensitive surface of the photographic plate is not in contact with the silver film of the reseau, the undeveloped photographic copy of the reseau may in such a case not be an exact reproduction of the silvered reseau. It is practically impossible to work with the sensitive film in contactwith the reseau-film, not only because dust particles and contact would injure the silver film, but also because the plate-glass used for the photographic plates is seldom a perfect plane. The discrepancies produced in this way are, however, very small, if care is taken to minimize the distance between the silver film and the photographic plate and to select a reasonably good piece of glass for the rfiseau. For very refined work, however, the irregularities in the reproduction of the reseau may be studied by comparing the measures of the original reseau with the mean of corresponding measures of a number of photographed copies of it. At Greenwich, Oxford and several other observatories, instead of measuring the distances of the star's image from the opposite sides of the 5 mm. reseau-square by means of a spider-line micrometer, a glass scale, on the plan shown in fig. 16, is employed in the common focus of the objective and the eyepiece. The image of the star is set upon the intersections of the lines of the central cross, and the positions of the reseau-lines are read off by estimation to 1io of a division on the glass scale. As each division corresponds to 3 sec. of arc, the nearest estimate corresponds with a nominal accuracy of 0•3". This involves a loss of accuracy because, with a spider-line micrometer, the accidental error of pointing is of the order of t o•1" of arc. In the measuring machines in general use the field of view, as in the case of the glass-scale micrometer, is sufficiently large to include the image of the 5 mm. square. The microscope or viewing telescope is fitted with a spider-line micrometer having two screws at right angles to each other, by means of which readings can be made first on one reseau-line, then on the star, and finally on the opposite reseau-line in both co-ordinates. This form of micrometer is of course capable of giving results of high precision, but the drawback is that the process involves a minimum of six pointings and the entering of six screw-head readings in order to measure the two co-ordinates of the star. Gill's Measuring Machine.—Sir David Gill (Monthly Notices, R.A.S. lix. 61) devised a measuring machine which combines the rapidity of the glass-scale micrometer with the accuracy of the spider-line micrometer and simplifies the reductions of the observations at the same time. The essential conditions of the instrument are: 1. The object glass of the micrometer-microscope is placed midway between the plane of the photographic plate and the plane of the micrometer webs. 2. The micrometer is provided with a " fixed square " 5 mm. X 5 mm., the sides of this square being parallel spider webs 4" of arc apart; the size of the square is reckoned from centre to centre of these double webs. Greenwich Astrographic Catalogue, vol. i., by permission of the Controller of H.M. Stationery office. measuring the plates of the Astrographic Catalogue. 3. The two micrometer screws (X and Y, fig. 17), which actuate the movable slides, have heads divided into too parts, one revolution =o•5 mm.; so that ten revolutions are =5 mm., or = the interval between two adjacent reseau-lines, or = the interval between the sides of the " fixed square." 4. Two other screws, o, p, the heads of which are not graduated, give motions to the whole micrometer box through t mm. in directions parallel to the axes of the two micrometer screws. 5. Each of the two micrometer screws X and Y moves a system of six parallel webs, placed 4" of arc apart from each other. These webs serve not only for pointing on stars to determine their co-ordinates (in manner afterwards described), but also for estimating the diameters of the star-images in terms of these 4" intervals. 6. All the essential parts of the micrometer, including the slides, micrometer box, tube, &c., are of steel or cast-iron, so that changes of temperature do not affect the adjustments. The necessary adjustments are the following: t. The webs of each set of movable webs shall, inter se, be strictly parallel, and the two sets shall be strictly at right angles to each other. 2. The double webs composing the sides of the fixed square shall be strictly parallel, and shall form a true square of exactly ten revolutions of the screw on the side. 3. The two micrometer screws shall be without sensible periodic or other error, and exactly alike in pitch. 4. The micrometer readings for coincidence of the movable webs with the webs of the fixed square shall.be exactly o•000R and to•000R. 5. The image of a normal reseau-square, as viewed in the micro-scope, shall exactly coincide with the square formed by the fixed webs—that is to say, the image of the sides of a normal reseau-square shall measure exactly to screw-revolutions. Assuming that these conditions can be rigidly realized,, we have the following very simple modus operandi: t. By means of the quick rack motions A and B move the plate so as to bring the reseau-square into the centre of the field of the micrometer; then, by means of the screw heads o, p, perfect the coincidence of the " fixed square " of webs, with the linage of the reseau-square. 