DESCRIPTION AND USES OF THE CIRCLE OF REFLECTION. THE Circle of Reflection was invented by the celebrated Professor Mayer, of Groningen, and has since been greatly improved by the Chevalier De Borda, Mr. Troughton, and Mr. Mendoza y Rios. In its present improved state, it has a decided superiority over the sextant, in measuring the distance of the moon from the sun or a star, on account of its correcting, in a great measure, the errors arising from a faulty division of the limb, want of parallelism in the surfaces of the mirrors and colored glasses, and entirely avoiding the error which might arise in a sextant from the mirrors not being parallel when the index is on 0. Figure 1, Plate X., represents the Circle of Reflection, as given by De Borda. In figure 2 is a section of the same instrument, marked with the same letters of reference as in figure 1. The principal parts of this instrument are, the circular limb LMV; the central index EF; the horizon index MD; the central glass or mirror A; the horizon glass or mirror B; the telescope GH; the colored glasses, figures 3, 4; the handle, figure 5; the ventelle, figure 6; and the adjusting tool, figure 7. The limb of the instrument LMV is a complete circle of metal, and is connecte with a perforated central plate by six radii; it is divided into 720°, because of the double reflection; each degree is generally divided into three equal parts, and the division is carried to minutes, or lower, by means of the verniers of the two indices. The two indices are movable round the same axis, which passes exactly through th centre of the instrument; the central index EF carries the central mirror A ; and the horizon index MD carries the telescope GH and the horizon mirror B; both indices are furnished with verniers and tangent screws at O and N. The central mirror A is placed on the central index immediately above the centre of the instrument; the plane of this mirror makes an angle of about 30° with the middle line of the index, and is adjusted perpendicular to the plane of the instrument, by means of the screws placed on the back part of the frame of the mirror. The horizon glass B is placed on the horizon index, near the limb, so as to interfere as little as possible with the rays proceeding from objects situated on the opposite side of that index with respect to the central mirror. The horizon glass is adjusted perpendicular to the plane of the instrument, in a similar manner to that of the horizon glass of a sextant; and in some circles, this mirror is movable about an axis perpendicular to the plane of the instrument; by this means the situation with respect to the telescope may be adjusted. The telescope GH, attached to the other end of the horizon index, is an astronomical one, inverting the observed objects, and has two parallel wires in the common focus of the glasses, distant from each other between two and three degrees. These wires, at the time of observation, must be placed parallel to the plane of the instrument: to effect this, marks are made on the eye-piece, and on the tube at G, and by making them coincide, the wires may be brought to their proper position. The telescope may be raised or depressed by two screws, I, K, so as to be directed to any part of the horizon glass; and, by means of the graduations on the two standards, i, k (Fig. 2), the telescope may be rendered parallel to the plane of the instrument. There are two sets of colored glasses (fig. 3, 4), each set usually containing four glasses of different shades; the glasses of the large set (fig. 4), which are placed before the central mirror at a, a, should have each about half the degree of shade with which the corresponding glasses (fig. 3) of the other set, placed at C, are tinged, because the rays from the luminous object pass twice through the colored glass placed before the central mirror, and only once through the other. The glasses placed at a, a, are kept tight in their places by small pressing screws at their ends, or by slides passing, in front, through perforations in the stems of their frames; when fixed for observation, they make an angle of about 85° with the plane of the instrument; by this means, the image from the colored glass is not reflected to the telescope. When the angle to be measured is between 5° and 35°, one of the large set is to be fixed at a, a; in other cases, one of the small set is to be placed in the socket C. The reason of using the large glass is this:-when the small glass is placed at C, it intercepts the direct light of the luminous object, in its passage towards the central mirror, if the object happens to be situated within the angular space included by the lines from the centre A, by the sides of the frame of the glass placed at C. This is avoided by using the large glasses. The handle (fig. 5) is of wood, and is fixed to the back of the instrument immediately under the centre. By this it is held during the time of observation. The ventelle (fig. 6) is used in terrestrial observations to diminish the light of the object seen directly, to render it equal in brightness to that of the object seen by reflection; this is performed by putting the ventelle in the socket D, and raising or depressing it till the objects appear of equal brightness. There are two adjusting tools, of the form represented in figure 7; they are exactly of the same size, and their height is nearly equal to that of the central mirror; they may be used in adjusting the central mirror perpendicular to the plane of the instrument, and in making the axis of the telescope parallel to that plane. The instrument, as we have now described it, is the same as it was left by De Borda. Mr. Troughton has since suggested the improvement of fixing to the horizon index the arc WSPR, and providing it with two sliding pieces U, X, in order to facilitate the fixing the indices at their proper angles with each other in taking successive observations. When the central and horizon glasses are parallel, the central index covers the space SP of the arc, and the spaces SW, PR, are each divided into degrees from S to W, and from P to R, and numbered 0 at S and P, and continued to 130° towards W and R. The use of this arc and sliding pieces will be explained hereafter.