MICROMETER, an astronomical instrument, by which small angles, or the apparent magnitudes of objects viewed through telescopes or microscopes are measured with great exactness.
1. The first TELESCOPIC micrometers were only mechanical contrivances for measuring the image of an object in the focus of the object-glass. Before these contrivances were thought of, astronomers were accustomed to measure the field of view in each of their telescopes, by observing how much of the moon they could see through it, the semidiameter being reckoned at 15 or 16 minutes; and other distances were estimated by the eye, comparing them with the field of view. Mr Gascoigne, an English gentleman, however, fell upon a much more accurate method before the year 1641, and had a Treatise on Optics prepared for the press; but he was killed during the civil wars in the service of Charles I. and his manuscript was never found. His instrument, however, fell into the hands of Mr R. Townly*, who says, that by the help of it he could mark above 40,000 divisions in a foot.
2. Mr Gascoigne's instrument being shown to Dr Hooke, he gave a drawing and description of it, and proposed several improvements†. Mr Gascoigne divided the image of an object in the focus of the object-glass, by the approach of two pieces of metal ground to a very fine edge, in the place of which Dr Hooke would substitute two fine hairs stretched parallel to one another.
3. Mr Huygens measured the apparent diameters of the planets, by first determining the quantity of the field of view in his telescope; which, he says, is best done by observing the time that a star takes up in passing over it, and then preparing two or three long and slender brass plates, of various breadths, the sides of which are very straight, and converging to a small angle. In using these pieces of brass, he made them slide in two slits, made in the sides of the tube, opposite to the place of the image, and observed in what place it just covered the diameter of any planet, or any small distance that he wanted to measure†. It was observed, however, by Sir Isaac Newton, that the diameters of planets, measured in this manner, will be larger than they should be, as all lucid objects appear to be when they are viewed upon dark ones.
4. In the Ephemerides of the Marquis of Malvasia, published in 1662, it appears that he had a method of measuring small distances between fixed stars and the diameters of the planets, and also of taking accurate draughts of the spots of the moon by a net of silver wire, fixed in the focus of the eye-glass. He likewise contrived to make one of two stars pass along the threads of this net, by turning it, or the telescope, as much as was necessary for that purpose; and he counted, by a pendulum-clock, beating seconds, the time that elapsed in its passage from one wire to another, which gave him the number of minutes and seconds
VOL. XIII. Part II.
of a degree contained between the intervals of the Micrometer-wires of his net, with respect to the focal length of his telescope.
5. In 1666, Messrs Auzout and Picard published a Auzout's description of a micrometer, which was nearly the same micrometer with that of the Marquis of Malvasia, excepting the method of dividing it, which they performed with more exactness by a screw. In some cases they used threads of silk, as being finer than silver wires. Dechales also recommends a micrometer consisting of fine wires, or silken threads, the distances of which were exactly known, disposed in the form of a net, as peculiarly convenient for taking a map of the moon.
6. M. de la Hire says, that there is no method more De la Hire's simple or commodious for observing the digits of an micrometer-eclipse than a net in the focus of the telescope. These, he says, were generally made of silken threads; and that for this particular purpose six concentric circles had also been made use of, drawn upon oiled paper; but he advises to draw the circles on very thin pieces of glass with the point of a diamond. He also gives several particular directions to assist persons in the use of them.
7. Construction of Different Micrometers. The first we Common shall describe is the common micrometer. Let ABCD micrometer be a section of the telescope at the principal focus of the object-glass, or where the wires are situated, which are placed in a short tube containing the eye-glass, and may be turned into any position by turning that tube; is a fine wire extended over its centre; , , are two parallel wires well defined, and perpendicular to ; is fixed, and moves parallel to it by means of a screw, which carries two indexes over a graduated plate, to show the number of revolutions and parts of a revolution which it makes. Now to measure any angle, we must first ascertain the number of revolutions and parts of a revolution corresponding to some known angle, which may be thus done: 1st, Bring the inner edges of the wires exactly to coincide, and set each index to 0; turn the screw, and separate the wires to any distance; and observe the time a star is in passing along the wire from one vertical wire to the other: for that time, turned into minutes and seconds of a degree, will be the angle answering to the number of revolutions, or the angle corresponding to the distance. Thus, if of the star's declination, we have , the angle corresponding to this distance; and hence, by proportion, we find the angle answering to any other. 2dly, Set up an object of a known diameter, or two objects at a given distance, and turn the screw till the vertical wires become tangents to the object, or till their opening just takes in the distance of the two objects upon the wire ; then from the diameter, or distance of the two objects from each other, and their distance from the glass, calculate the angle, and observe the number of revolutions and parts corresponding. 3dly, Take the diameter of the sun on any day, by making the wires tangents to the opposite limbs, and find, from the nautical almanac, his diameter on that day. Here it will be best to take the upper and lower limbs of the sun when on the meridian, as he has then no motion perpendicular to the horizon. If the edges do not coincide when the indexes stand at 0, we must allow for the error. Instead of making a proportion, it is better to have a table calculated to show the angle corresponding
Micrometer. ing to every revolution and parts of a revolution. But the observer must remember, that when the micrometer is fixed to telescopes of different focal lengths, a new table must be made. The whole system of wires is turned about in its own plane, by turning the eye-tube round with the hand, and by that means the wire mn can be thrown into any position, and consequently angles in any position may be measured. Dr Bradley added a small motion by a rack and pinion to set the wires more accurately in any position.
