Part 32

CONVERSATION VI.

CAUSES OF THE MOTION OF THE HEAVENLY BODIES.

OF THE EARTH'S ANNUAL MOTION. OF THE PLANETS AND THEIR MOTION. OF THE DIURNAL MOTION OF THE EARTH AND PLANETS.

CAROLINE.

I am come to you to-day quite elated with the spirit of opposition, Mrs. B.; for I have discovered such a powerful objection to your theory of attraction, that I doubt whether even your conjuror Newton, with his magic wand of gravitation, will be able to dispel it.

Mrs. B. Well, my dear, pray what is this weighty objection?

Caroline. You say that the earth revolves in its orbit round the sun once in a year, and that bodies attract in proportion to the quantity of matter they contain; now we all know the sun to be much larger than the earth: why, therefore does it not draw the earth into itself; you will not, I suppose, pretend to say that we are falling towards the sun?

Emily. However plausible your objection appears, Caroline, I think you place too much reliance upon it: when any one has given such convincing proofs of sagacity and wisdom as Sir Isaac Newton, when we find that his opinions are universally received and adopted, is it to be expected that any objection we can advance should overturn them?

Caroline. Yet I confess that I am not inclined to yield implicit faith even to opinions of the great Newton: for what purpose are we endowed with reason, if we are denied the privilege of making use of it, by judging for ourselves.

Mrs. B. It is reason itself which teaches us, that when we, novices in science, start objections to theories established by men of knowledge and wisdom, we should be diffident rather of our own than of their opinion. I am far from wishing to lay the least restraint on your questions; you cannot be better convinced of the truth of a system, than by finding that it resists all your attacks, but I would advise you not to advance your objections with so much confidence, in order that the discovery of their fallacy may be attended with less mortification. In answer to that you have just proposed, I can only say, that the earth really is attracted by the sun.

Caroline. Take care, at least, that we are not consumed by him, Mrs. B.

Mrs. B. We are in no danger; but Newton, our magician, as you are pleased to call him, cannot extricate himself from this difficulty without the aid of some cabalistical figures, which I must draw for him.

Let us suppose the earth, at its creation, to have been projected forwards into universal space: we know that if no obstacle impeded its course it would proceed in the same direction, and with a uniform velocity for ever. In fig. 1. plate 6, A represents the earth, and S the sun. We shall suppose the earth to be arrived at the point in which it is represented in the figure, having a velocity which would carry it on to B in the space of one month; whilst the sun's attraction would bring it to C in the same space of time. Observe that the two forces of projection and attraction do not act in opposition, but perpendicularly, or at a right angle to each other. Can you tell me now, how the earth will move?

Emily. I recollect your teaching us that a body acted upon by two forces perpendicular to each other, would move in the diagonal of a parallelogram; if, therefore, I complete the parallelogram, by drawing the lines C D, B D, the earth will move in the diagonal A D.

Mrs. B. A ball struck by two forces acting perpendicularly to each other, it is true, moves in the diagonal of a parallelogram; but you must observe that the force of attraction is continually acting upon our terrestrial ball, and producing an incessant deviation from its course in a right line, which converts it into that of a curve-line; every point of which may be considered as constituting the diagonal of an infinitely small parallelogram.

Let us retain the earth a moment at the point D, and consider how it will be affected by the combined action of the two forces in its new situation. It still retains its tendency to fly off in a straight line; but a straight line would now carry it away to F, whilst the sun would attract it in the direction D S; how then will it proceed?

Emily. It will go on in a curve-line, in a direction between that of the two forces.

Mrs. B. In order to know exactly what course the earth will follow, draw another parallelogram similar to the first, in which the line D F describes the force of projection, and the line D S that of attraction; and you will find that the earth will proceed in the curve-line D G.

Caroline. You must now allow me to draw a parallelogram, Mrs. B. Let me consider in what direction will the force of projection now impel the earth.

Mrs. B. First draw a line from the earth to the sun representing the force of attraction; then describe the force of projection at a right angle to it.

Caroline. The earth will then move in the curve G I, of the parallelogram G H I K.

Mrs. B. You recollect that a body acted upon by two forces, moves through a diagonal, in the same time that it would have moved through one of the sides of the parallelogram, were it acted upon by one force only. The earth has passed through the diagonals of these three parallelograms, in the space of three months, and has performed one quarter of a circle; and on the same principle it will go on till it has completed the whole of the circle. It will then recommence a course, which it has pursued ever since it first issued from the hand of its Creator, and which there is every reason to suppose it will continue to follow, as long as it remains in existence.

Emily. What a grand and beautiful effect resulting from so simple a cause!

Caroline. It affords an example, on a magnificent scale, of the curvilinear motion, which you taught us in mechanics. The attraction of the sun is the centripetal force, which confines the earth to a centre; and the impulse of projection, the centrifugal force, which impels the earth to quit the sun, and fly off in a tangent.

Mrs. B. Exactly so. A simple mode of illustrating the effect of these combined forces on the earth, is to cut a slip of card in the form of a carpenter's square, as A, B, C; (fig. 2. plate 6.) the point B will be a right angle, the sides of the square being perpendicular to each other; after having done this you are to describe a small circle at the angular point B, representing the earth, and to fasten the extremity of one of the legs of the square to a fixed point A, which we shall consider as the sun. Thus situated, the two sides of the square will represent both the centrifugal and centripetal forces; A B, representing the centripetal, and B C, the centrifugal force; if you now draw it round the fixed point, you will see how the direction of the centrifugal force varies, constantly forming a tangent to the circle in which the earth moves, as it is constantly at a right angle with the centripetal force.

Emily. The earth then, gravitates towards the sun, without the slightest danger either of approaching nearer, or receding further from it. How admirably this is contrived! If the two forces which produce this curved motion, had not been so accurately adjusted, one would ultimately have prevailed over the other, and we should either have approached so near the sun as to have been burnt, or have receded so far from it as to have been frozen.

Mrs. B. What will you say, my dear, when I tell you, that these two forces are not, in fact, so proportioned as to produce circular motion in the earth? We actually revolve round the sun in an elliptical or oval orbit, the sun being situated in one of the foci or centres of the oval, so that the sun is at some periods much nearer to the earth, than at others.

Caroline. You must explain to us, at least, in what manner we avoid the threatened destruction.