* That ingenious mathematician and navigator, Mr. Mendoza y Rios, has further improved the circular instrument, by the substitution of a circular ring (moving round the centre of the instrument, over or adjacent to the limb TMV) for a vernier, instead of those attached to the indices by De Borda; and, by fixing this circular vernier alternately to each of the indices, it serves as a vernier for both, and, after any number of observations, gives the compound motion of both indices; and thus double the number of distances are obtained by this instrument, that can be obtained by De Borda's circle, with the same number of observations. Mr. Rios has also improved the form of the handle for holding the instrument. In theory, the instrument as improved by Mr. Rios appears to be superior to that of De Borda; but not having used one of the former kind, I cannot, from my own experience, decide whether it is so much superior in practice; but Mr. Rios says that he found it answered his expectations. As the method of taking the observation is nearly the same with both instruments, I shall confine myself to the explanation of the uses of De Borda's, from which the method of using the other will be easily discovered. Adjustments of the circle of reflection. Before entering upon an explanation of the adjustments of this instrument, it will be proper to premise that there are three different methods of observing the angular distance of two objects with this instrument, viz. (1) by what is called an observation to the right, (2) by an observation to the left, and (3) by a cross observation. An observation to the right is that where the object whose image is to be reflected, and the central mirror, are on the same side of the telescope; an observation to the left, when the object to be reflected and the central mirror are on opposite sides of the telescope, which, in both cases, is supposed to be directed to the other object; and a cross observation is a combination of the fore-mentioned observations, the first being generally taken to the left, and the second to the right. The adjustments of a circle consist in placing the mirrors perpendicular to the plane of the instrument, and in making the axis of the telescope parallel to that plane. * Mr. Troughton suggested another alteration in the circle; but (as Mr. Rios justly observes) the instrument thus altered may be considered as a sextant, the limb of which is completed to the whole circumference. A circle of this description is usually furnished with three indices and verniers, by each of which every observation must be read off. This is very troublesome, particularly in the night. It is true that this method corrects, in a very great degree, the error of not having the index exactly on the centre, or that of not having an instrument perfectly circular; but errors of this kind in Borda's circle may be reduced in any ratio by taking a number of observations, and the error will in general be extremely small in taking a sufficient number to bring the index nearly to the point set out from ; These are all the adjustments necessary in measuring an angular distance by cross observations; but if one observation only be taken to the right, or to the left, it will be necessary to find the division on which the horizon index must be placed, to make the horizon glass parallel to the central glass, when the central index stands on 0 These adjustments are similar to those of a sextant; but a particular explanation of each will here be given. To set the central glass perpendicular to the plane of the instrument. This adjustment may be made by placing the eye in front of the central glass at L, a little above the plane of the instrument, and observing if the reflected image of that part of the limb nearest the eye appears to make one continued circular line with the parts of the limb towards T, seen to the right and left of the central glass; for, in this case, the glass is perpendicular to the plane of the instrument; otherwise it must be adjusted by means of the screws till the two images coincide.* By examining this adjustment in different parts of the limb, it will be known if the limb be in the same plane. If any difference should be found, the central glass must be so fixed that the reflected image of the limb may appear as much above the direct image in some places as below it in others. To set the horizon glass perpendicular to the plane of the instrument. The central glass being previously adjusted, and the telescope directed to the line separating the silvered from the transparent part of the horizon glass, hold the instrument nearly vertical, and move either index till the direct and reflected image of the horizon, seen through the telescope, coincide; then incline the instrument till it is nearly horizontal, and, if the images do not separate, the horizon glass is perpendicular to the plane of the instrument; but if they do separate, the position of the glass must be rectified by means of the screws in its pedestal. This adjustment may be also made by directing the sight through the telescope to any well-defined object; then if, by moving the central index, the reflected image passes exactly over the object seen directly, the glass is perpendicular; otherwise its position must be adjusted by means of the screws attached to the pedestal of the glass. A planet, or star of the first magnitude, will be a good object for this purpose. If the sun is used, one of the colored glasses must be placed at C, and another at D. To make the axis of the telescope parallel to the plane of the instrument. The telescope may be raised or depressed by means of two screws attached to the standards i, k (fig. 2), and passing through two pieces of brass connected with the tube of the telescope. On each of these pieces is a mark or index, by which the telescope is to be adjusted; for, by bringing the indices to the same mark on each standard, the telescope will be parallel to the plane of the