Fig. 2. 8. But the micrometer, as now contrived, is of use, not only to find the angular distance of bodies in the field of view at the same time, but also of those which, when the telescope is fixed, pass through the field of view successively; by which means we can find the difference of their right ascensions and declinations. Let Aa, Bb, Cc, be three parallel and equidistant wires, the middle one bisecting the field of view; HOR a fixed wire perpendicular to them passing through the centre of the field; and Ff, Gg, two wires parallel to it, each moveable by a micrometer screw, as before, so that they can be brought up to HOR, or a little beyond. Then to find the angular distance of two objects, bring them very near to Bb, and in a line parallel to it, by turning about the wires, and bring one upon HOR, and by the micrometer screw make Ff or Gg pass through the other; then turn the screw till that wire coincides with HOR, and the arc which the index has passed over shows their angular distance. If the objects be further remote than you can carry the distance of one of the wires Ff, Gg from HOR, then bring one object to Ff and the other to Gg; and turn each micrometer screw till they meet, and the sum of the arcs passed over by each index gives their angular distance. If the objects be two stars, and one of them be made to run along HOR, or either of the moveable wires as occasion may require, the motion of the other will be parallel to these wires, and their difference of declinations may be observed with great exactness; but in taking any other distances, the motion of the stars being oblique to them, it is not quite so easy to get them parallel to Bb; because if one star be brought near, and the eye be applied to the other to adjust the wires to it, the former star will have gotten a little away from the wire. Dr Bradley, in his account of the use of this micrometer, published by Dr Maskelyne in the Philosophical Transactions for 1772, thinks the best way is to move the eye backwards and forwards as quick as possible; but it seems to be best to fix the eye at some point between, by which means it takes in both at once sufficiently well defined to compare them with Bb. In finding the difference of declinations, if both bodies do not come into the field of view at the same time, make one run along the wire HOR, as before, and fix the telescope and wait till the other comes in, and then adjust one of the moveable wires to it, and bring it up to HOR, and the index gives the difference of their declinations. The difference of time between the passage of the star at either of the cross moveable wires, and the transit of the other star over the cross fixed wire (which represents a meridian), turned into degrees and minutes, will give the difference of right ascension. The star has been here supposed to be bi-
fected by the wire; but if the wire be a tangent to it, allowance must be made for the breadth of the wire, provided the adjustment be made for the coincidence of the wires. In observing the diameters of the sun, moon, or planets, it may perhaps be most convenient to make use of the outer edges of the wires, because they appear most distinct when quite within the limb; but if there should be any sensible inflection of the rays of light in passing by the wires, it will be best avoided by using the inner edge of one wire and the outward edge of the other; for by that means the inflection at both limbs will be the same way, and therefore there will be no alteration of the relative position of the rays passing by each wire. And it will be convenient in the micrometer to note at what division the index stands when the moveable wire coincides with HOR; for then you need not bring the wire when a star is upon it up to HOR, only reckon from the division at which the index then stands to the above division.
9. With a micrometer thus adapted to a telescope, Mr The divided object-glass micrometer, as now made, improved was contrived by the late Mr John Dollond, and by Mr John Savery of Exeter proposed a new way of measuring the difference between the greatest and least apparent diameters of the sun, although the whole of the sun was not visible in the field of view at once. The method we shall briefly describe. Place two object-glasses instead of one, so as to form two images whole limbs shall be at a small distance from each other; or instead of two perfect lenses, he proposed to cut a single lens into four parts of equal breadths by parallel lines, and to place the two segments with their straight sides against each other, or the two middle frustums with their opposite edges together; in either case, the two parts which before had a common centre and axis, have now their centres and axes separated, and consequently two images will be formed as before by two perfect lenses. Another method in reflectors was to cut the large concave reflector through the centre, and by a contrivance to turn up the outer edges whilst the straight ones remained fixed; by which means the axis of the two parts became inclined, and formed two images. Two images being formed in this manner, he proposed to measure the distance between the limbs when the diameters of the sun were the greatest and least, the difference of which would be the difference of the diameters required. Thus far we are indebted to Mr Savery for the idea of forming two images; and the admirable uses to which it was afterwards applied, we shall next proceed to describe.
