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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 See also:instrument generally applied to telescopes and microscopes for measuring small angular distances with the former or the dimensions of small See also:objects with the latter . Before the invention of the See also:telescope the accuracy of astronomical observations was necessarily limited by the See also:angle that could be distinguished by the naked See also:eye . The angle between two objects, such as stars or the opposite limbs of the See also:sun, was measured by directing an See also:arm furnished with See also:fine " See also:sights " (in the sense of the " sights " of a See also: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 See also:object and the second pair upon the other . The angle through which the arm was moved, or, in the latter See also:case, the angle between the two arms, was read off upon a finely graduated arc . With such means no very high accuracy was possible . See also:Archimedes concluded from his measurements that the sun's See also:diameter was greater than 27' and less than 32'; and even Tycho See also:Brahe was so misled by his See also:measures of the apparent diameters of the sun and See also:moon as to conclude that a See also:total See also:eclipse of the sun was impossible.' See also:Michael Maestlin in 1579 determined the relative positions of eleven stars in the See also:Pleiades (Historia coelestis Lucii See also:Baretti, See also:Augsburg, 1666), and A . Winnecke has shown (Monthly Notices R.A.S., xxxix . 146) that the probable See also: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 See also:planets were shown to have visible disks, and to be attended by satellites whose distance and position angle relative to the See also:planet it was desirable to measure . It became, in fact, essential to invent a " See also:micrometer " for measuring the small angles which were thus for the first See also:time rendered sensible . There is now no doubt that See also:William See also:Gascoigne, a See also:young See also:gentleman of See also:Yorkshire, was the first ' See also:Grant, See also:History of See also:Physical See also: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 See also:

powers of eyesight.inventor of the micrometer . William Crabtree, a friend of his, taking a See also:journey to Yorkshire in 1639 to see Gascoigne, writes thus to his friend See also:Jeremiah See also: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 See also:earth, most exactly through the See also:glass, to a second." The micrometer so mentioned See also:fell into the See also:possession of See also:Richard See also:Townley of See also:Lancashire, who exhibited it at the See also:meeting of the Royal Society held on the 25th of See also:July 1667 . The principle of Gascoigne .s micrometer is that two pointers having parallel edges at right angles to the measuring See also:screw, are moved in opposite directions symmetrically with and at right angles to the See also: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 See also:index attached to one end of the screw, See also:reading on a See also:dial divided into See also:loo equal parts . The whole arrangement is elegant and ingenious . A See also:steel See also:cylinder (about the thickness of a See also:goose-See also:quill), which forms the micrometer screw, has two threads cut upon it, one-See also:half being cut with a See also:thread See also:double the See also:pitch of the other . This screw is mounted on an oblong See also:box which carries one of the measuring edges; the other edge is moved by the coarser See also: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 .

See also:

Flamsteed, in the first See also:volume of the Historia coelestis, has inserted a See also: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 See also:great number of measurements of the diameter of the moon . Dr See also:John Bevis (Phil . Trans . (1773), p . 190) also gives results of measurements by Gascoigne of the diameters of the moon, See also:Jupiter, See also:Mars and See also:Venus with his micrometer . See also:Delambre gives ' the following comparison between the results of Gascoigne's measurements of the sun's semi-diameter and the computed results from See also:modern determinations: Gascoigne . See also:Conn. d. temps . See also:October 25 (o.s.) .. . . 16' II"or Io 16' Io"•o 31 .. 16' II" 16' II"•4 See also: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 See also:

des temps it amounts to 32".3.3 These results prove the enormous advance attained in accuracy by Gascoigne, and his indisputable See also:title to the See also:credit of inventing the micrometer . See also:Huygens, in his Systema saturnium (1659), describes a micrometer with which he determined the apparent diameters of the See also:principal planets . He inserted a slip of See also:metal, of variable breadth, at the See also:focus of the telescope, and observed at what part it exactly covered the object under examination; knowing the See also: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 See also:Marquis See also:Malvasia in his Ephemerides (See also:Bologna, 1662) describes a micrometer of his own invention . At the focus of his telescope he placed fine See also:silver wires at right angles to each other, which, by their intersection, formed a See also:net-See also:work of small squares . The mutual distances of the intersecting wires he determined by counting, with the aid of a pendulum See also:clock, the number of seconds required by an See also:equatorial See also:star to pass from See also: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 See also:Picard was provided with See also:silk See also: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 See also:

common focus of the two lenses of a See also:Kepler telescope appears as distinct and well-defined as the Delambre, Hist. See also:ast. moderne, ii . 590 . 4 Mem. acad. des sciences (17.17), pp . 78 seq . See also:image of a distant See also:body; and the micrometers of Malvasia, Auzout and Picard are the natural developments of this See also:discovery . Gascoigne was killed at the See also:battle of See also:Marston See also:Moor on the 2nd of July 1644, in the twenty-See also:fourth See also:year of his See also:age, and his untimely See also: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 See also:developed, it was found that the finest hairs or filaments of silk, or the thinnest silver wires that could be See also: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 See also:Fontana of See also: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 See also:attention of See also:Troughton had been directed to the subject by See also:Rittenhouse that the See also:idea was carried into practice .2 In 1813 See also:Wollaston proposed fine See also:platinum wires, prepared by surrounding a platinum See also:wire with a cylinder of silver, and See also:drawing out the cylinder with its platinum axis into a fine wire .3 The surrounding silver was then dissolved by nitric See also: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 See also:elasticity, have' led to its universal See also:adoption . Beyond the introduction of the spider See also: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 See also:Hooke,4 See also:Wren, See also:Smeaton, See also:Cassini, See also:Bradley, See also:Maskelyne, See also:Herschel, See also:Arago, See also:Pearson, .See also:Bessel, See also:Struve, See also:Dawes, &c., or the successive productions of the great artists See also:Ramsden, Troughton, See also:Fraunhofer, Ertel, See also:Simms, See also:Cooke, Grubb, See also:Clarke and See also: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 See also:

patience of the observer . For, on See also:account of the diurnal See also: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 See also:altitude and See also:azimuth . See also: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 See also:close double stars he estimated the distance in terms of the disk of the components . For the measurement of wider stars he invented his See also: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 See also:left eye . The distance of the lucid points was the tangent of the magnified angles subtended by the stars to a See also:radius of to ft . This angle, therefore, divided by the magnifying See also:power of the telescope gives the real angular distance of the centres of a double star . With a power of 46o the See also:scale was a See also:quarter of an See also:inch for every second . The Modern Filar Micrometer .

When equatorial mountings for telescopes became more See also:

general, no filar micrometer was considered See also: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 See also:matter of regret that Fontana's See also:suggestion was unknown to him . 2 J . T . Quekett in his See also:Treatise on the See also:Microscope ascribes to Ramsden the See also:practical introduction of the spider web in micrometers . The See also: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 See also:

original construction (Hooke's See also:Posthumous See also:Works, p . 497) . ' Herschel and See also:South (Phil . Trans., 1824, part iii. p. to) claim that became universal; the methods of See also:illumination were improved; and micrometers with screws of previously unheard of fineness and accuracy were produced . These facilities, coupled with the wide and fascinating See also:field of See also:research opened up by Sir William Herschel's discovery of the binary See also:character of double stars, gave an impulse to micrometric research which has continued unabated to the See also: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 See also:liberty.' The micrometer represented in See also:figs . I, 2, 3 is due to Troughton . Fig. t is a See also:horizontal See also:section in the direction of the axis of the tele- See also:scope . The eyepiece ab consists of two plano-See also: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 See also:tube cd, which screws into the See also:brass See also:ring ef, through two openings in which the oblong See also: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 See also:

female screws tapped in the heads m and n acting on the screws o and p respectively . Two pins q, r, with See also:spiral springs coiled See also:round them, pass loosely through holes in the forks k, 1, and keep the See also:bearings of the heads m and n firmly pressed against the ends of the micrometer box . Thus the smallest rotation of either See also: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 See also: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 See also:fork k, the other (s) in a similar groove cut in the See also:outer fork 1 . These grooves are simultaneously cut in situ by the maker, with the aid of an See also: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 See also:

fault occur (technically called " fiddling ") it is fatal to accurate measurement . One of the most essential points in a See also:good micrometer is that all the webs shall be so nearly in the same See also:plane as to be well in focus together under the highest powers used, and at the same time absolutely See also:free from " fiddling." For measuring position angles a brass circle gh (fig . 3), fixed to the telescope by the screw i, has See also:rack See also: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 See also: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 See also:Claude See also:Simeon Passemant (Mem . Acad., See also:Paris, 1746) . In 1757 he presented a telescope to the See also:king, so accurately driven by clockwork that it would follow a star all See also:night See also:long . Spider Web . S The See also: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 See also:shoulder of the screw a See also:flat bearing See also:surface, they have given the screw a spherical bearing resting in a hollow See also:cone (fig .

4) attached to the end of the box . Troughton's See also:

form . Fraunhofer's Filar Micrometer.—The micrometer represented in fig . 5 I is the original Merz micrometer of the Cape See also:Observatory, made on Fraunhofer's See also: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 See also:illuminating the webs in a dark field; the See also: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 See also:simple dovetails . The lowest of these slides reposes upon a See also:foundation-See also:plate pp, into one end of which the screw s is tapped .

In the See also:

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-See also:meter . For the See also:internal structural details of the micrometer the reader is referred to the See also:article " Micrometer " in the 9th edition of the See also: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 See also: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 See also: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 See also:equator and so that the star's image in its diurnal motion shall pass across the intersection of the two webs which See also: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 See also: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, See also:Secchi, the Bonds, Maclear and of most modern See also: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 See also:century were made . 2 For the corrections applicable to measures of position-angle in different See also:hour angles, on account of errors of the equatorial instrument and of See also:refraction, see Chauvenet's Practical and Spherical Astronomy, ii . 392 and 450 .

The position-angles of double stars are reckoned from See also:

north through See also: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 See also: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 See also:plan has the See also: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 See also:constant, the remedy is to determine that angle (always very nearly a right angle) by any See also: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 See also:

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 See also: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 See also: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 See also:finger on the side of the tube, one is puzzled whether more to wonder at such poor See also: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 See also: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 See also: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. See also:xxxv . 1 9) . The micrometer shown in fig . 8 was made by Repsolds for the Cape Observatory . Fig .

9 represents the same 3 See also:

Professor See also:Watson used to say, " After all the most important part of a telescope is the See also: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 See also: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 See also: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 See also: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 See also:

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 See also: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 See also:lens e ; at night the lamp which illuminates the webs and the position-circle also illuminates the drum-heads (see on illumination p . 385). See also:aaaa is the web-frame (fig . 9), See also:fry is a single See also: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 See also: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 See also: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 See also: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 See also:

paper (fig . 9) is only prevented by good fitting of the holes fl' -y'; and, since the See also: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-See also: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 See also:reversing in position-angle—a precaution, however, which no careful observer would neglect . In measuring See also: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 See also: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 See also: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 See also:

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 See also:projection attached to the side of the box . The amount of this pressure is regulated by the screw z' . The See also: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 See also:bronze of very close texture, which appears capable of receiving a finish having almost the truth and See also:polish of an See also: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, See also:

touch the surface r . The See also:varnish to See also:fix the webs is applied, not on the surface r as is usual, but on a See also: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 See also:lie as much in the estimation of the fraction of the See also: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 See also: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 See also:Clark of See also:Cambridge, See also:Massachusetts, has been largely used by See also: