12,000

the proportion of the distance of these parts is nearly as 60 to 59, and then the difference of the attractions is about th of the whole attraction of the moon. But, for the sun, the proportion of distances is nearly as 24,000 to 23,999, and then the difference of the attractions is about th of the whole attraction of the sun. The consequence is, that the difference of attractions of the moon is actually three times as great as that of the sun, and the precession produced by the moon is three times as great as that produced by the sun. Now the moon's orbit does not coincide with the ecliptic, but is inclined to it at an angle of 5°; and this orbit, from the disturbing effect of the sun's attraction, moves so that its nodes or intersections with the ecliptic travel entirely round in the space of nineteen years, preserving its constant inclination of 5. The earth's equator is inclined to the ecliptic at a constant angle of 23, and therefore the inclination of the moon's orbit to the earth's equator is constantly changing, and the moon's orbit is, for half the nineteen years, very little inclined to the earth's equator, and for the remaining half is very much inclined to it. In the former case, precession goes on very slowly, and in the latter very rapidly; and this irregularity in the rate constitutes the great part of lunar nutation. The tilting of the axis from side to side of its normal position is modified by the earth's rotation into motion in a small ellipse, having a major axis of 18", which is completed in about nineteen years. Bradley, in fact, found that the star 7 Draconis continued to move north of its proper place from 1727 to 1736, a motion totally inconsistent with parallax, which would have been complete in a year; and having formed his hypothesis of the cause, he continued his observations, and found the star then returned, and went south for nearly ten years, so that in 1748 he was enabled to announce his discovery of the nutation (or nodding) of the earth's axis. The effect of this nutation, if existing alone, would be the motion of the earth's pole in the small ellipse previously described; but, as precession is going on at the same time, and carrying the pole of the earth round the pole of the ecliptic in a circle of 23 radius, the two motions become compounded, and the result is an undulation of the precession curve, the small ellipses of nutation never being completed, but the motion of the pole turned into an undulatory circle instead of a uniform sweep round the ecliptic pole.

As the precession of the equinoxes alters the places of the

*For these proportions, and the general idea of the treatment of the causes of the motions of precession and nutation, the author is indebted to Airy's Ipswich Lectures on Astronomy, a work which is unrivalled for the lucidity and completeness of its explanations, and is invaluable alike to both student and teacher.

stars so materially, it becomes necessary, in constructing catalogues and maps of the stars, to name the precise period or epoch at which they represent the places; and this is done by affixing the proper date of the catalogue or map to which all the observations have been reduced, and then by adding to the lists of the stars' right ascensions and declinations other columns showing the annual variation in these co-ordinates caused by precession, the place of each star can be calculated for any other time, either before or after the catalogue epoch.

From the preceding explanation of the motions of precession and nutation, which has been given in the simplest form possible, it will be seen that the subject is one presenting some difficulty in its conception to the non-mathematical student; and even with the aid of diagrams the difficulty is not readily obviated. It has therefore always been a desideratum to obtain for educational purposes some piece of mechanism which should imitate the motions in question, and render tangible that which had to be comprehended by the mental faculties. Accordingly, Bohnenberger, the late Professor Baden Powell, and others, have devised such pieces of apparatus, in which a conical motion of an inclined axis round a perpendicular was obtained, but an exact representation of the earth itself was not attempted.

About nine years since, the writer having occasion to explain these motions to a popular audience, contrived an apparatus for the purpose of illustration, which is admitted to imitate them perfectly, and which having been found extremely useful by him, and the limited circle to whom it has hitherto been known, is now made more generally public.*

Its conception was founded on two well-known data. First, it has long been known that the motions of a child's top in spinning afford an excellent illustration of the conical movement of the earth's axis in precession, although, from the force being opposite in character, the tendency there is to increase the distance between the axis of the top and the perpendicular to the horizon, while in the earth's case the tendency is to bring the axis of the earth nearer to the axis of the ecliptic; still the tilting force, modified by rotation, produces in the axis of the top while spinning a motion describing a cone round the perpendicular, preserving (until near the end of its spin) the same inclination; but in this case the motion is in the same direction as that of the rotation, instead of being the reverse, as in precession, and the analogy, therefore, here fails. The