10. The divided object-glass micrometer, as now made, improved was contrived by the late Mr John Dollond, and by Mr John Savery of Exeter proposed a new way of measuring the difference between the greatest and least apparent diameters of the sun, although the whole of the sun was not visible in the field of view at once. The method we shall briefly describe. Place two object-glasses instead of one, so as to form two images whole limbs shall be at a small distance from each other; or instead of two perfect lenses, he proposed to cut a single lens into four parts of equal breadths by parallel lines, and to place the two segments with their straight sides against each other, or the two middle frustums with their opposite edges together; in either case, the two parts which before had a common centre and axis, have now their centres and axes separated, and consequently two images will be formed as before by two perfect lenses. Another method in reflectors was to cut the large concave reflector through the centre, and by a contrivance to turn up the outer edges whilst the straight ones remained fixed; by which means the axis of the two parts became inclined, and formed two images. Two images being formed in this manner, he proposed to measure the distance between the limbs when the diameters of the sun were the greatest and least, the difference of which would be the difference of the diameters required. Thus far we are indebted to Mr Savery for the idea of forming two images; and the admirable uses to which it was afterwards applied, we shall next proceed to describe.
turn the glass about in its own plane. The brass-work carries a vernier to measure the distance of the centres of the two segments. Now let E, and H be the centres of the two segments, F their principal focus, and PQ two distant objects in FE, FH, produced, or the opposite limbs of the same object PBQD; then the images of P and Q, formed by each segment, or the images of the opposite limbs of the object PBQD, coincide at F: hence two images , of that object are formed, whose limbs are in contact; therefore the angular distance of the points P and Q is the same as the angle which the distance EH subtends at F, which, as the angles supposed to be measured are very small, will vary as EH extremely nearly; and consequently if the angle corresponding to one interval of the centres of the segments be known, the angle corresponding to any other will be found by proportion. Now to find the interval for some angle, take the horizontal diameter of the sun on any day, by separating the images till the contrary limbs coincide, and read off by the vernier the interval of their centres, and look into the nautical almanac for the diameter of the sun on that day, and you have the corresponding angle. Or if greater exactness be required than from taking the angle in proportion to the distances of their centres, we may proceed thus:—Draw FG perpendicular to EH, which therefore bisects it; then one half EH, or EG, is the tangent of half the angle EFH; hence, half the distance of their centres is to the tangent of half the angle corresponding to that distance as half any other distance of the centres is to the tangent of half the corresponding angle (A).
11. From this the method of measuring small angles is manifest; for we consider P, Q either as two objects whose images are brought together by separating the two segments, or as the opposite limbs of one object PBQA, whose images, formed by the two segments E, H, touch at F; in the former case, EH gives the angular distance of the two objects; and in the latter, it gives the angle under which the diameter of the object appears. In order to find the angular distance of two objects, therefore, separate the segments till the two images which approach each other coincide; and to find the diameter of an object, separate the segments till the contrary limbs of the images touch each other, and read off the distance of the centres of the segment from the vernier (B), and find the
angle as directed in the last article. Hence appears one great superiority in this above the wire micrometer; as, with the one any diameter of an object may be measured with the same ease and accuracy; whereas with the other we cannot with accuracy measure any diameter, except that which is at right angles to the direction of motion.
12. But, besides these two uses to which the instrument seems so well adapted, Dr Maskelyne* has shown how it may be applied to find the difference of right ascensions and declinations. For this purpose, two wires at right angles to each other, bisecting the field of view, must be placed in the principal focus of the eye-glass, and moveable about in their own plane.—Let HCR be the field of view, HR and Cc the two wires; turn the wires till the westernmost star (which is the best, having further to move) run along ROH; then separate the two segments, and turn about the micrometer till the two images of the same star lie in the wire Cc; and then, partly by separating the segments, and partly by raising or depressing the telescope, bring the two innermost images of the two stars to appear and run along ROH, as , , and the vernier will give the difference of their declinations; because, as the two images of one of the stars coincided with Cc, the image of each star was brought perpendicularly upon HR, or to HR in their proper meridian. And, for the same reason, the difference of their times of passing the wire Cc will give their difference of right ascensions. These operations will be facilitated, if the telescope be mounted on a polar axis. If two other wires KL, MN, parallel to Cc, be placed near H and R, the observation may be made on two stars whose difference of meridians is nearly equal to HR the diameter of the field of view, by bringing the two images of one of the stars to coincide with one of these wires. If two stars be observed whose difference of declinations is well settled, the scale of the micrometer will be known.
13. It has hitherto been supposed, that the images of the two stars can be both brought into the field of view at once upon the wire HOR; but if they cannot, set the micrometer to the difference of their declinations as nearly as you can, and make the image which comes first run along the wire HOR, by elevating or depressing the telescope; and when the other star comes in, if it do not also run along HOR, alter
(A) If the object is not distant let be the principal focus; then (FG being produced to meet a line joining the apparent places of the two objects P, Q), dividendo, , and alternando, (by similar triangles) , hence , therefore the angle subtended by EH at = the angle subtended by PQ at G; and consequently, as is constant, the angle measured at G is, in this case, also proportional to EH. The instrument is not adapted to measure the angular distance of bodies, one of which is near and the other at a distance, because their images would not be formed together.
(B) To determine if there be any error in the adjustment of the micrometer scale, measure the diameter of any small well-defined object, as Jupiter's equatorial diameter, or the longest axis of Saturn's ring, both ways, that is, with on the vernier to the right and left of on the scale, and half the difference is the error required. This error must be added to or subtracted from all observations, according as the diameter measured with on the vernier, when advanced on the scale, is less or greater than the diameter measured the other way. And it is also evident, that half the sum of the diameters thus measured gives the true diameter of the object.