2. By means of one of the micrometer screws X place the star's image in the middle of the six parallel webs which are moved by X. 3. Similarly, place the star's image in the middle of the webs moved by Y. 4. Estimate the diameter of the star's image in terms of the 4" intervals of the movable webs. By employing both hands, operation (I) can be made as quickly as a single pointing with the ordinary spider-line micrometer, and operations (2) and (3) can be similarly performed in the time required for a single pointing. The reading (2) is then the required co-ordinate in x and that of (3) is the required co-ordinate in y; or, if the plate is reversed, 18o°, these readings have to be subtracted from 10.0008. A general idea of the construction of the machine can be gathered from fig. 17 above, but the reader will find a detailed account of it, and of the manner in which the requisite adjustments are made, in the paper already quoted. The apparatus has been used with complete success at the Royal Observatory, Cape of Good Hope, and at Melbourne, Sydney and Cordoba. Effects"of Wear on the Micrometer Screws.—The accuracy of this apparatus has been frequently criticized on the ground that errors are produced in the screws by the effect of wear. One reply to this is that it is not difficult to determine from time to time the errors of the screws and to apply the necessary corrections to the observations. But a little consideration will show that when the plate is reversed 18o° the effects of errors of the screws produced by. wear are practically eliminated. In discussing the effect of wear upon a screw, it will be convenient to imagine the thread unrolled and forming a wedge, of which we can represent the unworn bearing-side by a straight line AB (fig. 18), Cl JD A E F FIG. t8. on which rubs the block CD, which represents the female screw or bush, and moves between the points E and F, sometimes towards E, sometimes towards F, but having as often to measure short distances as long distances from the middle point of this range, and these as often towards E as towards F. Now, if CD is pressed by its weight or by a spring on the surface AB, the effect of wear will be to produce a symmetrical grinding away of both surfaces, which may be represented thus, fig. 19. That is to say, the screw-errors will be A Ec----Ci D ~F B identical for revolution n and for lo–n, and thus will disappear in their effect in the mean of observations made in reversed positions of the plate. At the Cape of Good Hope, after more than 200,000 pointings had been made, the screw-errors were redetermined; the results proved the truth of the above conclusions, viz. the absolute freedom of the derived co-ordinates from the effects of wear of the screws in the mean of measures made in reversed positions of the plate. Hinks's Measuring Machine.—A very refined modification of the Cape machine is described by A. Hinks (Monthly Notices, R.A.S., vol. 6r, p. 444), and the instrument contains many elegant mechanical and optical details due to Horace Darwin and Messrs Zeiss respectively. Its fundamental principle is that, by a combination of glass scales with a micrometer screw, " the chief part of the distance to be measured is read off on the scale; the fractional part of the scale-space is not estimated but measured by the screw." Hinks claims that thus never more than one- or two-tenths of a revolution of the screw need be used in making the measure, and little time is lost in running the screw backwards and forwards. All this is true, but three readings instead of one for each pointing, much more figure-work in computation (especially if corrections have to be applied to the scale readings to reduce them to exact normal screw readings), are factors which involve a far greater expenditure of time than making a few additional turns of a screw in the process of measurement. Hinks's further claim that, in consequence of the small motion of the screw, less error is produced in the screw by wear is not true; for, although large movements of the screw produce a large amount of wear, that wear is spread over longer parts of the screw but remains the same for any particular part of the screw; the resulting errors are exaggerated towards the extremity of the range of screw employed (see Monthly Notices, R.A.S., vol. 45, p. 83), and are therefore more likely to produce errors which are not eliminated on reversal of the plate in cases where the screw range is not strictly limited, and the wear therefore not strictly symmetrical. The excellent manner in which the scales and micrometers are mounted, the employment of a compound microscope for viewing the scales, with its ingeniously arranged and admirably efficient reversing prism, and the perfection of its slow motions for focusing and reading, combine to render this a most accurate and convenient instrument for very refined measures, although too slow for work in which the measures must depend on single pointings in each of two reversed positions of the plate, and where speed of working is essential. Apparatus for Measuring Star-Spectra, &c.