Part 42

Mrs. B. You know that the revolution of the earth on its axis, must give to every particle a tendency to fly off from the centre, that this tendency is stronger, or weaker, in proportion to the velocity with which the particle moves; now a particle situated near to one of the poles, makes one rotation in the same space of time as a particle at the equator; the latter, therefore, having a much larger circle to describe, travels proportionally faster, consequently the centrifugal force is much stronger at the equator than in the polar regions: it gradually decreases as you leave the equator and approach the poles, at which points the centrifugal force, entirely ceases. Supposing, therefore, the earth to have been originally in a fluid state, the particles in the torrid zone would recede much farther from the centre than those in the frigid zones; thus the polar regions would become flattened, and those about the equator elevated.

As a large portion of the earth is covered with water, the Creator gave to it the form, denominated an oblate spheroid, otherwise the polar regions would have been without water, and those about the equator, would have been buried several miles below the surface of the ocean.

Caroline. I did not consider that the particles in the neighbourhood of the equator, move with greater velocity than those about the poles; this was the reason I could not understand you.

Mrs. B. You must be careful to remember, that those parts of a body which are farthest from the centre of motion, must move with the greatest velocity: the axis of the earth is the centre of its diurnal motion, and the equatorial regions the parts most distant from the axis.

Caroline. My head then moves faster than my feet; and upon the summit of a mountain, we are carried round quicker than in a valley?

Mrs. B. Certainly; your head is more distant from the centre of motion than your feet; the mountain-top than the valley; and the more distant any part of a body is from the centre of motion, the larger is the circle it will describe, and the greater therefore must be its velocity.

Emily. I have been reflecting, that if the earth is not a perfect circle----

Mrs. B. A sphere you mean, my dear: a circle is a round line, every part of which is equally distant from the centre; a sphere or globe is a round body, the surface of which is every where equally distant from the centre.

Emily. If, then, the earth is not a perfect sphere, but prominent at the equator, and depressed at the poles, would not a body weigh heavier at the equator than at the poles? For the earth being thicker at the equator, the attraction of gravity perpendicularly downwards must be stronger.

Mrs. B. Your reasoning has some plausibility, but I am sorry to be obliged to add, that it is quite erroneous; for the nearer any part of the surface of a body is to the centre of attraction, the more strongly it is attracted; because it is then nearest to the whole mass of attracting matter. In regard to its effects, you might consider the whole power of gravity, as placed at the centre of attraction.

Emily. But were you to penetrate deep into the earth, would gravity increase as you approached the centre?

Mrs. B. Certainly not; I am referring only to any situation on the surface of the earth. Were you to penetrate into the interior, the attraction of the parts above you, would counteract that of the parts beneath you, and consequently diminish the power of gravity in proportion as you approach the centre; and if you reached that point, being equally attracted by the parts all around you, the effects of gravity would cease, and you would be without weight.

Emily. Bodies, then, should weigh less at the equator than at the poles, since they are more distant from the centre of gravity in the former than in the latter situation?

Mrs. B. And this is really the case; but the difference of weight would be scarcely sensible, were it not augmented by another circumstance.

Caroline. And what is this singular circumstance, which seems to disturb the laws of nature?

Mrs. B. One that you are well acquainted with, as conducing more to the preservation than the destruction of order,--the centrifugal force. This we have just observed to be strongest at the equator; and as it tends to drive bodies from the centre, it is necessarily opposed to, and must lessen the power of gravity, which attracts them towards the centre. We accordingly find that bodies weigh lightest at the equator, where the centrifugal force is greatest; and heaviest at the poles, where this power is least: the weight being diminished at the equator, by both the causes mentioned.

Caroline. Has the experiment been made in these different situations?

Mrs. B. Louis XIV. of France, sent philosophers both to the equator, and to Lapland, for this purpose: the severity of the climate, and obstruction from the ice, have hitherto rendered every attempt to reach the pole abortive; but the difference of gravity at the equator, and in Lapland is very perceptible.

Caroline. Yet I do not comprehend how the difference of weight could be ascertained, for if the body under trial decreased in weight, the weight which was opposed to it in the opposite scale must have diminished in the same proportion. For instance, if a pound of sugar did not weigh so heavy at the equator as at the poles, the leaden pound which served to weigh it, would not be so heavy either; therefore they would still balance each other, and the different force of gravity could not be ascertained by this means.

Mrs. B. Your observation is perfectly just: the difference of gravity in bodies situated at the poles, and at the equator, cannot be ascertained by weighing them; a pendulum was therefore used for that purpose.

Caroline. What, the pendulum of a clock? how could that answer the purpose?

Mrs. B. A pendulum consists of a line, or rod, to one end of which a weight is attached, and by the other end it is suspended to a fixed point, about which it is made to vibrate. When not in motion, a pendulum, obeying the general law of attraction, hangs like a plumb line, perpendicular to the surface of the earth, but if you raise the pendulum, gravity will bring it back to its perpendicular position. It will, however, not remain stationary there, for the momentum it has acquired during its descent, will impel it onwards, and if unobstructed, it will rise on the opposite side to an equal height; from thence it is brought back by gravity, and is again forced upwards, by the impulse of its momentum.

Caroline. If so, the motion of a pendulum would be perpetual, and I thought you said, that there was no perpetual motion on the earth.

Mrs. B. The motion of a pendulum is opposed by the resistance of the air in which it vibrates, and by the friction of the part by which it is suspended: were it possible to remove these obstacles, the motion of a pendulum would be perpetual, and its vibrations perfectly regular; each being of equal distance, and performed in equal times.

Emily. That is the natural result of the uniformity of the power which produces these vibrations, for the force of gravity being always the same, the velocity of the pendulum must consequently be uniform.

Caroline. No, Emily, you are mistaken; the force is not every where the same, and therefore the effect will not be so either. I have discovered it, Mrs. B.; since the force of gravity is less at the equator than at the poles, the vibrations of the pendulum will be slower at the former place than at the latter.

Mrs. B. You are perfectly right, Caroline; it was by this means that the difference of gravity was discovered, and the true figure of the earth ascertained.

Emily. But how do they contrive to regulate their time in the equatorial and polar regions? for, since in our part of the earth the pendulum of a clock vibrates exactly once in a second, if it vibrates faster at the poles, and slower at the equator, the inhabitants must regulate their clocks in a manner different from us.