Micrometer. the micrometer till it does, and half the sum of the numbers shown by the micrometer at the two separate observations of the two flats on the wire HOR will be the difference of their declinations. That this should be true, it is manifestly necessary that the two segments should recede equally in opposite directions; and this is effected by Mr Dollond in his new improvement of the object-glass micrometer.
14. The difference of right ascensions and declinations of Venus or Mercury in the sun's disk and the sun's limb may be thus found. Turn the wires so that the north limb of the sun's image AB, or the north limb of the image V of the planet, may run along the wire RH, which therefore will then be parallel to the equator, and consequently Cc a secondary to it; then separate the segments, and turn about the micrometer till the two images Vv of the planet pass Cc at the same time, and then by separating the segments, bring the north limb of the northernmost image V of the planet to touch HR, at the time the northernmost limb of the southernmost image AB of the sun touches it, and the micrometer shows the difference of declinations of the northernmost limbs of the planet and sun, for the reason formerly given (Art. 11.) we having brought the northernmost limbs of the two innermost images V and AB to HR, these two being manifestly interior to and the northernmost limb N of the image PQ. In the same manner we take the difference of declinations of their southernmost limbs; and half the difference of the two measures (taking immediately one after another) is equal to the difference of the declinations of their centres, without any regard to the sun's or planet's diameters, or error of adjustment of the micrometer; for as it affects both equally, the difference is the same as if there were no error: and the difference of the times of the transits of the eastern or western limbs of the sun and planet over Cc gives the difference of their right ascensions.
15. Instead of the difference of right ascensions, the distance of the planet from the sun's limb, in lines parallel to the equator, may be more accurately observed thus: Separate the segments, and turn about the wires and micrometer, so as to make both images V, v, run along HR, or so that the two intersections I, T of the sun's image may pass Cc at the same time. Then bring the planet's and sun's limbs into contact, as at V, and do the same for the other limb of the sun, and half the difference gives the distance of the centre of the planet from the middle of the chord on the sun's disk parallel to the equator, or the difference of the right ascensions of their centres, allowing for the motion of the planet in the interval of the observations, without any regard to the error of adjustment, for the same reason as before. For if you take any point in the chord of a circle, half the
difference of the two segments is manifestly the distance of the point from the middle of the chord; and as the planet runs along HR, the chord is parallel to the equator.
In like manner, the distances of their limbs may be measured in lines perpendicular to the equator, by bringing the micrometer into the position already described, (Art. 13.), and instead of bringing V to HR, separate the segments till the northernmost limbs coincide as at V; and in the same manner make their southernmost images to coincide, and half the difference of the two measures, allowing for the planet's motion, gives the difference of the declinations of their centres.
Hence the true place of a planet in the sun's disk may at any time of its transit be found; and consequently the nearest approach to the centre and the time of ecliptic conjunction may be deduced, although the middle should not be observed.
16. But however valuable the object-glass micrometer undoubtedly is, difficulties sometimes have been found in its use, owing to the alteration of the focus of the object-glass eye, which will cause it to give different measures of the same angle at different times. For instance, in measuring the sun's diameter, the axis of the pencil coming through the two segments from the contrary limbs of the sun, as PE, QF, fig. 3, crossing one another in the focus F under an angle equal to the sun's semidiameter, the union of the limbs cannot appear perfect, unless the eye be disposed to see objects distinctly at the place where the images are formed; for if the eye be disposed to see objects nearer to or further off than that place, in the latter case the limbs will appear separated, and in the former they will appear to lap over (c). This imperfection led Dr Maskelyne to inquire, whether some method might not be found of producing two distinct images of the sun, or any other object, by bringing the axis of each pencil to coincide, or very nearly so, before the formation of the images, by which means the limbs when brought together would not be liable to appear separated from any alteration of the eye; and this he found would be effected by the refraction of two prisms, placed either without or within the telescope; and on this principle, placing the prisms within, he constructed a new micrometer, and had one executed by Mr Dollond, which upon trial answered as he expected. The construction is as follows.
17. Let AB be the object-glass; the image, suppose of the sun, which would have been formed in Maskelyne's principal focus Q; but let the prisms PR, SR be placed to intercept the rays, and let EF, WG, be two rays proceeding from the eastern and western limbs of the sun, converging, after refraction at the lens, to and ; and suppose the refraction of the prisms to be such, that in fig. 8. the ray EFR, after refraction at R
(c) For if the eye can see distinctly an image at F, the pencils of rays, of which PE, QF are the two axes, diverging from F, are each brought to a focus on the retina at the same point; and therefore the two limbs appear to coincide: but if we increase the refractive power of the eye, then each pencil is brought to a focus, and they cross each other before the rays come to the retina, consequently the two limbs on the retina will lap over; and if we diminish the refractive power of the eye, then each pencil being brought to a focus beyond the retina, and not crossing till after they have passed it, the two limbs on the retina must be separated.
