end of one second, in the line BD; and, notwithstanding the application of a second force, at the end of that time it is still found in the same line; but the approach of the body to this line, if the direction of the second force were in any way inclined to or tending to cross it, must have been either accelerated or retarded; so that in the same time the body would either have passed or not have reached that line. And in the same manner it may be proved that CD is parallel to AB.

A. One difficulty only occurs to me in this demonstration. I had supposed, from the first law of motion, that a body in motion would have a tendency to continue in that straight line in which it was moving, and would therefore resist any force by which it was disturbed from that line.

B. But in order to resist any force, a force must be exerted in the contrary direction. You supposed therefore that the body could, by virtue of its motion, exert a force in a direction crossing the original direction of that motion; for which, I think, you had no warrant.

A. Am I then to infer that the original determination was not simply to proceed in the line AB, but in that or any other line parallel to it?

B. Just so; on the ground that the body has no choice, but moves on from mere inertness. The proposition which I have just proved to you is confirmed, not only by a vast variety of remote consequences, but by every day's immediate expe

rience; for all actions are carried on in a ship, in full sail, on a smooth sea, exactly in the same way as when she was at anchor. Thus, if I roll a ball on the deck from A towards C; and, in the time which it would take for reaching that point if we were fast moored, the ship has moved on so that the point A is transferred to B, the ball will in the same time reach the point C which is transferred to D. And on the same principle every thing will take place on the surface of the earth in the same manner, whether the globe be actually in a state of rest or of rotation.

A. Stay: If the globe be in rotation, can all parts of it move equally fast? The felly of a wheel flies round more rapidly than the nave.

B. Your objection, as far as it goes, is just; and it reminds me of the most probable cause I have ever heard assigned for the constant east wind under the equator. The air in those parts, being heated by the sun, expands, becomes lighter, and ascends; the cold air therefore from the north and south rushes in to supply its place. But this air, coming from those latitudes where the rotatory motion from west to east (of which it partakes) is slower than at the equator, is distanced in the course in that direction by the new regions of earth which it visits. Now whoever outstrips the wind, will find a new wind blowing in his face; and if the wind blow across your road, you will find that it is two or three points more

a-head of you when travelling fast, than when you are standing still. Instead therefore of a north wind on this side of the equator, and a south wind on the other, there is a north-east and a south-east wind; and at the equator itself, the opposite motions neutralizing each other, no wind remains but from the east.

A. I remember to have heard a different and more simple explanation of this phenomenon. The equatorial regions are heated successively by the sun in his passage from east to west; and not all at the same time equally. Then, as you say, the heated air ascends; but the cooler air comes in from the east, as well as from the north and south.

B. And why not from the west?

A. I confess I can't tell.

B. But I think I can tell you why it should; for when it is noon here, the air must in general be colder in the regions to the west of us, where it is morning, than in those to the east, where it is evening.

A. That is true, and proves my reason for the east wind to be wrong, whatever may be thought of yours. But is there no way of putting this to the proof? Cannot you send a cannon ball for the purpose from north to south? The great mortar in St. James's Park would perhaps be more successful in an attempt to settle this question, than in its military enterprises before Cadiz.

C

B. Let me see whether any thing could be made of it. I find that in the latitude of London the difference of velocity in the rotatory motion of the earth's surface, as you go one mile further north or south, amounts to about six miles in twenty-four hours, or twenty-two feet in a minute. If therefore you could send a ball to the distance of a mile, which should be one minute in the air, and could be sure of your aim within two or three feet, the experiment would be pretty decisive.

A. This would be much more satisfactory to me than any thing I have yet heard on the subject. For instance, when I am told that the earth is flattened at the poles; would not the same argument apply to every turnip that grows?

B. Perhaps it might, if it could first be made a question whether the turnip was in the habit of spinning on its axis, or the whole field of making a circuit about the turnip. But it is time that you and I should attend to other affairs; which will not move in the right direction, if we remain stationary.

DIALOGUE III.

B. NOW let us return to our geometry. Tri-Prop. XI. angles on the same base, and between the same parallels, are equal to each other.

A. This is evident; for they are the halves of parallelograms under the same conditions.

B. And do you think it can make any difference whether they have the same base, or equal bases in the same straight line?

A. Certainly not; because they may be supposed to slide along between the parallels till their bases coincide.

B. And on the other hand, equal triangles Prop. XII. upon the same base (or upon equal bases in the same straight line) and upon the same side of it, are between the same parallels. For if the straight line which joins the vertices of the two triangles be not parallel to the base, some other line may be drawn from either vertex which shall be parallel to the base; and then it may be shewn that one of the triangles is greater than the other.

A. This follows from Prop. XI.

B. And another inference from the same pro- Prop. XIII. position is, That triangles between the same parallels are to one another in the ratio of their bases. For into whatever number of equal parts