—These machines may be divided into three classes, viz. A, in which the motion of the slide which carries the photographic plate is measured entirely by a screw; B, in which that motion is measured by combination of a scale and screw; and C, in which the B photographic plate is fixed and the measuring microscope Is moved. The chief drawback to type A is that the errors of the screw are liable to change by wear, otherwise the apparatus, as made and used at Potsdam, is, on the whole, a convenient and accurate one. In determining the errors of the screw of the Potsdam form `4 of machine it is necessary to have regard to the fact that the screw is placed at one side of the slide, as in fig. 20. The result is that, if the screw is bent—if, for example, the end of the frame next the screw-head is raised and that next the end p is lowered in the diagram—a twist will be given to the web-frame, and the centre of the web will be moved nearer to the micrometer-drum than it should be, whilst the reverse effect will follow when the head has been turned 18o°. This would, of course, create a periodic error, which would be determinable for the motion of any particular point (say the middle) of the web, but which would be smaller for a point near the axis of the screw and greater for a point farther from that axis. In the Potsdam form of this apparatus the micrometer is, for convenience, provided with a motion at right angles to the axis of the screw, and it has been found at the Cape Observatory that the periodic errors in this apparatus do vary very sensibly according as the microscope is directed to a point, more or less distant from the measuring screw. Since the discovery of this fact all measurements have been made in that fixed position of the microscope with respect to the axis of the screw for which the errors of the screw have been determined. In the apparatus of type B as made by Zeiss there are two microscopes attached to a base-plate, one of which views the spectrum-plate (or other object) to be measured, while the other views a scale that moves with the slide on which the spectrum-plate is mounted. In this way the scale can be viewed by a micro-scope of much higher magnifying power than can be employed for the photographed spectrum. Indeed, if the scale were sub-divided to i'a mm. the power employed might only be limited by the sharpness of the division-lines. But for refined work this would imply the investigation of too many divisions of the scale; it is therefore more usual to divide the scale into single millimetres or half-millimetres and to provide a micrometer which subdivides the millimetre into woo or, by estimation, into 10,000 parts. For very accurate work it is desirable that the base-plate, the slide and the scale should be of nickel steel, having the same thermal coefficient of expansion as glass. The forms of measuring machines of type C, often seen in physical laboratories, should be at once rejected for refined measurements, because it is impossible to construct slides of such perfection that the axis of the microscope will remain absolutely normal to the surface of the plate (assumed to be a plane) throughout the range of measurement. Even if the slide itself is mechanically perfect, the irregularity in the thickness of the lubricating oil between the bearing surfaces of the slide is apt to produce a variable error. Bakhuyzen (Bulletin de Corn. perm. congres. astrog, i. 164) de-scribed a measuring-machine by Repsolds, in which the micrometer-microscope tilts in the bearings of the chariot on which it moves, so that it can view either a graduated scale or the photographic plate. We have, in fact, in this instrument a combination of types B and C. Even in this apparatus if the slide on which the chariot moves is not perfect (and no slide is perfect), the azimuth of the axis of the microscope is liable to change in the course of movement of the slide, and thus equal spaces on the scale will not be represented by equal spaces on the plate under measurement. The remedy proposed by Repsold for this proved fault is to cause the whole slide to tilt instead of the microscope only; this should prove a complete remedy. The Travelling Wire Micrometer.—An important modern application of the micrometer, which is not dealt with in the article TRANSIT CIRCLE, is that which is now called " the travel-ling wire micrometer." In the Astronomische Nachriehten, No. 2940, Dr Repsold proposed a method of meridian observing which consists in causing a web to follow the image of a star in transit by motions communicated by the observer's hands alone, whilst electrical contacts on the drum of the micrometer screw register on the chronograph the instants corresponding to known intervals from the line of collimation. The purpose of his paper was to show that if the axis, by which theobserver imparts motion to the slide on which the travelling web is mounted, is provided with two disks at its extremities, so that the observer can use the thumb and finger of both hands in rotating it, there is no difficulty, after a little practice, in keeping the web constantly bisecting the star in transit, and that with a little practice the mean of the absolute errors in following the star becomes nearly zero. In the Astron. Nach., No. 3377, Repsold gives a detailed description of two forms of eye-ends of transit circles, fitted with means of observing in this manner, to which he gives the name of " the impersonal micrometer." This method of observation was very successfully employed, under Seeliger at Munich, in an extensive series of meridian observations, and, under the auspices of the Geodetic Institute at Potsdam, in telegraphic longitude operations. Still more recently the method has been largely employed at the Cape of Good Hope and elsewhere. Under the date March 1901 Dr H. Struve published an account of the application of clockwork as an aid in Repsold's method; and, later, Dr Cohn published a more elaborate paper on the same subject in the Astron. Nach., 3767. The method consisted in having motion transmitted to the micrometer screw from an axis on which is mounted a disk that presses with friction-contact upon a cone that revolves uniformly by clockwork. The velocity of rotation of the micrometer-screw could therefore be varied for stars of different declination by varying the distance from the apex at which