R by the prism PR, may proceed in the direction RQ; and as all the rays which were proceeding to a suffer the same refraction at the prism, they will all be refracted to Q; and therefore, instead of an image , which would have been formed by the lens alone, an image is formed by those rays which fall on the prism PR; and for the same reason, the rays falling on the prism SR will form an image ; and in fig. 9. the image of the point is brought to Q, by the prism PR, and consequently an image is formed by those rays which fall on PR; and for the same reason, an image is formed by the rays falling on SR. Now in both cases, as the rays EFR, WGR, coming from the two opposite limbs of the sun, and forming the point of contact of the two limbs, proceed in the same direction RQ, they must thus accompany each other through the eye-glass and also through the eye, whatever refractive power it has, and therefore to every eye the images must appear to touch. Now the angle is twice the refraction of the prism, and the angle is the diameter of the sun; and as these angles are very small, and have the same subtense , we have the angle .—Now as is constant, and also the angle being twice the refraction of the prism, the angle varies as . Hence the extent of the scale for measuring angles becomes the focal length of the object-glass, and the angle measured is in proportion to the distance of the prisms from the principal focus of the object-glass; and the micrometer can measure all angles (very small ones excepted, for the reason given in Art. 19.) which do not exceed the sum of the refractions of the prisms; for the angle , the diameter of the object to be measured, is always less than the angle , the sum of the refractions of the prisms, except when the prisms touch the object-glass, and then they become equal. The scale can never be out of adjustment, as the point , where the measurement begins, answers to the focus of the object-glass, which is a fixed point for all distant objects, and we have only to find the value of the scale answering to some known angle: for instance, bring the two limbs of the sun's images into contact, and measure the distance of the prisms from the focus, and look in the nautical almanac for the sun's diameter, and you get the value of the scale.
18. In fig. 8. the limb Q of the image , is illuminated by the rays falling on the object-glass between A and F, and of the image by those falling between B and G; but in fig. 9. the same limbs are illuminated by the rays falling between B and F, A and G respectively, and therefore will be more illuminated than in the other case; but the difference is not considerable in achromatic telescopes, on account of the great aperture of the object-glass compared with the distance FG.
It might be convenient to have two sets of prisms, one for measuring angles not exceeding , and therefore fit for measuring the diameters of the sun and moon, and the lucid parts and distances of the cusps in their eclipses; and another for measuring angles not much greater than , for the convenience of measuring the diameters of the planets. For as sum of the refractions of the prisms : angle , the apparent diameter of the object, it is evident that if you diminish the third term, you must increase the se-
cond in the same ratio, in order to measure the same angle; and thus by diminishing the refractive angle of the prisms, you throw them further from Q, and consequently avoid the inconvenience of bringing them near to Q, for the reason in the next paragraph; and at the same time you will increase the illumination in a small degree. The prisms must be achromatic, each composed of two prisms of flint and crown glass, placed with their refracting angles in contrary directions, otherwise the images will be coloured.
19. In the construction here described, the angle measured becomes evanescent when the prisms come to the principal focus of the object-glass, and therefore on the scale then begins: but if the prisms be placed in the principal focus they can have no effect, because the pencil of rays at the junction of the prisms would then vanish, and therefore it is not practicable to bring the two images together to get on the scale. Dr Maskelyne, therefore, thought of placing another pair of prisms within, to refract the rays before they came to the other prisms, by which means the two images would be formed into one before they came to the principal focus, and therefore on the scale could be determined. But to avoid the error arising from the multiplication of mediums, he, instead of adding another pair of prisms, divided the object-glass through its centre, and sliding the segments a little it separated the images, and then by the prisms he could form one image very distinctly, and consequently could determine on the scale; for by separating the two segments you form two images, and you will separate the two pencils so that you may move up the two prisms, and the two pencils will fall on each respectively, and the two images may be formed into one. In the instrument which Dr Maskelyne had made, on the scale was chosen to be about of the focal length of the object-glass, and each prism refracted . By this means all angles are measured down to .
20. In the Philosophical Transactions for 1779, Mr Ramsden has described two new micrometers, which he contrived with a view of remedying the defects of the object-glass micrometer.
21. 1. One of these is a catoptric micrometer, which, Ramsden's before the advantage it derives from the principle of reflecting micrometer. reflection, of not being disturbed by the heterogeneity of light, avoids every defect of other micrometers, and can have no aberration, nor any defect arising from the imperfection of materials or of execution; as the extreme simplicity of its construction requires no additional mirrors or glasses to those required for the telescope; and the separation of the images being effected by the inclination of the two specula, and not depending on the focus of any lens or mirror, any alteration in the eye of an observer cannot affect the angle measured. It has peculiar to itself the advantages of an adjustment, to make the images coincide in a direction perpendicular to that of their motion; and also of measuring the diameter of a planet on both sides of the zero, which will appear no inconsiderable advantage to observers who know how much easier it is to ascertain the contact of the external edges of two images than their perfect coincidence.
22. A represents the small speculum divided into two equal parts; one of which is fixed on the end of the arm B; the other end of the arm is fixed on a fixed axis.
axis X, which crosses the end of the telescope C. The other half of the mirror A is fixed on the arm D, which arm at the other end terminates in a socket g, that turns on the axis X; both arms are prevented from bending by the braces a g. G represents a double screw, having one part e cut into double the number of threads in an inch to that of the part g: the part e having 100 threads in one inch, and the part g 50 only. The screw e works in a nut F in the side of the telescope, while the part g turns in a nut H, which is attached to the arm B; the ends of the arms B and D, to which the mirrors are fixed, are separated from each other by the point of the double screw pressing against the stud h, fixed to the arm D, and turning in the nut H on the arm B. The two arms B and D are pressed against the direction of the double screw e g by a spiral spring within the part n, by which means all shake or play in the nut H, on which the measure depends, is entirely prevented.
