point, and the movement of the north pole of the heavens, to a common origin, and has demonstrated, in the clearest manner, that they are both consequences of the spheroidal figure of the earth, which we have just examined. It is not my design to enter into an elaborate investigation of this wonderful subject, but, in accordance with the plan already announced, I cannot leave you with a mere announcement of a truth so startling, without some effort to explain how this may be. The subject is difficult, but, favoured by your close attention, I do not despair of rendering it approximately intelligible.

Let us conceive the earth's axis to be a solid bar of iron driven through the centre of the earth, coming out at the poles, and extending indefinitely towards the sphere of the fixed stars. Now turn this axis up until it stands perpendicular to the plane of the orbit in which the earth revolves around the sun. Then do the equator and the ecliptic exactly coincide, and if the fixed stars are at a distance nearly infinite, the point in which the earth's axis prolonged pierces the heavens will appear stationary, so far as the revolution of the earth in its orbit is concerned. Now if this iron axle could be grasped by some giant hand, and drawn away from its upright or perpendicular position, the solid earth would turn with it, and the equator, ceasing to coincide with the ecliptic or plane of the earth's orbit, comes to be inclined to it, under an angle precisely equal to the angle through which the axis has been inclined. It is thus seen that no change can be wrought on the position of the axis, that does not involve a corresponding change in the whole earth, and especially in the plane of the equator, which must ever remain perpendicular to the axis in all its positions.

The reverse of this proposition is equally manifest. If the solid earth be seized at the equator, and be turned up or down, the axis will participate in this movement, and its change will exhibit itself in the changed position of the point in which it meets the celestial sphere. One step more, and the difficulty is surmounted. Conceive a flat wheel of wood floating on still water. Through its centre pass an axle which stands perpendicular to the surface of the wheel and water. So long as the wheel floats level, the axle stands erect, but in case the north half of the wheel is tilted down under the water, the south half at the same time rising out of the water, the axis will tilt towards the north. Bring the wheel again to its level position. Now

plunge the eastern portion of the wheel below the surface. The axis now is tilted towards the east. The experiment is simple, and shows that, in case the successive portions of the wheel be submerged, the axis will always be tilted towards the point which goes under first. To reverse the experiment: in case we take hold of the axle and turn it east, it sinks the eastern half of the wheel below the surface of the water, while the western half is raised out of it; and then in case we make the upper extremity of the axis follow round the circumference of a circle whose surface is parallel to that of the water, and whose centre is exactly above the centre of the wheel, it will be seen that, as the axle moves round, successive portions of the wheel are submerged, until finally the water line will have divided the wheel into all its successive halves, and will have successively coincided with every possible diameter of the wheel.

Now for the application. The level surface of the water is the level plane of the earth's orbit, the wheel is the earth's equator, and the axle is the earth's axis of rotation. One half of the equator is constantly submerged below the plane of the ecliptic, the other half rises above it. But the water line, or the intersection of these two planes, the equinoctial line, cannot remain fixed in the same line. A power does seize the equator, and plunge successive halves of it beneath the plane of the ecliptic, changing perpetually the water line, until finally each half in succession, into which all its diameters can be divided, are sunk below the surface or plane of the ecliptic, thus causing the earth's axis to tilt over towards the portions successively submerged, until it finally sweeps entirely round, and comes to resume its first position.

But do you now demand what power seizes the earth's protuberant equator, and tilts it successively towards every point of the compass? I answer, that the power is lodged in the sun and moon, and it is their combined action which works out these wonderful results. In case the sun and moon were so situated as always to be in the plane of the earth's equator, then they would have no power to change the position of the equator. But we know that they are not in this plane, except when passing through it, and are found sometimes on the north and sometimes on the south side of it. Wherever either of them may be, the nearest half of the redundant matter about the earth's equator will be more forcibly attracted than the remote half, and the

equator will be tilted towards the attracting body, and the axis of the earth will follow the movement of the equator to which it is firmly fixed.

Thus does the earth's whole solid mass sway to the motion of the ring of matter heaped up around the equator, delicately and beautifully sensitive to all the changes in the relative places of the sun and moon. Neither the earth nor its axis are ever, for one moment, released from the action of these remote bodies. However slight the effects, however varied in action, oscillating to every point within certain prescribed limits, the stability is preserved, and the final effect is a small retrograde motion of the equinox at the end of every year, and a slight change in the place of the pole of the heavens.

But there is no isolated matter in the universe. Every particle of matter attracts every other particle of matter, and it is impossible for the sun and moon to exert any influence on the equatorial ring of matter which belongs to our globe, without feeling, in their turn, the reaction of this ring on themselves. The remote and ponderous sun may, in consequence of its vast size and distance, escape from any effect capable of being detected by observation. But this is not the case with the moon. Her proximity to the earth, and diminutive mass, render her peculiarly sensitive to the influence of the redundant matter at the earth's equator, and as her attraction tilts the plane of the earth's equator, so does the equatorial ring tilt the plane of the moon's orbit. These effects have been accurately observed and measured, and, strange to relate, their exact values have exhibited the figure which belongs to the earth with far greater precision than can be obtained from measures on its surface. We may even go farther, for such is the intimate relationship between the earth and its attendant satellite, that there is scarcely a question an be asked with reference to the one, that is not answered by the other.

If we demand the weight of the earth when compared with the sun, the moon answers. If the excess of the equatorial diameter of the earth over the polar be required, the moon answers. If the homogeneity of the interior of the solid earth be required. the moon replies. If the thickness of the earth's crust be sought for, question the moon, and the answer comes. If you would know the sun's distance from the earth, ask the moon. If the permanency of the axis of rotation be required, ask the moon

and she alone yields a satisfactory reply. Finally, if curiosity leads us to inquire whether the length of the day and night, the revolution of the earth on its axis, be uniform, or whether it may not have changed by a single second in a thousand years, we go to the moon for an answer, and in each and every instance her replies to all these profound and mysterious questions are clear and satisfactory. How wonderful the structure of the universe! How gigantic the power of the human intellect! If all the stars of heaven were struck from existence; if every planet and satellite which the eye and the telescope descry, inside and beyond the earth's orbit, were swept away for ever, and the sun, earth, and moon, alone remained for the study of man, and as evidences of the being and wisdom of God, in the exquisite adjustments or this system, in the reciprocal influences of its three bodies, in their vast cycles of configuration, in their relative masses, magnitudes, distances, motions, and perturbations, there would remain themes sufficient for the exercise of the most exalted genius, and proof of the being of God, so clear and positive, that no sane mind could comprehend it and disbelieve.

LECTURE VI.

THE STABILITY OF THE PLANETARY SYSTEM.

HEN, by the application of a singe great law, the mind had succeeded in resolving the difficult problems presented by the motions of the earth and its satellite, the moon, it rose to the examination of the higher and more complicated questions of the stability of the entire system of planets, satellites, and comets, which are found to pursue their courses round the sun. The number or bodies involved in this investigation, their magnitudes and vast periods of revolution, their great distances from the observer, and the exceeding delicacy of the required observations, combined with the high interest which attaches itself to the final result, have united to render this investigation the most wonderful which has ever employed the energies of the human mind.

To comprehend the dignity and importance of this great bject, let us rapidly survey the system, and, moving outward to its known boundaries, mark the number and variety of worlds involved in the investigation. Beginning, then, at the great centre, the grand controlling orb, the sun, we find its magnitude such as greatly to exceed the combined masses of all its attendant planets. Indeed, if these could all be arranged in a straight line on the same side of the sun, so that their joint effect might be