instrument. † To find that division to which the horizon index must be placed to render the mirrors parallel when the central index is on 0. Place the central index on 0; direct the telescope to the horizon glass, so that the line joining the silvered and transparent parts of that glass may appear in the middle of the telescope; hold the instrument vertically, and move the horizon index till the direct and reflected horizons agree, and the division shown by the horizon index will be that required. This adjustment may also be made by measuring the diameter of the sun in *When the instrument is furnished with adjusting tools, this adjustment may be made in the following manner-Set the two tools on opposite parts of the limb at T and L; place the eye at e, at nearly the same height as the upper edge of the tools, so that part of the tool at T may be hid by the central glass; move the central index till the reflected image of the tool nearest the eye appears in the central glass at the side of the other tool seen directly; then, if the upper edges of the tools are apparently in the same straight line, the central glass is perpendicular to the plane of the instrument; otherwise its position must be adjusted by the screws at the back of the frame. If you suspect that the marks on the standards are inaccurate, you may examine them in the following manner-Lay the circle horizontally on a table; place the two adjusting tools on opposite parts of the limb, at T and L; and at about 12 or 15 feet distance let a well-defined mark be placed, so as to be in the same straight line with the tops of the tools; then raise or lower the telescope till the mark is apparently in the middle between the two wires; then the axis of the telescope will be parallel to the plane of the instrument, and the difference (if any) between the divisions pointed out by the indices on the graduation of the standards i, k (fig. 2), will be the error of the indices, and, this being known, it will be easy, in future adjustments, to make allowance for it. contrary directions; thus, the central index being fixed on 0, place a dark glass at C, and another at D; direct the telescope (through the transparent part of the horizon glass) to the sun, and move the horizon index till his reflected image appear in the elescope; bring the upper edge of the direct image to coincide with the lower of the other, and note the angle shown by the index; then, by moving the horizon index, bring the lower edge of the direct image to coincide with the upper edge of the reflected one, and note also the angle pointed out by the index; half the sum of these wo angles will be the point of the limb where the horizon index must be placed to ender the mirrors parallel. Thus, if the index, in the first observation, is on 473° 30′, and, in the second, on 474° 34', the half sum of the two, 474° 2, will be the point where the horizon index must be placed to make the mirrors parallel. These are all the adjustments necessary to be made* preparatory to measuring any angular distance. When the angle is measured by cross observations, the error arising from the want parallelism of the surfaces of the mirrors and screens, will in general be very small; however, the method of verifying those glasses, and making allowance for any error in them, will be given hereafter. To observe th idian altitude of any celestial object, either by an observation to the right or to the left. The method serving the meridian altitude of an object with a circle, is exactly similar to that with a quadrant or sextant. The central index must be fixed on 0, and the horizon index on the point which renders the two mirrors parallel; then the altitude may be taken either by an observation to the right or to the left; but the former method, in which the large colored glasses are not necessary, is in general to be preferred, because these large glasses are more liable to cause an error in the observation than the small ones. If an observation to the right is to be taken, a small dark glass must be placed at C, if The object be bright; then hold the instrument in the right hand, in a vertical position; ove the central index, according to the order of the divisions of the limb, till the eflected image of the object, seen in the telescope, nearly touches the direct image of the horizon; tighten the index by the screw at the back of the instrument; make the contact complete in the middle between the parallel wires of the telescope, by the tangent screw, and by sweeping, exactly in the same manner as when observing with a quadrant, and the central index will point out the altitude of the object. If an observation to the left is taken, and the object be bright, a large dark glass must be placed at a, a, if the altitude be between 5° and 35°, otherwise a small glass at C; hold the instrument in the left hand, in a vertical position; move the central index contrary to the order of the divisions, and bring the reflected image in contact with the horizon as above; the angle shown by the central index, being subtracted from 720°, will be the sought altitude. In both these methods of observing the meridian altitude of an object, the circle, the radius of which is only five inches, will hardly be so accurate as a good sextant of a larger radius; but, by the help of a well-regulated watch, the meridian altitude may be obtained, by the circle, to a much greater degree of accuracy than by a sextant, by observing in the following manner:-A few minutes before the object passes the meridian, begin to observe the altitude by cross observations (in the manner to be described in the next article), and note the time of each observation by the watch; continue to observe till a few minutes after the object has passed the meridian; then the angles shown by the central index, being divided by the whole number of observations, will give the approximate meridian altitude; the correction to be applied to it to obtain the true meridian altitude, may be found by means of Tables XXXII. and XXXIII., by a method which will be explained hereafter, when treating of finding the latitude