DORPAT TELESCOPE.

THE late Joseph Fraunhofer, of Munich, a most skilful artist and experimenter in optics (whose demise in 1826, in the prime of life, was a great loss to science), constructed a magnificent refracting telescope for the observatory of the Imperial University at Dorpat. It was received by Professor Struve, in the year 1825, and has since been found to fulfil most satisfactorily his expectation and the intentions of the maker. As this is one of the most magnificent instruments of the kind that has hitherto been constructed, and described by a figure, we have given an engraving of it, copied from the "Memoirs of the Astronomical Society."

The object-glass of this telescope is about 9/ inches in diameter, and its focal length about 14 English feet. The main tube is 13-8 feet; and, in addition, there is the small tube which holds the eye-pieces. Of these there are four; the least magnifying power is 175, and the greatest 700. After the telescope was received at Dorpat, a perfect micrometrical apparatus was ordered to be made for it. This was to consist of four annular micrometers, of which two were to be double; a lamp circular micrometer, with four eye-pieces; a refracting lamp net micrometer, with position cireles, and four eye-pieces.

The frame-work of the stand is made of oak, and the tube of deal, veneered with mahogany. The whole weight of the telescope and its counterpoises is supported at one point, namely, at the common centre of gravity of all the ponderous parts. These weigh 3000 Russian pounds, of which the framework contains 1000; the remaining 2000 are so balanced in every position, that the telescope may be turned, with rapidity and certainty, in every direction towards the heavens.

The basis of the frame is formed of two cross beams, each 9 feet 7 inches long. The ends of these are seen in the figure at A, B, C, D. They are braced by four smaller bars, forming a square, one of which is seen at E. This braced cross is fastened to the floor by eight screws, 6 of which are seen in the figure. A perpendicular post, about 6 feet high, and 7 inches square, is fixed over the centre of the cross, and is propped at the north, east, and west sides by three curved stays, denoted by G, G, G, which are fixed at their lower ends to the beams of the cross, and at the upper to the vertical post. An inclined beam H of the same thickness rests on the southern side of the meridian beam of the cross, and is attached to the vertical beam in a position parallel to the polar axis. This axis, shown in the figure at I, is a cylinder of steel, 39 inches long, and proportionally thick. It turns in two collars, and its lower end, which is rounded and polished, rests on a steel plate attached to the bearing piece K, which is secured to the inclined beam H, and has, therefore, very little friction, the weight being supported by friction rollers near the common centre of gravity; and a counterpoise L is applied, to support the axis in any position. There is a circle, 13 inches in diameter, graduated to minutes of time, fixed to the lower end of the axis, and furnished with verniers. The axis of vertical motion of the telescope, which has nearly the dimensions of the polar axis, passes through a brass tube at right angles to the latter; the tube, which is seen at M, forms a part of the frame, and is fastened at the upper end of the polar axis by twelve screws. This axis carries the circle of declination,

which is 19 inches in diameter, and is divided to every 10', with a vernier reading 10" or 5" by estimation. The tube of the telescope is fixed to the frame-work nearer to the eye end than the middle, and has two counterpoises attached to levers, which balance the two ends, and prevent the natural tendency of the longer end to bend. The brass frame holding the two axes appears on the figure clamped to the tube by two strong rings, one at each end of the centre of motion. A bent lever, carrying the weight O, embraces, by a double ring, the near end of the axis of the declination circle. The axis itself carries another weight; and by this and the weight O it is counterpoised. The slow motion in altitude is given to the telescope by a joint applied to the screw of the clamp, which has a spring urging it against a strong iron bar P, attached to the end of a cylinder M, that forms a stop to the circle; and a slow equatorial motion is given by a second joint taking hold of an endless screw, acting with the racked edge of the hour circle, while a spring presses it into action uniformly, and a lever is employed to raise it out of the rack when necessary. The handles taking hold of these screws extend to the reach of the observer, who can thus point his telescope in right ascension and declination with the same certainty as the best meridian instrument.

