the threads of the male screw, and is of course passed over by either of the wires, during one complete revolution of the nut L or M. The graduated heads N and P are each divided into 100 parts, so that the distance between the wires can at any time be ascertained to the 15th part of one of the divisions of the scale a. These divisions are generally the fiftieth of an inch each, so that every unit on the graduated head corresponds to the 18th part of an inch. A third wire b, lying in the direction of the screws, bisects the other two wires at right angles, and is intended to point out the direction in which the angle is to be measured. The angle subtended by the wires, when separated to any distance, is found by counting the number of revolutions, and parts of a revolution, of the divided head N or M, which are necessary to make the one wire move up to the other, and coincide with it. The number of seconds passed over by any of the wires, during one revolution of the head N or M, must be ascertained by actual experiment, that is, by measuring a base, and observing the space comprehended between the wires at the end of that base, where they are separated by so many revolutions; or by observing the time employed by an equatorial star in passing from the one wire to the other. When the angle is thus determined which corresponds to any given number of revolutions it may be found by simple proportion for any other number of revolutions; and these results may be conveniently put down in the form of a table, to prevent the necessity of future calculation. Let it be required, for example, to measure the sun's diameter, and let us suppose that two revolutions of the divided head separate the wires to such a distance that they subtend exactly an angle of sixty seconds. Having directed the telescope to the sun, turn round the micrometer by means of the screw D, till the lower limb of the sun Ss, fig. 4, just passes along the lowest parallel wire CD. Then turn the nut which moves the other wire A B, till it is at such a distance from CD that the upper limb of the sun just passes along it. The sun Ss is now comprehended exactly between the wires, and the angle which they subtend is, therefore, a measure of his diameter. Let the wire AB be now moved towards CD till they coincide, and suppose that it requires sixty revolutions of the divided head, andths of a revolution, to produce this coincidence. Then, since two revolutions are equal to sixty seconds, 60-45 revolutions will be equal to 30-235', or 30′ 13-5", the diameter of the sun required. The diameter thus measured is obviously perpendicular to the direction of the sun's notion; but, when we wish to measure the diameter which is parallel to the line of his daily motion, we must guide his upper or his lower limb along the wire which bisects the parallel wires, and then separate the wires till the one extremity of the diameter is in contact with the first wire, at the very instant that the other extremity is in contact with the second wire. The motion of the sun, however, renders this observation so extremely difficult, that it is almost impossible to make it with any degree of accuracy. By attending to the principles upon which this instrument is constructed, it will be easy to discover the numerous sources of error to which it is liable. The difficulty of finding the real zero of the scale, or the instant when the two wires appear to be in contact; the error arising from the want of parallelism in the wires, or from a lateral shake in the forks which carry them; the inflexion of light which takes place when the wires are near each other; the complicated structure of the instrument; the minuteness of the scale and all its parts; but especially the difficulty of procuring screws in which the distance of the thread is always the same, are objections inseparable from the construction of this in strument. The lamp micrometer, contrived by the late Sir William Hercshel, appears well calculated for its intended purpose, and is described by the inventor in vol. Ixxii. of the Transactions of the Royal Society. ABGCFE, fig. 5, is a stand nine feet high, upon which a semi-circular board ghogp is moveable upwards or downwards, in the manner of some fire-screens, as occasion may require, and is held in its situation by a peg p, put into any one of the holes of the upright piece A B. This board is a segment of a circle of fourteen inches radius, and is about three inches broader than a semi-circle, to give room for the handles, r D, e P, to work. The use of this board is to carry au 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 semi-circle pgo hq; the string is fastened to a hook at o (not expressed in the figure, being at the back of the arm L), and passing along the groove from oh to q is turned over a pulley at 9, and goes down to a small barrel e, within the plane of the circular board, where a doublejointed handle e 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. 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 m, and returns under the arm from m, n, 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 r, to which the handler D is fastened. Á second string is fastened to the slider, at the right side, and goes towards the centre, where it passes over a pulley n, and the weight w, 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. a and b are two small lamps, two inches high, one and a half in breadth by one and a quarter 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 folding-door. The flame in the lamp a is placed three-tenths of an inch 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 lampcotton 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 also a small opening in one side near the upper part, to permit air enough to circulate to feed the flame. To prevent every reflexion 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 cut down, and every thing dark, nothing shall be seen but two fine lucid points of the size of the 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 remains fixed. The lamp b is hung to the little slider which moves in the rabbet of the arm, so that its lucid point, in a 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 always to remain upright, when the arm is either lifted above, or depressed below, the horizontal position. The double-jointed handles r D, e P, consist of light deal rods ten feet long, and the lowest 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. From this construction we see that a person at à distance of ten 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 reflexion 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 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. 