From the difference of the threads on the screw at e and g, it is evident, that the progressive motion of the screw through the nut will be half the distance of the separation of the two halves of the mirror; and consequently the half mirrors will be moved equally in contrary directions from the axis of the telescope C.
23. The wheel V fixed on the end of the double screw has its circumference divided into 100 equal parts, and numbered at every fifth division with 5, 10, &c. to 100, and the index I shows the motion of the screw with the wheel round its axis, while the number of revolutions of the screw is shown by the divisions on the same index. The steel screw at R may be turned by the key S, and serves to incline the small mirror at right angles to the direction of its motion. By turning the finger head T, the eye tube P is brought nearer or farther from the small mirror, to adjust the telescope to distinct vision; and the telescope itself hath a motion round its axis for the convenience of measuring the diameter of a planet in any direction. The inclination of the diameter measured with the horizon is shown in degrees and minutes by a level and vernier on a graduated circle, at the breech of the telescope.
24. Besides the table for reducing the revolutions and parts of the screw to minutes, seconds, &c. it will require a table for correcting a small error which arises from the eccentric motion of the half-mirrors. By this motion their centres of curvature will approach a little towards the large mirror: the equation for this purpose in small angles is insensible; but when angles to be measured exceed ten minutes, it should not be neglected. Or, the angle measured may be corrected by diminishing it in the proportion the versed sine of the angle measured, supposing the eccentricity radius, bears to the focal length of the small mirror.
25. Mr Ramsden preferred Cassigrain's construction of the reflecting telescope to either the Gregorian or Newtonian; because in the former, the errors of one speculum are corrected by those of the other. From a property of the reflecting telescope, not generally known, that the apertures of the two specula are to each other very nearly in the proportion of their focal lengths, it follows, that their aberrations will be in the same proportion; and these aberrations will be in the same direction, if the two specula are concave; or in contrary
directions, if one speculum is concave and the other convex. In the Gregorian telescope, both specula being concave, the aberration at the second image will be the sum of the aberrations of the two mirrors; but in the Cassigrainian telescope one mirror being concave and the other convex, the aberration at the second image will be the difference between the two aberrations. By assuming such proportions for the foci of the specula as are generally used in the reflecting telescope, which is about as 1 to 4, the aberration in the Cassigrainian construction will be to that in the Gregorian as 3 to 5.
26. The other is a dioptric micrometer, or one suited to the principle of refraction. This micrometer is applied to the erect eye-tube of a refracting telescope, and is placed in the conjugate focus of the first eye-glass: in which position, the image being considerably magnified before it comes to the micrometer, any imperfection in its glass will be magnified only by the remaining eye-glasses, which in any telescope seldom exceeds five or six times. By this position also the size of the micrometer glass will not be the part of the area which would be required if it was placed in the object-glass; and, notwithstanding this great disproportion of size, which is of great moment to the practical optician, the same extent of scale is preserved, and the images are uniformly bright in every part of the field of the telescope.
27. Fig. 12. represents the glasses of a refracting telescope; xy, the principal pencil of rays from the object-glass O; tt and uu, the axis of two oblique pencils; a, the first eye-glass; m, its conjugate focus, or the place of the micrometer; b the second eye-glass; c the third; and d the fourth, or that which is nearest the eye. Let p be the diameter of the object-glass, e the diameter of a pencil at m, and f the diameter of the pencil at the eye; it is evident, that the axes of the pencils from every part of the image will cross each other at the point m; and e, the width of the micrometer-glass, is to p the diameter of the object-glass, as ma is to go, which is the proportion of the magnifying power at the point m; and the error caused by an imperfection in the micrometer-glass placed at m will be to the error, had the micrometer been at O, as m is to p.
28. Fig. 13. represents the micrometer; A, a convex or concave lens bisected by a plane across its centre; one of these semi-lenses is fixed in a frame B, and the other in the frame E; which two frames slide on a plate H, and are pressed against it by thin plates a a: the frames B and E are moved in contrary directions by turning the button D: L is a scale of equal parts on the frame B; it is numbered from each end towards the middle with 10, 20, &c. There are two verniers on the frame E, one at M and the other at N, for the convenience of measuring the diameter of a planet, &c. on both sides the zero. The first division on both these verniers coincides at the same time with the two zeros on the scale, L; and, if the frame is moved towards the right, the relative motion of the two frames is shown on the scale L by the vernier M; but if the frame B be moved towards the left, the relative motion is shown by the vernier N.—This micrometer has a motion round the axis of vision, for the convenience of measuring the diameter of a planet, &c. in any direction, by turning
ing an endless screw F; and the inclination of the diameter measured with the horizon is shown on the circle by a vernier on the plate V. The telescope may be adjusted to distinct vision by a screw, which moves the whole eye-tube with the micrometer nearer to or farther from the object-glass, as telescopes are generally made; or the same effect may be produced without moving the micrometer, by sliding the part of the eye tube on the part , by help of a screw or pinion.
