Conversations on Natural Philosophy, in which the Elements of that Science are Familiarly Explained Part 17

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?

[Ill.u.s.tration: PLATE VI.]

_Caroline._ You say that the earth revolves in its...o...b..t round the sun once in a year, and that bodies attract in proportion to the quant.i.ty 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 wis.h.i.+ng 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 s.p.a.ce: 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 s.p.a.ce of one month; whilst the sun's attraction would bring it to C in the same s.p.a.ce 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 const.i.tuting 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 pa.s.sed through the diagonals of these three parallelograms, in the s.p.a.ce 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 ill.u.s.trating 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.

_Mrs. B._ Let us suppose that when the earth is at A, (fig. 3.) its projectile force should not have given it a velocity sufficient to counterbalance that of gravity, so as to enable these powers conjointly to carry it round the sun in a circle; the earth, instead of describing the line A C, as in the former figure, will approach nearer the sun in the line A B.

_Caroline._ Under these circ.u.mstances, I see not what is to prevent our approaching nearer and nearer the sun, till we fall into it: for its attraction increases as we advance towards it, and produces an accelerated velocity in the earth, which increases the danger.

_Mrs. B._ There is another seeming danger, of which you are not aware.

Observe, that as the earth approaches the sun, the direction of its projectile force is no longer perpendicular to that of its attraction, but inclines more nearly to it. When the earth reaches that part of its...o...b..t at B, the force of projection would carry it to D, which brings it nearer the sun instead of bearing it away from it.

_Emily._ If, then, we are driven by one power, and drawn by the other to this centre of destruction, how is it possible for us to escape?

_Mrs. B._ A little patience, and you will find that we are not without resource. The earth continues approaching the sun with a uniformly increasing accelerated motion, till it reaches the point E; in what direction will the projectile force now impel it?

_Emily._ In the direction E F. Here then the two forces act perpendicularly to each other, the lines representing them forming a right angle, and the earth is situated just as it was in the preceding figure; therefore, from this point, it should revolve round the sun in a circle.

_Mrs. B._ No, all the circ.u.mstances do not agree. In motion round a centre, you recollect that the centrifugal force increases with the velocity of the body, or in other words, the quicker it moves the stronger is its tendency to fly off in a right line. When the earth, therefore, arrives at E, its accelerated motion will have so far increased its velocity, and consequently its centrifugal force, that the latter will prevail over the force of attraction, and force the earth away from the sun till it reaches G.

_Caroline._ It is thus then that we escape from the dangerous vicinity of the sun; and in proportion as we recede from it, the force of its attraction, and, consequently, the velocity of the earth's motion, are diminished.

_Mrs. B._ Yes. From G the direction of projection is towards H, that of attraction towards S, and the earth proceeds between them with a uniformly r.e.t.a.r.ded motion, till it has completed its revolution. Thus you see that the earth travels round the sun, not in a circle, but an ellipsis, of which the sun occupies one of the _foci_; and that in its course, the earth alternately approaches and recedes from it, without any danger of being either swallowed up, or being entirely carried away from it.

_Caroline._ And I observe, that what I apprehended to be a dangerous irregularity, is the means by which the most perfect order and harmony are produced.

_Emily._ The earth travels then at a very unequal rate, its velocity being accelerated as it approaches the sun, and r.e.t.a.r.ded as it recedes from it.

_Mrs. B._ It is mathematically demonstrable, that, in moving round a point towards which it is attracted, a body pa.s.ses over equal areas, in equal times. The whole of the s.p.a.ce contained within the earth's...o...b..t, is in fig. 4, divided into a number of areas or surfaces; 1, 2, 3, 4, &c. all of which are of equal dimensions, though of very different forms; some of them, you see, are long and narrow, others broad and short: but they each of them contain an equal quant.i.ty of s.p.a.ce. An imaginary line drawn from the centre of the earth to that of the sun, and keeping pace with the earth in its revolution, pa.s.ses over equal areas in equal times; that is to say, if it is a month going from A to B, it will be a month going from B to C, and another from C to E, and so on; and the areas A B S, B C S, C E S, will be equal to each other, although the lines A B, B C, C E, are unequal.

_Caroline._ What long journeys the earth has to perform in the course of a month, in one part of her orbit, and how short they are in the other part!

_Mrs. B._ The inequality is not so considerable as appears in this figure; for the earth's...o...b..t is not so eccentric as it is there described; and in reality, differs but little from a circle: that part of the earth's...o...b..t nearest the sun is called its _perihelion_, that part most distant from the sun, its _aphelion_; and the earth is above three millions of miles nearer the sun at its perihelion than at its aphelion.

_Emily._ I think I can trace a consequence from these different situations of the earth; are not they the cause of summer and winter?

_Mrs. B._ On the contrary, during the height of summer, the earth is in that part of its...o...b..t which is most distant from the sun, and it is during the severity of winter, that it approaches nearest to it.

_Emily._ That is very extraordinary; and how then do you account for the heat being greatest, when we are most distant from the sun?

_Mrs. B._ The difference of the earth's distance from the sun in summer and winter, when compared with its total distance from the sun, is but inconsiderable. The earth, it is true, is above three millions of miles nearer the sun in winter than in summer; but that distance, however great it at first appears, sinks into insignificance in comparison with 95 millions of miles, which is our mean distance from the sun. The change of temperature, arising from this difference, would scarcely be sensible, even were it not completely overpowered by other causes which produce the variations of the seasons; but these I shall defer explaining, till we have made some further observations on the heavenly bodies.

_Caroline._ And should not the sun appear smaller in summer, when it is so much further from us?

_Mrs. B._ It actually does, when accurately measured; but the apparent difference in size, is, I believe, not perceptible to the naked eye.

_Emily._ Then, since the earth moves with the greatest velocity in that part of its...o...b..t in which it is nearest the sun, it must have completed its journey through that half of its...o...b..t, in a shorter time than through the other?

_Mrs. B._ Yes, it is about seven days longer performing the summer-half of its...o...b..t, than the winter-half; and the summers are consequently seven days longer in the northern, than they are in the southern hemisphere.

The revolution of all the planets round the sun, is the result of the same causes, and is performed in the same manner, as that of the earth.

_Caroline._ Pray what are the planets?