A regular sidereal motion is communicated to the instrument by clock-work, which keeps a star apparently at rest in the centre of the field of view; and there is a contrivance by which the sidereal can be changed into a solar, also to a lunar angular motion.

This almost invaluable instrument cost 10,500 florins (about 950 pounds sterling). The price, although it may appear considerable, yet barely covered the expenses of the workmanship of its construction. This relinquishment of the profit of trade does great credit to the ingenious and liberalminded artists, Fraunhofer, and Utzchneider, the chief of the optical establishment at Munich.

THE TIDES.

ONE of the most immediate and remarkable effects of a gravitating force external to the earth, is the alternate rise and fall of the surface of the sea twice in the course of a lunar day, or 24 hours, 50 minutes, 28 seconds of mean solar time. As it depends upon the action of the sun and moon, it je classed among astronomical problems, of whichết is by far the most difficult, and its explanation the least satisfactory. The form of the surface of the ocean in equilibrio, when revolving with the earth round its axis, is an ellipsoid flattened at the poles; but the action of the sun and moon, especially of the moon, disturbs the equilibrium of the ocean. If the moon attracted the centre of gravity of the earth and all its particles with equal and parallel forces, the whole system of the earth and the waters that cover it, would yield to these forces with a common motion, and the equilibrium of the sess would remain undisturbed. The difference of the forces, and the inequality of their directions, alone disturb the equilibrium.

It is proved by daily experience, as well as by strict mathematical reasoning, that if a number of waves or oscillations be excited in a fluid by dif ferent forces, each pursues its course, and has its effect independently of the rest. Now, in the tides there are three kinds of oscillations, depending on

different causes, and producing their effects independently of each other, which may therefore be estimated separately.

The oscillations of the first kind, which are very small, are independent of the rotation of the earth; and as they depend upon the motion of the disturbing body in its orbit, they are of long periods. The second kind of oscillations depends upon the rotation of the earth; therefore their period is nearly a day. The oscillations of the third kind vary with an angle equal to twice the angular rotation of the earth, and consequently happen twice in twenty-four hours. The first afford no particular interest, and are extremely small; but the difference of two consecutive tides depends upon the second. At the time of the solstices, this difference, which ought to be very great, according to Newton's theory, is hardly sensible on our shores. La Place has shown that the discrepancy arises from the depth of the sea; and that if the depth were uniform, there would be no difference in the consecutive tides but that which is occasioned by local circumstances. It follows, therefore, that as this difference is extremely small, the sea, considered in a large extent, must be nearly of uniform depth; that is to say, there is a certain mean depth from which the deviation is not great. The mean depth of the Pacific Ocean is supposed to be about four miles, that of the Atlantic only three, which, however, is mere conjecture. From the formula which determine the difference of the consecutive tides, it is proved, that the precession of the equinoxes, and the nutation of the earth's axis, are the same as if the sea formed one solid mass with the earth.

Oscillations of the third kind are the semidiurnal tides so remarkable on our coasts. They are occasioned by the combined action of the sun and moon; but as the effect of each is independent of the other, they may be considered separately.

The particles of water under the moon are more attracted than the centre of gravity of the earth, in the inverse ratio of the square of the distances. Hence they have a tendency to leave the earth, but are retained by their gravitation, which is diminished by this tendency. On the contrary, the moon attracts the centre of the earth more powerfully than she attracts the particles of water in the hemi'sphere opposite to her; so that the earth has a tendency to leave the waters, but is retained by gravitation, which is again diminished by this tendency. Thus the waters immediately under the moon are drawn from the earth at the same time that the earth is drawn from those which are diametrically opposite to her; in both instances producing an elevation of the ocean of nearly the same height above the surface of equilibrium; for, the diminution of the gravitation of the particles in each position is almost the same, on account of the distance of the moon being great in comparison of the radius of the earth. Were the earth entirely covered by the sea, the water thus attracted by the moon would assume the form of an oblong spheroid, whose greater axis would point towards the moon, since the columns of water under the moon and in the direction diametrically opposite to her, are rendered lighter in consequence of the diminution of their gravitation; and in order to preserve the equilibrium, the axes 90° distant would be shortened. The elevation, on account of the smaller space to which it is confined, is twice as great as the depression, because the contents of the spheroid always remain the same. If the waters were capa