the revolving disk presses upon the revolving cone. In the Konigsberg transit instrument used by Struve and Cohn, the clockwork was attached to the eye-end of the instrument—a condition which is obviously undesirable both from the necessarily unsymmetrical position of the clockwork with respect to the optical axis, and from the impossibility of securing the uniform going of the clock in different positions of the instrument. In more recent instruments at the observatories of the Cape of Good Hope and Paris the motion is transmitted from a separately mounted cone and clock by a light rod passing through a perforation in the pivot of the transit instrument and thence through bevel-wheels in the cube of the axis to a second rod leading to the eyepiece. This rod turns a worm-screw which acts on a worm-wheel fitted " spring tight " upon the axis of the micrometer-screw. It should be mentioned that an essential feature of the travelling wire micrometer is that the eyepiece as well as the wire shall be moved by the micrometer-screw. Thus, if the star's image is kept in bisection by the wire, both star and wire will appear at rest in the field of view. The distinction between the old and new method of observation may thus, in one sense, be described as the difference between shooting at a moving object and in shooting at one at rest. In the case of the original Repsold plan without clockwork the description is not quite exact, because both the process of following the object and correcting the aim are simultaneously performed; whilst, if the clockwork runs uniformly and the friction-disk is set to the proper distance from the apex of the cone, the star will appear almost perfectly at rest, and the observer has only to apply delicate corrections by differential gear—a condition which is exactly analogous to that of training a modern gun-sight upon a fixed object. It is impossible in this article to give a detailed description of the apparatus, but the reader is referred to Astron. Nach-, 3377, for an illustrated account of the original Repsolds instrument and to the History and Description of the Cape Observatory for a complete description of the most modern form of its application to the Cape transit circle, with and without clockwork. The Hartmann Spectrocomparator.-For accurate measurement of the displacements of lines of stellar spectra which are produced by the relative motion of star and observer in the line of sight, a very beautiful instrument has been devised by Dr J. Hartmann of Potsdam, and is described by him in the Publicationen des astrophysikalischen Observatoriums zu Potsdam, Bd. 18, Stuck 53 (1906). An English translation of this paper is given in the Astrophysical Journal, xxiv. 285-302. The method originally used by Huggins, who first conceived and proved the possibility of measuring stellar velocities in the line of sight, was to measure with a filar micrometer the displacement of some well-known line in a stellar spectrum relative to the corresponding line of a terrestrial spectrum. Vogel of Potsdam introduced the method of photographing stellar and terrestrial spectra on the same plate, and in this way obtained an immense advance in the ease and precision of observation. Vogel and his successors employed one or other form of measuring machine, provided with a micro-scope having single or close parallel webs which could be successively pointed on the photographed lines of the star spectrum and the lines of the terrestrial spectrum. To derive the stellar velocity in the line of sight relative to the observer it was then necessary to assume that the normal wave-lengths of the stellar and terrestrial spectra are accurately known. But in the complex spectra of stars of the solar type this is by no means the case; for, as Dr Hartmann remarks, " in the first place the lines in these spectra are so numerous that their complete . measurement and reduction would require many days, and in the second place a rigorous reduction of such material has hitherto not been at all possible because the wave-lengths of the lines are not known with sufficient accuracy. On this account, observers have until now iimited themselves to a partial treatment of such spectra, measuring only a small number of lines, whereby the major part of the rich material present in the plate remains unutilized." But the spectroscopes that can be employed for stellar spectro- P graphs are not sufficiently powerful to separate fully lines which are very closely adjacent, and therefore a line, assumed to be of a known wave-length, may be apparently displaced by the near neighbourhood of an unknown line. Hartmann overcame these and many other difficulties by directly superposing the image of the spectrogram of a star, having iron comparison lines, upon the image of a spectrogram of the sun taken also with iron comparison lines. The apparatus for this purpose is shown in fig. 21, its principle of construction is shown in figs. 22 and 23. The solar spectrograph is attached by clamps to the plate Al, the stellar spectrograph to the plate A2. The plate Al is mounted on the dove-tailed slide B,, upon the metallic stage T, and can be moved to right or left relative to T by the micrometer-screw S; whilst the plate A2 is mounted on the dove-tailed slide B2 and can From Zeitschr, fur Inslrun,enlenkunde, by permission of Julius Springer, Berlin. FIG. 22. be moved at right angles to its greatest length by the screw G. The micrometer-screw S has a pitch of o•5 mm., its head is divided into loo parts. Two spiral springs underneath press the plate BI with its agate end-bearing against the rounded end of the screw S. The whole number of revolutions of the screw is read by the scale X (fig. 23). The whole stage T, carrying both spectrograms, can be moved from right to left on the steel cylinder Z, by turning the head K, on the axis of which is a pinion that gears into a toothed rack attached to the lower side of the cylinder Z. A scale N on the cylinder Z serves for setting the slide to any required position. The preliminary conditions of measurement are: I. The centre of both spectrographs shall be parallel to the axis of the cylinder Z. 2. The distance between the centres of the two spectrographs shall be equal to the distance between the optical axes of the two viewing microscopes. 