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Micrometer
1911 Encyclopedia Britannica
or (from Gr. µcxp6s, small, i tthrpov, 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 2'.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 1 Gran, 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 3 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' I I" or Io" 16' Io"o 31 „.. 16' II" 16'11"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 network of small squares. The mutual distances of the intersecting wires he determined by counting, with the aid of a pendulum clock, the number of seconds required by an equatorial star to pass from web to web, while the telescope was adjusted so that the star ran parallel to the wires at right angles to those under investigation. 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 3 Delambre, Hist. ast. moderne, ii. 590.
4 Mem. acad. des sciences (1717), 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 p p 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, 1 755) first proposed the use of spider webs in micrometers,' but it was not till the attention of Troughton had been directed to the subject by Rittenhouse that the idea was carried into practice.' In 1813 Wollaston proposed fine platinum wires, prepared by surrounding a platinum wire with a cylinder of silver, and drawing out the cylinder with its platinum axis into a fine wire. 3 The surrounding silver was then dissolved by nitric acid, and a platinum wire of extreme fineness remained. But experience soon proved the superiority of the spider web; its perfection of shape, its lightness and elasticity, have led to its universal adoption.
Beyond the introduction of the spider line it is unnecessary to mention the various steps by which the Gascoigne micrometer assumed the modern forms now in use, or to describe in detail the suggestions of Hooke, 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, 500. 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 io 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 io 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 460 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 1 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.
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.
Phil. Trans. (1813), pp. 114-118.
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).
5 Herschel and South (Phil. Trans., 1824, part iii. p. io) 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. I is a horizontal section in the direction of the axis of the tele FIG. I. FIG. 2. FIG. 3. 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 eyepiece, 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 in 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 Ioo equal parts on the drums u and v, so that, by estimation, the reading can easily be carried to ivioDth 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 brasswork. Should either fault occur (technically called " fiddling ") it is fatal to accurate measurement. One of the most essential points in a good micrometer is that all the webs shall be so nearly in the same plane as to be well in focus together under the highest powers used, and at the same time absolutely free from " fiddling." For measuring position angles a brass circle gh (fig. 3), fixed to the telescope by the screw i, has rack teeth on its circumference that receive the teeth;of an endless screw w, which, being fixed by the arms xx to the oblong box mn, gives the latter a motion of rotation round the axis of the telescope; an index upon this box points out on the graduated circle gh the angular rotation of the instrument.
the micrometer by Trough ton, fitted to their 5 ft. equatorial telescope, is the first position micrometer constructed capable of measuring position angles to 1' of arc.
' 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.
The English micrometer still retains the essential features of Troughton's original construction above described. The later English artists have somewhat changed the mode of communicating motion to the slides, by attaching the screws pdrmanently to the micrometer head and tapping each micrometer screw into its slide. Instead of making the shoulder of the screw a flat bearing surface, they have given the screw a spherical bearing resting in a hollow cone (fig. 4) attached to the end of the box.
The French artists still retain FIG ' 4. Troughton's form.
Fraunhofer's Filar Micrometer
The micrometer represented in fig. 5 is the original Merz micrometer of the Cape Observatory, made FIG. 5.
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 eyepiece 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 micrometer. 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 180° 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 270 °.2 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 FIG. 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 F IG- the same accuracy; because, whilst by means of the screw s 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 positionweb 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 micrometers is to provide a screw s, which, not as in the Fraunhofer micrometer, 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 stars, used to complete their bisections of the fixed 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. I, 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. I 9). The micrometer shown in fig. 8 was made by Repsolds for the Cape Observatory. Fig. 9 represents the same ' Professor Watson used to say, " After all the most important part of a telescope is the man at the small end." (?
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