ble of assuming the form of equilibrium instantaneously, that is, the form of the spheroid, its summit would always point to the moon, notwithstanding the earth's rotation. But on account of their resistance, the rapid motion produced in them by rotation, prevents them from assuming, at every instant, the form which the equilibrium of the forces acting upon them requires. Hence, on

account of the inertia of the waters, if the tides be considered relatively to the whole earth, and open sea, there is a meridian about 30° eastward of the moon, where it is always high water both in the hemisphere where the moon is, and in that which is opposite. On the west side of this circle the tide is flowing, on the east it is ebbing, and on every part of the meridian at 90° distant, it is low water. This great wave, which follows all the motions of the moon as far as the rotation of the earth will permit, is modified by the action of the sun, the effects of whose attraction are in every respect like those produced by the moon, though greatly less in degree. Consequently, a similar wave, but much smaller, raised by the sun, tends to follow his motions, which at times combines with the lunar wave, and at others opposes it, according to the relative positions of the two luminaries; but as the lunar wave is only modified a little by the solar, the tides must necessarily happen twice in a day, since the rotation of the earth brings the same point twice under the meridian of the moon in that time, once under the superior, and once under the inferior, meridian.

In the semidiurnal tides there are two phenomena particularly to be distinguished, one occurring twice in a month, and the other twice in a year.

The first phenomenon is, that the tides are much increased in the syzigies, or at the time of new and full moon. In both cases the sun and moon are in the same meridian; for when the moon is new, they are in conjunction, and when she is full, they are in opposition. In each of these positions, their action is combined to produce the highest or spring tides under that meridian, and the lowest in those points that are 90° distant. It is observed that the higher the sea rises in full tide, the lower it is in the ebb. The neap tides take place when the moon is in quadrature; they neither rise so high nor sink so low as the spring tides. The spring tides are much increased when the moon is in perigee, because she is then nearest to the earth. It is evident that the spring tides must happen twice in a month, since in that time the moon is once new and once full.

The second phenomenon in the tides is the augmentation, which oecurs at the time of the equinoxes, when the sun's declination is zero, which happens twice every year. The greatest tides take place when a full or new moon happens near the equinoxes while the moon is in perigee. The inclination of the moon's orbit to the ecliptie is 5° 8' 47"-9; hence, in the equinoxes, the action of the moon would be increased if her node were to coincide with her perigree. For it is clear, that the action of the sun and moon on the ocean is most direct and intense when they are in the plane of the equator, and in the same meridian, and when the moon in conjunction or opposition is at her least distance from the earth. The spring tides which happen under all these favourable circumstances must be greatest possible. The equinoctial gales often raise them to a great height. Bssides these remarkable variations, there are others arising from the declination or angular distance of the sun and

moon from the plane of the equator, which have a great influence on the ebb and flow of the waters. The sun and moon are continually making the circuit of the heavens at different distances from the plane of the equator, on account of the obliquity of the ecliptic, and the inclination of the lunar orbit. The moon takes about twenty-nine days and a half to vary through all her declinations, which sometimes extend 28 degrees on each side of the equator, while the sun requires nearly 3654 days to accomplish his motion from tropic to tropic through about 23 degrees; so that their combined motion causes great irregularities, and, at times, their attractive forces counteract each other's effects to a certain extent; but, on an average, the mean monthly range of the moon's declination is nearly the same as the annual range of the declination of the sun consequently, the highest tides take place within the tropics, and the lowest towards the poles.

Both the height and time of high water are thus perpetually changing; therefore, in solving the problem, it is required to determine the heights to which the tides rise, the times at which they happen, and the daily variations. Theory and observation show, that each partial tide increases as the cube of the apparent diameter, or of the parallax of the body which produces it, and that it diminishes as the square of the cosine of the declination of that body. For the greater the apparent diameter, the nearer the body, and the more intense its action on the sea; but the greater the declination, the less the action, because it is less direct.