29. Notwithstanding these improvements on micrometers, they are still liable to many sources of error. The imperfections of the wire micrometer, (which was still the most correct instrument for measuring small angles) when employed to determine the distance of close double stars, have been ably pointed out by Dr Herschel.
30. When two stars are taken between the parallel wires the diameters must be included. Dr Herschel* has in vain attempted to find lines sufficiently thin to extend them across the centres of the stars so that their thickness might be neglected. The threads of the silk-worm, with such lenses as he uses, are so much magnified that their diameter is more than that of many of the stars. Besides, if they were much smaller, the deflection of light would make the attempt to measure the distance of the centres this way fruitless; for he has always found the light of the stars to play upon those lines and separate their apparent diameters into two parts. Now since the spurious diameters of the stars thus included, are continually changing with the state of the air, and the length of time we look at them, we are, in some respect, left at an uncertainty; and our measures taken at different times, and with different degrees of attention, will vary on that account. Nor can we come at the true distance of the centres of any two stars, unless we know the semidiameters of the stars themselves; for different stars have different apparent diameters, which, with a power of 227, may differ from each other as far as two seconds (D).
31. The next imperfection arises from a deflection of light upon the wires when they approach very near to each other; for if this be owing to a power of repulsion lodged at the surface, it is easy to see that such powers must interfere with each other, and give the measures larger in proportion than they would have been if the repulsive power of one wire had not been opposed by a contrary power of the other wire.
32. Another disadvantage of these micrometers is an uncertainty of the real zero. The least alteration in the situation and quantity of light will affect the zero; and a change in the position of the wires will sometimes produce a difference. To remove this difficulty Dr Herschel always found his zero while the apparatus preserved the situation which it had when his observations were made; but this introduces an additional observation.
33. The next imperfection, is that every micrometer hitherto used requires either a screw, or a divided bar and pinion, to measure the distance of the wires or the two images. Those acquainted with works of this kind are sensible how difficult it is to have screws perfectly equal in every thread or revolution of each thread; or pinions and bars that shall be so evenly divided as to be depended upon in every leaf and tooth to the
two or three thousandth part of an inch: and yet, on account of the small scale of those micrometers, these quantities are of the greatest consequence; an error of a single thousandth part inducing in most instruments a mistake of several seconds.
34. The greatest imperfection of all is, that the wires require to be illuminated; and when Dr Herschel had double stars to measure, one of which was very obscure, he was obliged to be content with less light than is necessary to make the wires distinct; and several stars on this account could not be measured at all, though not too close for the micrometer.
Dr Herschel, therefore, was led to direct his attention to the improvement of these instruments; and the result of his endeavours has been a very ingenious lamp-micrometer, which is not only free from the imperfections above specified, but also possesses the advantages of a large scale.
35. It is represented in fig. 14. where ABCFE is a Dr Herschel's lamp-micrometer. stand nine feet high, upon which a semicircular board phogp is moveable upwards or downwards, and is held in its situation by a peg put into any one of the holes of the upright piece AB. This board is a segment of a circle of fourteen inches radius, and is about three inches broader than a semicircle, to give room for the handles D, P, to work. The use of this board is to carry an arm L, thirty inches long, which is made to move upon a pivot at the centre of the circle, by means of a string, which passes in a groove upon the edge of the semicircle pgolq; the string is fastened to a hook at (not expressed in the figure, being at the back of the arm L), and passing along the groove from to is turned over a pulley at , and goes down to a small barrel , within the plane of the circular board, where a double-jointed handle P commands its motion. By this contrivance, we see, the arm L may be lifted up to any altitude from the horizontal position to the perpendicular, or be suffered to descend by its own weight below the horizontal to the reverse perpendicular situation. The weight of the handle P is sufficient to keep the arm in any given position; but if the motion should be too easy, a friction spring applied to the barrel will moderate it at pleasure.
36. In front of the arm L a small slider, about three inches long, is moveable in a rabbet from the end L towards the centre backwards and forwards. A string is fastened to the left side of the little slider, and goes towards L, where it passes round a pulley at , and returns under the arm from , , towards the centre, where it is led in a groove on the edge of the arm, which is of a circular form, upwards to a barrel (raised above the plane of the circular board) at , to which the handle D is fastened. A second string is fastened to the slider, at the right side, and goes towards the centre, where it passes over a pulley ; and the weight , which is suspended by the end of this string, returns the slider towards the centre, when a contrary turn of the handle permits it to act.
