at the equator, and this divided by 24, gives 1000 miles for the space passed through, in an hour.

Tutor. You are right. The sun, I have already told you, is 95 millions of miles distant from the earth: tell me therefore, Charles, at what rate that body must travel to go round the earth in 24 hours?

Charles. I will; 95 millions multiplied by six will give 570 millions of miles for the length of his circuit, this divided by 24 gives nearly 24 millions of miles for the space he must travel in an hour, to go round the earth in a day.

Tutor. Which now is the more probable conclusion, either that the earth should have a diurnal motion on its axis of 1000 miles in an hour, or that the sun, which is a million of times larger than the earth, should travel 24 millions of miles in the same time?

James. It is certainly more rational to conclude that the earth turns on its axis, the effect of which you told us was the alternate succession of day and night.

Tutor. I did; and on this and some other topics we will enlarge to-morrow.

0 2

CONVERSATION XXIX.

Of Day and Night.

James. You are now, sir, to apply the rotation of the earth about its axis to the succession of day and night.

Tutor. I will; and for this purpose, suppose GRCB (Plate VI. Fig 5.) to be the earth, revolving on its axis, according to the order of the letters, that is, from G to R, R to C, &c. If the sun be fixed in the heavens at z, and a line o be drawn through the centre of the earth T, it will represent that circle, which when extended to the heavens is called the rational horizon.

Charles. In what does this differ from the sensible horizon?

Tutor. The sensible horizon is that circle in the heavens which bounds the spectator's view, and which is greater or less, according as he stands higher or lower. For example; an eye placed at five feet above the surface of the earth or sea, sees 23 miles every way: But if it be at 20 feet high, that is four times the height, it will see 51⁄2 miles, or twice the distance.

*

* See Dr. Ashworth's Trigonometry, Prop. 31. 2d Edition, 1803.

Charles. Then the sensible differs from the rational horizon in this, that the former is seen from the surface of the earth, and the latter is supposed to be viewed from its centre.

Tutor. You are right; and the rising and setting of the sun and stars are always referred to the rational horizon.

James. Why so? they appear to rise and set as soon as they get above, or sink below that boundary which separates the visible from the invisible part of the heavens.

Tutor. They do not, however: and the reason is this, that the distance of the sun and fixed stars is so great in comparison of 4000 miles (the difference between the surface and centre of the earth,) that it can scarcely be taken into

account.

Charles. But 4000 miles seem to me an immense space.

Tutor. Considered separately, they are so, but when compared with 95 millions of miles, the distance of the sun from the earth, they almost vanish as nothing.

James. But do the rising and setting of the moon, which is at the distance of 240,000 miles only, respect also the rational horizon?

Tutor. Certainly; for 4000 compared with 240,000, bear only the proportion of 1 to 60. Now if two spaces were marked out on the earth in different directions, the one 60, and the

other 61 yards, should you at once be able to distinguish the greater from the less?

Charles. I think not.

Tutor. Just in the same manner does the distance of the centre from the surface of the earth vanish in comparison of its distance from the moon.

James. We must not, however, forget the succession of day and night.

Tutor. Well then; if the sun be supposed at z, it will illuminate by its rays all that part of the earth that is above the horizon нo: to the inhabitants at G, its western boundary, it will appear just rising: to those situated at R, it will be noon; and to those in the eastern part of the horizon c, it will be setting.

Charles. I see clearly why it should be noon to those who live at R, because the sun is just over their heads, but it is not so evident, why the sun must appear rising and setting to those who are at G and c.

Tutor. You are satisfied that a spectator cannot, from any place, observe more than a semicircle of the heavens at any one time; now what parts of the heavens will the spectator at & observe?

James. He will see the concave hemisphere

ZON.

Tutor. The boundary to his view will be N and z, will it not?

Charles. Yes; and consequently the sun at z, will to him be just coming into sight.

Tutor. Then, by the rotation of the earth, the spectator at G will in a few hours come to R, when, to him, it will be noon; and those who live at R, will have descended to c; now what part of the heavens will they see in this situation ?

James. The concave hemisphere N н z, and z, being the boundary of their view one way, the sun will to them be setting.

Tutor. Just so. After which they will be turned away from the sun, and consequently it will be night to them till they come again to G. Thus, by this simple motion of the earth on its axis, every part of it is, by turns, enlightened and warmed by the cheering beams of the sun.

Charles. Does this motion of the earth account also for the apparent motion of the fixed stars?

Tutor. It is owing to the revolution of the earth round its axis, that we imagine the whole starry firmament revolves about the earth in 24 hours.

James. If the heavens appear to turn on an axis, must there not be two points, namely, the extremities of that imaginary axis, which always keep their position?

Tutor. Yes, we must be understood to except the two celestial poles which are opposite to the poles of the earth, consequently each fixed star