The centre of the pair of compasses is made moveable, like those of the common proportional compasses, so as to permit the legs BB, and CC, to be considerably lengthened or shortened, when the two pieces are applied to each other. The fixed leg BB, is represented as beneath the moveable one CC, or radius, measuring 90°, and the lower end of the centre-pin, which could not be shown in the wood-cut, is made to fit the hole or centre in the protractor precisely at the same time that a stud or projecting piece of brass, being admitted into the long perforation of the leg BB, the piece becomes steadily attached to the protractor or semicircle, as is seen in the figure.

The application of this instrument is obvious.The crystal to be measured is applied between the compasses, which being thus set, are applied to the protractor, and the value of the angle may be read off at the edge of the leg CC. It is, however, seldom that accurate results can thus be attained, for the surfaces of crystals are generally too small or too imperfect to admit of such method of measurement.

The reflective goniometer, invented by Dr. Wollaston, is a more useful and perfect instrument. It enables us to determine the angles even of minute crystals with great accuracy; a ray of light reflected from the surface of the crystal being employed as radius, instead of the surface itself, Mr. W. Phillips has given the following description and practical details for the use of this instrument, ia his "Introduction to Mineralogy."

A is the principal circle, graduated on one edge to half degrees, and divided, for convenience, into two parts of 180° each. B is a brass plate, screwed upon, and supported by, the pillar C, and graduated as a vernier. F is the axle of the circle A, and passes through the upper part of the two pillars CE, the other ends of which are inserted into s wooden base. G is an axle, enclosed within F, and turned by means of the smallest circle H, which communicates a motion to all the apparatus on the left of I, without moving the principal circle A.K is a circle, to which is attached the axle of the principal circle. If, therefore, we would move the latter, it will be done by moving K; and as the axle of the principal circle includes that of the apparatus on the left of I, we necessarily give a motion to the whole instrument by moving the circle K.

These two movements being understood, let us now suppose that we want to measure a crystal; a rhomboid of carbonate of lime for instance. Let D be the rhomboid, attached by means of wax to one end of a plate of brass H; the other end of the plate being placed in a slit in the upper part of the circular brass stem O, which passes through the tube, to which it is so adjusted as to allow of being moved either up or down, or circularly, by means of the nut. The tube is fixed to the curved brass plate P, which is attached, but so as to allow of motion, to another curved plate Q, by means of a pin, the other end of the latter plate being connected with the concealed axle G, to which a motion is given by turning the little circle H. By means of the pin and the tube, therefore, we have two motions, in addition to the two before described as belonging to the axles of the instrument. The inner axle, however, may be said to be the centre of all

the motions. It will, therefore, be of advantage that the rhomboid of carbonate of lime should be placed as nearly on a line with that axle as possible: this will be sufficiently adjusted by means of the stem O, which admits of being raised or depressed at pleasure.