37. By and are represented two small lamps, two inches high, in breadth by in depth. The sides, back, and top, are made so as to permit no light to be seen, and the front consists of a thin brass sliding door. The flame in the lamp is placed three-tenths of an inch from
(D) These imperfections are remedied in the instrument described in p. 801.
from the left side, three-tenths from the front, and half an inch from the bottom. In the lamp b it is placed at the same height and distance, measuring from the right side. The wick of the flame consists only of a single very thin lamp cotton-thread; for the smallest flame being sufficient, it is easier to keep it burning in so confined a place. In the top of each lamp must be a little slit lengthways, and a small opening in one side near the upper part, to permit the air to circulate to feed the flame. To prevent every reflection of light, the side opening of the lamp a should be to the right, and that of the lamp b to the left. In the sliding door of each lamp is made a small hole with the point of a very fine needle just opposite the place where the wicks are burning, so that when the sliders are shut down, and every thing dark, nothing shall be seen but two fine lucid points of the size of two stars of the third or fourth magnitude. The lamp a is placed so that its lucid point may be in the centre of the circular board where it is fixed. The lamp b is hung to the little slider which moves in the rabbet of the arm, so that its lucid point, in an horizontal position of the arm, may be on a level with the lucid point in the centre. The moveable lamp is suspended upon a piece of brass fastened to the slider by a pin exactly behind the flame, upon which it moves as a pivot. The lamp is balanced at the bottom by a leaden weight, so as to remain upright, when the arm is either lifted above or depressed below the horizontal position. The double-jointed handles rD, eP, consist of deal rods, 10 feet long, and the lower of them may have divisions, marked upon it near the end P, expressing exactly the distance from the central lucid point in feet, inches, and tenths.
38. Hence we see, that a person at a distance of 10 feet may govern the two lucid points, so as to bring them into any required position south or north preceding or following from 0 to 90° by using the handle P, and also to any distance from six-tenths of an inch to five or six and twenty inches by means of the handle D. If any reflection or appearance of light should be left from the top or sides of the lamps, a temporary screen, consisting of a long piece of pasteboard, or a wire frame covered with black cloth, of the length of the whole arm, and of any required breadth, with a slit of a half an inch broad in the middle, may be affixed to the arm by four bent wires projecting an inch or two before the lamps, situated so that the moveable lucid point may pass along the opening left for that purpose.
Fig. 15. represents part of the arm L, half the real size; S the slider; m the pulley, over which the cord xyx is returned towards the centre; u the other cord going to the pulley n of fig. 14. R the brass piece moveable upon the pin e, to keep the lamp upright.
At R is a wire rivetted to the brass piece, upon which is held the lamp by a nut and screw. Fig. 16, 17. represent the lamps a, b, with the sliding doors open, to show the situation of the wicks. W is the leaden weight with a hole d in it, through which the wire R of fig. 15. is to be passed when the lamp is to be fastened to the slider S. Fig. 18 represents the lamp a with the sliding door shut; l the lucid point; and it the openings at the top, and r at the sides, for the admission of air.
39. The motions of this micrometer are capable of great improvement by the application of wheels and pinions,
and other mechanical resources; but as the principal Micrometer object is only to be able to adjust the two lucid points to the required position and distance, and to keep them there for a few minutes, while the observer measures their distance, it will be unnecessary to say more upon the subject.
40. It is well known that we can with one eye look in to a telescope, and see an object much magnified, while the other eye may see a scale upon which the magnified picture is thrown. In this manner Dr Herschel generally determined the power of his telescopes; and any one who has been accustomed to make such observations will seldom mistake so much as one in fifty in determining the power of an instrument, and that degree of exactness is fully sufficient for the purpose.
41. When Dr Herschel uses this instrument he puts it at ten feet distance from the left eye, in a line perpendicular to the tube of his Newtonian telescope, and raises the moveable board to such a height that the lucid point of the central lamp may be upon a level with the eye. The handles, lifted up, are passed through two loops fastened to the tube, just by the observer, to as to be ready for his use. The end of the tube is cut away, so as to leave the left eye entirely free to see the whole micrometer.
42. The telescope being directed to a double star, it is viewed with the right eye, and at the same time with the left it is seen projected upon the micrometer; then, by the handle P, the arm is raised or depressed so as to bring the two lucid points to a similar situation with the two stars; and, by the handle D, the moveable lucid point is brought to the same distance of the two stars, so that the two lucid points may be exactly covered by the stars.
43. With a rule, divided into inches and fortieth parts, the distance of the lucid points is thus determined with the greatest accuracy; and the measure thus obtained is the tangent of the magnified angle under which the stars are seen to a radius of ten feet; therefore, the angle being found and divided by the power of the telescope, the real angular distance of the centres of a double star is ascertained. On September 25. 1781, Dr Herschel measured α Herculis with this instrument. Having caused the two lucid points to coincide with the stars, he found the radius or distance of the central lamp from the eye 10 feet 4.15 inches; the tangent or distance of the two lucid points 30.6 fortieth parts of an inch; this gives the magnified angle 35', and dividing by the power 460, we obtain 4" 34" for the distance of the centres of the two stars. The scale of the micrometer at this convenient distance, with the power of 460, is above a quarter of an inch to a second; and by putting on a power of 932, we obtain a scale of more than half an inch to a second, without increasing the distance of the micrometer; whereas the most perfect micrometers, with the same instrument, had a scale of less than the two thousandth part of an inch to a second.
44. Mr Brewster has lately directed his attention to Mr Brewster's improvement of micrometers, and has invented one in his particular which appears to be highly deserving of notice in this place. In this instrument a pair of fixed wires is made to subtend different angles by varying the magnifying power of the telescope, by sliding one tube within another; whereas in all other micrometers with wires