6 represents part of the arm L, half the real size; S the slider; m the pulley, over which the cord rty z is returned towards the centre; v the other cord going to the pulley n of fig. 5; R the brass-piece moveable upon the pin c, to keep the lamp upright. At R is a wire riveted to the brass piece, upon which is held the lamp by a nut and screw. Figs. 7 and 8 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. 6 is to be passed when the lamp is to be fastened to the slider S. Fig. 9 represents the lamp a with the sliding door shut, i the lucid point, and ik the openings at the top, and s at the sides for the admission of air. Every ingenious artist will soon perceive that the motions of this micrometer are capable of great improvement by the application of wheels and pinions, &c.; but as the principal 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 goes to measure their distance, it will not be necessary to say more on the subject. We have now to show the application of this instrument. It is well known to opticians and others, who have been in the habit of using optical instruments, that we can with one eye look into a microscope or telescope, and see an object much magnified, while the naked eye may see a scale upon which the magnified picture is thrown. In this manner Sir William Herschel generally determined the power of his telescopes; and any one who has acquired a facility of taking such observations, will very 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. The Newtonian form is admirably adapted to the use of this micrometer; for the observer stands always erect, and looks in a horizontal direction, notwithstanding the telescope should be elevated to the zenith. Besides, his face being turned away from the object to which his telescope is directed, this micrometer may be placed very conveniently without causing the least obstruction to the view. Sir W. Herschel observed that, when he used this instrument, he put it at ten feet distance from the left eye, in a line perpendicular to the tube of the telescope, and raised 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, so as to be ready for his use. It may be proper to state that the end of the tube is cut away so as to leave the left eye entirely free to see the whole micrometer. Having now directed the telescope to a double star, view it with the right eye, and at the same time with the left see it projected upon the micrometer: then, by the handle P, which commands the position of the arm, raise or depress it so as to bring the two lucid points to a similar situation with the two bars; and, by the handle D, approach or remove the moveable lucid point to the same distance of the two stars, so that the two lucid points may be exactly covered by, or coincide with, the stars. A little practice in this business soon makes it easy, especially to one who has already been used to look with both eyes open. What remains to be done is very simple. With a proper rule, divided into inches and fortieth parts, take the distance of the lucid points, which may be done to the greatest nicety, because the little holes are made with the point of a very fine needle. 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 gives the real angular distances of the centres of a double star. round its axis, while the number of revolutions of the screw is shown by the divisions on the same index. The steel screw, R, may be turned by the key S, and serves to incline the small mirror at right angles to the direction of its motion. The other micrometer, invented by Mr. Ramsden, is suited to the principle of refraction, and is thus described by Mr. Partington :-"This micrometer is applied to the erect eye-tube of a refracting telescope, and is placed in the conjugated focus of the first eye-glass; in which position, as the image is 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; and besides, the size of the micrometer glass will not be the th part of the area which would be required, if it were placed at the object-glass; and yet the same extent of scale is preserved, and the images are uniformly bright in every part of the field of the telescope. This micrometer is represented at fig. 11. A is a convex or concave lens, divided into two equal parts 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 aa; the frames B and É 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 12, 20, &c. There are two verniers on the frame E, one at M and the other at N, for the conveniency of measuring the diameter of a planet, &c., on both sides of 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. The late Mr. Ramsden described two valuable micrometers, which he contrived with the view of remedying the defects of those that had been previously constructed. One of these is a catoptric micrometer, and can have no aberration, nor is it liable to any defect arising from the imperfection of the materials or 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 image 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 also 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 is of no small 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. A, fig. 10, represents the small speculum of a reflecting telescope, of Cassegrain's construction, to which this micrometer is adapted, 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 steel 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 y, that turns on the axis X; both arms are prevented from bending by the braces a a. 