3. The scales of the images formed in the focus of the eyepiece common to both microscopes shall be identical. To fulfil condition (I) the plates Al and A2 are mounted in circular slides, whose centres are El and E2 respectively, so that by means of the screws Di, D2, with their corresponding opposing springs F1 and F2, the operation can be very easily accomplished. To fulfil condition (2) the two microscopes whose object glasses are 0i and 02 (fig. 22) are attached to the plate L. their optical axes being normal to the stage T. The screw Q serves to adjust the axis o€ 01 to coincidence with the centre of the lines of the solar spectrograph, and the screw G then serves to move the slide B2 till the optical axis of O2 is coincident with the centre of the lines of the stellar spectrograph. Suppose now the solar spectrogram to be viewed in the focus of 0r, and the converging rays to be reflected by the prisms PI and Pa, till an image is formed in the focus of the eyepiece at the point where the axis of the eyepiece intersects 389 From Zeitschr. fur Instrumentenkunde, by permission of Julius Springer, Berlin. the upper face of the prism P3. Then if the prism P4 is cemented to P3, a sharp image of such lines of the solar -spectrograph as are visible in the field of view will be seen in the eyepiece. If the stellar spectrograph is viewed in the focus of 02 and the converging rays are reflected by the prism P2 to P4, no image would be seen in the eyepiece, for the rays would pass out directly through the parallel glass plate which is formed by the cementing together of the prisms P3 and P4. But if the cemented face of P4 is silvered, neighbourhood of each comparison line. For the special purpose of determining the solar parallax this instrument has been used in a most refined and perfect manner by Dr Halm at the Cape of Good Hope (Annals of the Cape Observatory, vol. x. part 3). From Zeitschr. fur Instrumentenkunde, by permission of Julius Springer, Berlin, FIG. 25. _N \-0---/ \/K From Zeitschr. fur Instrumentenkunde by permission of Julius Springer, Berlin. FIG. 23. then the lines of the stellar spectrogram would be seen in focus of the eyepiece and the image of the solar spectrograph would be obliterated. Therefore, if one-half of the cemented face of P4 is silvered, it becomes possible to view, side by side, one-half of the image of the solar spectrograph formed by 01 and one-half of the image of the stellar spectrograph formed by 02. A prism half silvered in this way is provided, which enables the observer to compare the equality of scale of both photographs. If, for example, it is found that the image of the solar spectrograph is the larger of the two it becomes necessary to adjust the object glass 01 farther is from the stellar spectrograph. This has the effect of forming the image of the latter farther from the observer's eye, and so it becomes necessary to turn the handle of the rack-pinion V in such a way as to move the prisms P3 and P4 nearer to P2 till the lines of the stellar spectrograph are again sharply in focus. The effect of turn- ing the pinion V is, of course, to displace the focus both of the solar and stellar spectrographs in the field of the eyepiece, but t h i s displacement, is easily restored by From Zeitschr. fu. Instrumeuen- the focussing screws 01 and 02. By kunde, by permission of Julius successive adjustments of this kind Springer, Berlin. condition realized. These three adjustments having been made, the prisms P3 and P4 are removed and replaced by another prism in which the silvering is arranged as in fig. 24, where the hatched lines denote the silvered surfaces. The narrow tongues of the silvered surface will now reflect corresponding parts of the star-spectrograph, and will obliterate corresponding parts of the solar spectrograph—as shown in figs. 25 and 26. Fig. 25 shows the stellar and solar lines of the two spectrographs in coincidence, whilst the metallic lines of comparison are non-coincident. Fig. 26 shows the metallic lines of comparison in coincidence whilst the solar and stellar lines are non-coincident. It is obvious that these two conditions can be produced at the will of the observer by simply turning the screw S, and that the difference of the readings of the screw-head, which are required to reproduce the two conditions in question, gives a measure of the displacement of the stellar lines relative to the solar lines. If then the screw-value in kilometres per second is known for the neighbourhood of each of the comparison lines employed, the radial velocity of the star can be independently derived directly from coincidences made in above manner in the From Zeitschr. fur Instrumentenkunde, by permission of Julius Springer, Berlin. Double Image Micrometers are described in the article HELIo-METER (q.v.). (D. GL.)
End of Article: MICROMETER (from Gr. wcp6c, small, jArpov, a measure)
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