by a single altitude of the sun. In this article, the meridian altitude only has been spoken of, though it is eviden' * In some instruments, there is an adjustment of the horizon glass, to place it at its proper angle with the axis of the telescope; if an adjustment of this kind is necessary, it ought to be made before the other adjustments, in such manner that a colored glass be fixed at C, none of the rays from the central glass can be reflected to the telescope from the horizon glass, without passing the colored glass. To effect this, the ventelle must be placed at D, and lowered so as to intercept the direct light entirely; then place the colored glass at C, and direct the telescope to the silvered part of the horizon glass move the central index, and if no uncolored images appear (reflected from the central glass), but a have the same tinge as that of the colored glass used, the horizon glass is in its proper position; otherwise it must that the method is applicable to an object not on the meridian; but, in this case, the cross observations, which give to the circle all its advantages, may be used, and the mean of the altitudes taken instead of a single altitude. This method is peculiarly adapted to the taking of altitudes for regulating a watch; for this reason it will be particularly explained in the following article: To take altitudes of the sun, or any celestial object, by cross observations, for regulating a watch. Times of obs. 4 21 10 4 23 0 4 24 45 4 25 30 Fix the central index on 0, and if the object be bright, and the altitude between 5° and 35°, place a large colored glass before the central glass at a, a, otherwise a small one at C; hold the instrument in the left hand, in a vertical position; move the horizon index till the image of the reflected object be brought in complete contact with the horizon, in the middle between the two parallel wires of the telescope, as directed in the preceding article, and note the time of observation by the watch; then fasten the horizon index; hold the instrument in the right hand, in a vertical position; move the central index according to the order of the divisions, till the reflected image be again brought into complete contact with the horizon as above, and note the time of observation. Then half the sum of the times, and half the angle shown by the index, will be a mean time, and a mean altitude corresponding thereto. 6)26 16 40 Angle. 6)60° 21 4 22 47 10 4 If greater accuracy be required, the observation must be repeated, setting out from the points where the indices then are, and observing in the same manner by moving first the horizon index, then the central one; continue taking as many of these cross observations as are judged necessary, and note the times of each observation; then the sum of the times, divided by the whole number of observations, will be a mean time; and the angle shown by the central index, divided by the number of observations, will be a mean altitude corresponding thereto. Thus, if six † observations were taken, and the times noted as in the adjoined table, the angle shown by the index being 60° 24′, the mean time would be obtained by dividing the sum of the times, 26h. 16m. 40s., by 6, and the mean altitude by dividing 60° 24′ by 6; therefore the mean time would be 4h. 22m. 47s., and the mean altitude corresponding 10° 4'. To measure the distance between the sun and moon by a circular instrument. The instrument being well adjusted, fix the central index on 0, and, if the object be bright, place a small dark glass at C; hold the instrument so that its plane may be directed to the objects with its face downwards when the sun is to the right of the moon; otherwise, with its face upwards; direct the sight through the telescope to the moon; move the horizon index, according to the order of the divisions of the limb, till the reflected image of the sun appears in the telescope, and the nearest limbs of the sun and moon are almost in contact; fasten the index, and make the coincidence of the limbs perfect, in the middle between the two parallel wires of the telescope, by means of the tangent screw of the horizon glass, and note the time of observation; *The are described on the limb by the central index, will be equal to twice the altitude of the object, or twice the angle passed over by the other index: if more cross observations be taken, each of the indices, when moved, will describe an arc equal to double the altitude of the object; the same is to be observed in measuring any other angular distance. If the instrument is furnished with the arc WSR, and sliding pieces U, X, you must bring the slide X to the central index, after taking the first observation to the left, and place the slide U at the same degree, on the arc SW, that X is on the are PR; then, in the next observation, the central index is to be brought to touch the slide U; in the next observation to the left, the slide X is to be brought to the central index, and so on for the other observations. Thus, by means of the slides, the indices may be placed at nearly their proper angles with each other at the beginning of the observation, which will save considerable time. After being thus fixed, the contact must be completed by means of the tangent screw of the index, which is to be moved. The number 6 is a convenient number to use, because the remainder of the division of the hours by 6 gives the first figure of the minutes; and the remainder of the division of the minutes by 6 gives the first figure of the seconds. Thus, in the above example, in dividing 26h. by 6, we get 4h., and the remainder 2 is set down immediately for the first figure of the minutes; the second figure of the minutes is the quotient 2, found by dividing 16m. by 6, and the remainder 4 of this last division is the first figure of the seconds. We may remark that, as the term 4h. 20m. is common to all the 6 observations, it may be neglected; then adding the minutes in the column of units, and the seconds, the sum becomes 16m. 40s; dividing this by 6 gives 2m. 47s., to be connected with 4h. 20m., making, as above, 4h. 22m. 473. |