*It has only been previously described and figured in the monthly Notices of the Royal Astronomical Society, vol. xv., and in Worms' excellent work, The Earth and its Mechanism.

second principle of the author's apparatus, however, removes this difficulty. It had been shown by Mr. Atkinson, in the first volume of the monthly Notices of the Royal Astronomical Society, that by altering the position of the centre of gravity with respect to the point of suspension in a rotating disk, the conical motion could be made to coincide with, or be the reverse of, that of rotation. Guided by these principles, and adding such improvements as would more effectually represent the real motions of the earth, the apparatus shown in elevation and section by the accompanying engravings was constructed. It

consists of a small terrestrial globe, having a brass disk passing through the centre, and representing the equator projecting from the globe. The base of the globe is hollowed out, to allow its suspension on a point which rises in the interior to the level of a horizontal graduated circle, representing the ecliptic. Through the upper hemisphere runs a steel axis projecting above the North Pole, and terminating in a cup at the middle of the globe, which axis is capable of being raised and lowered by a screw motion in the brass socket at the

pole.* If now the axis be so adjusted that the point of suspension is above the equatorial disk, and consequently above the centre of gravity, and the globe be rotated rapidly from west to east, by winding a silk cord round the axis, and spinning it like a top, it will be seen that while the rotation from west to east on the axis imitates the diurnal motion of the earth, there is also generated a slow conical movement of the projecting axis round the pole of the horizontal circle, representing the ecliptic, in a direction opposite to that of the diurnal rotation, that is, from east to west; and that the equinoctial points or intersections of

PRECESSION APPARATUS, FIG. 2, SECTION.

the equator and ecliptic move slowly round in the same way. It is necessary that either a small weight should be attached to the equatorial disk, which may be done by putting a little piece of brass on a pin, or the equator may be made to preponderate a little on one side, or a simple inclination of the axis at starting will suffice to produce the precessional motion; but it is better to have the equator slightly weighted on one side, as in this case it is found that besides describing the circle representing precession, it will be seen that the projecting axis

* Mr. Hislop, of 108, St. John Street Road, constructs the apparatus.

performs a number of minute oscillations, or noddings, which render the principal curve undulatory in character, and give a perfect imitation of the nutation of the earth's axis, as well as of the precession of the equinoxes.

By carefully adjusting the distance between the point of suspension and centre of gravity, the rate of the motion can be adjusted to any desired proportion between it and the rotatory movement; and of course by lowering the centre of gravity, the directions of the two motions may be made to coincide as in the spinning top; while by getting the two points to meet at the same place, the tendency to conical motion is neutralized, and the rotating globe can then be carried round a central ball or lamp, representing the sun, with its axis constantly pointing in one direction, affording an illustration of the parallelism of the earth's axis, producing the phenomena of the seasons, thus rendering the apparatus useful in another way, as well as in its original purpose of exemplifying the mechanical principles which produce the important phenomena of the Precession of the Equinoxes.

MICROSCOPIC PURSUITS.*

THE highly successful efforts of many opticians in London and elsewhere, to make good and cheap microscopes, have supplied thousands of individuals and families with the means of perpetual recreation of a scientific kind, and we are glad to observe the publication of numerous works calculated to suit the wants and the pockets of those who may be disposed to let amusement and improvement go hand in hand. To gaze for a few moments at a well prepared slide, or at a small natural object, placed on the stage of a microscope, is an agreeable, but very transient and unsatisfactory employment, unless the observer knows the character and uses of the structure he sees; and hence there is no possibility of deriving permanent pleasure from such a source, without taking the trouble to become acquainted with at least the elements of many branches of knowledge. We recently heard a gentleman, who had carried off many prizes in his university career, complain "that the worst of the microscope was, that it required you to learn so much." This is one view of the question; but what, at first sight, appears an objection and a stumbling-block, must be seen upon considera

*Objects for the Microscope; being a popular description of the Most Instructive and Beautiful Subjects for Exhibition, by L. Lane Clarke. Second edition. Groombridge and Sons.