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 "This micrometer has a motion round the axis fifty only. The screw e works in a nut F, in of vision, for the conveniency of measuring the the side of the telescope, while the part g turns diameter of a planet, &c., in any direction, by in a nut H, which is attached to the arm B; the turning an endless screw F; and the inclination ends of the arms B and D, to which the mirrors of the diameter measured with the horizon is are fixed, are separated from each other by the shown on the circle g, by a vernier on the plate point of the double screw pressing against the V. The telescope may be adjusted to distinct stud h, fixed to the arm D, and turning in the vision by means of an adjusting screw, which nut H on the arm B. The two arms, B and D, moves the whole eye-tube with the micrometer, are pressed against the direction of the double nearer or farther from the object-glass, as telescrew eg, by a spira! spring within the part n, scopes are generally made; or the same effect by which means all shake or play in the nut H, may be produced in a better manner, without on which the measurement depends, is entirely moving the micrometer, by sliding the part of prevented. the eye-tube m on the part n, by the help of a screw or pinion. The micrometer is made to take off occasionally from the eye-tube, that the telescope may be used without it.' Vide Manual of Natural and Experimental Philosophy, by C. F. Partington. 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. 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 Mr. Cavallo has contrived a micrometer of very simple and easy construction. It consists of a thin and narrow slip of mother-of-pearl finely divided, and situated in the focus of the eye-glass of a telescope, just where the image of the object is formed. It is immaterial whether the telescope be a refractor or reflector, pro vided the eye-glass be a convex lens, and not a tant from each other, and as strictly parallel, and at right angles to the perpendicular as possible. A rod being placed upright at twenty chains distance, or any other convenient distance on level ground, an index, consisting of a round disc of about eight inches in diameter, painted white, with a horizontal line of one inch wide, painted on its horizontal diameter with vermilion, was fixed upon the rod about one foot from the ground, and another similar index was moved up and down the rod, until, upon looking through the telescope, the two horizontal hairs covered the red stripes on the lower and upper indexes, the telescope being turned on its axis until the perpendicular hair was parallel to the rod. The indexes being thus covered accurately by the horizontal hairs, the upper index was fixed to the rod, and the distance between the middle of the red stripes on the two indexes was divided upon the rod into twenty parts, representing so many chains, which, with the instrument Mr. Watt used, were upon the rod about four inches and a half each; and, for distances exceeding five chains, this division into equal parts was sufficiently accurate; but for shorter distances it is not strictly so. He therefore fixed a pin at every chain, and, holding up the rod at each of them, made the necessary correction; and, as the focus of the object-glass is also affected by the distance, it is proper to adjust the eye-glass to it at each station. The divisions on the rod being marked with the number of chains they represent, it was only necessary to send an assistant with the rod to any place the distance of which was wanted to be measured, and by signs to make him move the upper index up and down, until the two horizontal hairs covered the red stripes on the upper and lower indexes; the divisions on the rod then showed the distance, which could be ascertained to within less than th part of the whole distance, and with a higher magnifying power could be done proportionally more accurate. The rod commonly used was twelve feet long, and consequently could measure thirty chains; but by sliding another rod upon it, so as to lengthen it, he measured greater distances; and, where still greater were wanted, a tape was stretched horizontally, and turning the telescope on its axis, Mother-of-pearl was found by Cavallo, after made the single hair parallel to it, fixing one many trials, to be a much more convenient sub-index at the end of the tape, and sliding the stance than either glass, ivory, horn, or wood, as it is a very steady substance, the divisions are easily marked upon it, and, when made as thin as common writing-paper, it has a very useful degree of transparency. The mother-of-pearl micrometer may be applied to a microscope, and it will thus serve to measure the lineal dimensions of the object. The value of its divisions may be ascertained by placing an object of a known dimension before the microscope, and by observing how many divisions of the micrometer measure its magnified image. For instance, place a piece of paper, which is exactly one-tenth of an inch long, before the microscope; and, if it is found that fifty divisions of the micrometer measure its magnified image, the observer may conclude that each division denotes an extension of th part of an inch in the object; for, if fifty divisions measure one-tenth, 500 divisions must measure the whole jach. Mr. Watt has furnished a description of several micrometers that he contrived, and of which he published an account in the Edinburgh Philosophical Journal. One was suggested about the year 1770, and was used in the surveys for the Crinan and Caledonian Canals. The instrument he used was a telescope, with an object-glass of twelve inches, and an eye-glass of one inch and a half focus, consequently magnifying eight times. In the focus of the eyeglass there were placed two horizontal hairs, fig. I. plate 2, and one perpendicular hair. The horizontal hairs were about one-tenth of an inch dis other along it subtended the distance between the wires. Mr. Watt then measured the subtended tape with the rod, and so ascertained the distance. It is plain that this instrument possesses the advantage of measuring all distances with equal accuracy, until the imperfection of vision at great distances interposes, as the scale on which they are measured expands with the distances, and in uneven ground it possesses more accuracy than the chain, and is very valuable in measuring distances from one hill to another, and across bays of the sea, where the chain cannot be used. Another micrometer, with a prism, Mr. Watt invented about that time; it consisted of a thin prism, with its surfaces nearly parallel, or inclined one degree or two as in fig. 2. This prism was |