The use of this instrument depends on the reflecting power of the polish on the natural planes, or fractured surfaces of minerals; and that this is in some cases very powerful, any one may convince himself by looking upon a very brilliant plane, held beneath the eye, with its edge nearly touching the lower lid, and not far distant from a window; he will then observe the reflection of the bars very distinctly. Let us then suppose the goniometer, as above represented, to be distant from a window from eight to twenty feet. Let there be, then, a black line (the use of this is essential) drawn on the wainscot between the window and the floor, and perfectly parallel with the horizontal bars of the window. If, then, the eye be placed almost close to the rhomboid or crystal, a reflection of one of the bars will be seen on one of its planes. Let us suppose the reflection to be in the direction of the lower dotted line on the plane; and it will be clear that it cannot be parallel with the bar of the window, not being even with the black line. If, however, the reflection appears to be like the upper dotted line, that is, parallel with the black line, we must first convince ourselves that it is so, simply by depressing the crystal a little, by means of moving the little circle H, so as to bring the reflection upon the black line. This being adjusted, which must be done precisely, we then turn the crystal, by turning the little circle H, until the reflection of the same bar be seen on the next plane, perfectly on a line with and upon the black line. However, in adjusting the second, we may disturb the first reflection. By perseverance it will be found that both can be adjusted by means of one or the other of the movements, or by the help of both, and a short experience will do away the chief difficulties. Both reflections being precise, we are now, by means of the circle K, to turn the principal circle until it is arrested by a stop on the pillar C; it will then be found that 180 on the principal circle coincides with cipher on the vernier. In doing this, however, we may slightly disarrange the reflections on the plane of crystal, which may be re-adjusted simply by moving the little circle I, which will not disturb the principal circle A; we must be certain, however, that 180 on it forms a line with cipher on the vernier, at the same time that the reflection of the ber is seen along the black line. One movement more, and the measurement will have been made. Turn the circle K, keeping the eye almost close to the rhomboid, until the reflection of the same bar is seen on the adjoining plane precisely upon the black line on the wainscot, and the operation is completed. It must then be observed what proportion of the principal circle has been moved. Suppose that 105° on it, be now on a line with cipher on the vernier ;-it is the value of the angle. But suppose it to be a little more than 105, and less than 1054 it must then be observed which line of the ternier touches, or forms but one line with, another line on the principal circle; suppose it to be 5 on the vernier, the angle is then 105° 5', which is the true value of the obtuse angle of a rhomboid of carbonate of lime.

POLARIZATION OF LIGHT.

THE following valuable paper on the polarization of light is by Mr. Goddard, the inventor of a polaziscope and other apparatus on this subject.

The beautiful phenomena of colors produced by the transmission of polarized light through doubly refracting crystals, the various bands and concentric rings, composed of all the most brilliant and delicate tints of the solar spectrum, and the different forms, changes, and modifications, that they may be made to undergo and exhibit, are so numerous and varied as to furnish a display of the most splendid experiments within the whole range of science; whilst their value and importance in the sciences of mineralogy and chemistry, from the deep insight which polarized light affords of the minute structure and constitution of transparent bodies, which appear, upon every other mode of examination, to be perfectly homogeneous, yet, when viewed in polarized light, exhibit the most exquisite structure, (as is seen in the extraordinary configurations of apophyllite, analcine, and many others, displaying the influence of laws of combination, of which it is impossible, by any other means, to obtain the least knowledge,) renders an exhibition of these experiments not only interesting, but most desirable and important. For this purpose, after having tried numerous experiments upon the different methods now in use, I have constructed a polariscope, adapted to Mr. Cary's hydro-oxygen microscope, which is capable of exhibiting, upon a disc, on a highly magnified scale, all the beautiful and curious phenomena of this interesting branch of science.

But, previous to describing the polarizing apparatus, and the effects that may be produced by means of it, it may be as well to give a short and popular explanation of what polarized light is; and, to do this, we must notice the principal hypothesis upon which the Huygenian or undulatory theory of light is founded, at least so far as relates to the phenomena under consideration: but in so doing, I beg that I may not be understood as advocating this theory in opposition to any other, but merely using it as affording a popular explanation, which those who give a preference to its rival will have no difficulty in understanding, and can, if they please, substitute the language of its rival, the corpuscular theory.

The following are the principal postulata, according to Sir W. J. Herschel, upon which this, the undulatory theory, is founded.

1. It is supposed that a rare, elastic, and imponderable medium, or ether, fills all space, and pervades all material bodies, occupying the intervals between their molecules, and possessing inertia, but not gravity.

2. That the molecules of ether are susceptible of being set in motion by the motions of particles of ponderable matter, which motion it communicates in a similar manner to adjacent molecules; thus propagating it, in all directions, according to the same mechanical laws which regulate the propagation of undulations in other elastic media, as air and water, according to their respective constitutions.

3. That vibrations communicated to the ether, in free space, are propagated, through refractive media, by means of the ether in their interior, but with a velocity decreasing with its inferior degree of elasticity.

4. That when regular vibratory motions, of a