(49.) Hitherto we have considered only appearances, and have not made the least inquiry as to the nature, magnitude, or distances of the celestial objects.

Abstractly, there is no such thing as great and small, near and remote; relatively speaking, however, we may apply the terms great, and very great, as regards both magnitude and distance. Thus an error of ten feet, in the measure of the length of a building, is very great-when an error of ten rods, in the measure of one hundred miles, would be too trifling to mention.

Now if we consider the distance to the stars, it must be relative to some measure taken as a standard, or our inquiries will not be definite, or even intelligible. We now make this

Fig. 6.

C

general inquiry: Are the heavenly bodies near to, or remote from, the earth? Here, the earth itself seems to be the natural standard for measure; and if any body were but two, three, or even ten times the diameter of the earth, in distance, we

CHAP. I.

Distance is but relative.

Are the heavenly bodies remote?

CHAP. I. should call it near; if 100, 200, or 2000 times the diameter of the earth, we should call it remote. To answer the inquiry, Are the heavenly bodies near or remote? we must put them to all possible mathematical tests; a mere opinion is of no value, without the foundation of some positive knowledge. Let 1, 2 (Fig. 6), represent the absolute position of two stars; and then, if A B C represents the circumference of the earth, these stars may be said to be near; but if a b c represents the circumference of the earth, the stars are many times

the diameter of the earth, in distance, and therefore may The means be said to be remote. If ABC is the circumference of

of deciding the earth, in relation to these stars, the apparent distance of this question pointed out. the two stars asunder, as seen from A, is measured by the

The con

clusion.

angle 1A 2; and their apparent distance asunder, as seen from the point B, is measured by the angle 1 B 2; and when the circumference A B C is very large, as represented in our figure, the angle A, between the two stars, is manifestly greater than B. But if abc is the circumference of the earth, the points a and b are relatively the same as A and B. And, it is an ocular demonstration that the angle under which the two stars would appear at a is the same, or nearly the same, as that under which they would appear at b; or, at least, we can conceive the earth so small, in relation to the distance to the stars, that the angle under which two stars would appear, would be the same seen from any point on the earth.

Conversely, then, if the angle under which two stars appear is the same as seen from all parts of the earth's surface, it is certain that the diameter of the earth is very small, compared with the distance to the stars; or, which is the same thing, the distance to the stars is many times the diameter of the earth. Therefore observation has long since decided this important point. Sir John Herschel says: "The nicest measurements of the apparent angular distance of any two stars, inter se, taken in any parts of their diurnal course (after allowing for the unequal effects of refraction, or when taken at such times that this cause of distortion shall act equally on both), manifest not the slightest perceptible variation. Not only this, but

at whatever point of the earth's surface the measurement is CHAP. I.
performed, the results are absolutely identical. No instruments
ever yet invented by man are delicate enough to indicate, by
an increase or diminution of the angle subtended, that one
point of the earth is nearer to or farther from the stars than
another."

(50.) Perhaps the following view of this subject will be more intelligible to the general reader.

Another illustration of the great distance

the stars.

to

H represent

the celestial equator, as seen from the

equator

on

the earth; and if the earth be large, in rela

tion to the

distance

to

the stars, the

observer will

be at z'; and

the part of the

N

celestial arc above his horizon would be represented by AZ B, and the part below his horizon by ANB, and these arcs are obviously unequal; and their relation would be measured by the time a star or heavenly body remains above the horizon, compared with the time below it; but by observation (refraction being allowed for), we know that the stars are as long above the horizon as they are below; which shows that the observer is not at z', but at z, and even more near the center; so that the arc A Z B, is imperceptibly unequal to the arc H NH; that is, they are equal to each other; and the earth is comparatively but a point, in relation to the distance to

the stars.

The moon

This fact is well established, as applied to the fixed stars, sun, and planets; but with the moon it is different: that body tion.

an

excep.

CHAP. I. is longer below the horizon than above it; which shows that its distance from the earth is at least measurable.

vex.

Earth's

(51.) It is improper, at present, or rather, it is too advanced an age, to pay any respect to the ancient notion, that the earth is an extended plane, bounded by an unknown space, inaccessible to men. Common intelligence must convince even the child, that the earth must be a large ball, of a regular, or an irregular shape; for every one knows the fact, that the earth. has been many times circumnavigated; which settles the question.

In addition to this, any observer may convince himself, that surface con- the surface of the sea, or a lake, is not a plane, but everywhere convex; for, in coming in from sea, the high land, back in the country, is seen before the shore, which is nearer the observer; the tops of trees, and the tops of towers, are seen before their bases. If the observer is on shore, viewing an approaching vessel, he sees the topmast first; and from the top, downward, the vessel gradually comes in view. This being the case on every sea, and on every portion of the earth, proves that the surface of the earth is convex on every part· hence it must be a globe, or nearly a globe. These facts, last mentioned, are sufficiently illustrated by

Fig. 8.

(52.) On the supposition that the earth is a sphere, there are several methods of measuring it, without the labor of applying the measure to every part of it. The first, and most natural method (which we have already mentioned ), is that of measuring any definite portion of the meridian, and from thence computing the value of the whole circumference. Thus, if we can know the number of degrees, and parts of find the cir- a degree, in the arc A B (Fig. 9), and then measure the disof the earth. tance in miles, we in fact virtually know the whole circumfe

How to

cumference

rence; for whatever part the arc AB is of 360 degrees, the CHAP. I. same part, the number of miles in AB, is of the miles in the whole circumference.

To find the arc AB, the latitudes of the two points, A and B, must be very accurately taken, and their difference will give the arc in degrees, minutes, and seconds. Now A B must be measured simply in distance, as miles, yards, or feet; but this is a laborious operation, requiring great care and perseTo measure directly any considerable portion of a meridian, is indeed impossible, for local obstructions would soon compel a deviation from any definite line; but still the measure can be continued, by keeping an account of the deviations, and reducing the measure to a meridian line.

verance.

Let m be the miles or feet in AB; then the whole circum

member of this equation is known, CM is known; and as part of it (MB) is already known, the other part, BC, the diameter of the earth, thus becomes known.

thod.

Objection

This method would be a very practical one, if it were not for the uncertainty and variable nature of refraction near the to this me horizon; and for this reason, this method is never relied upon, although it often well agrees with other methods. As an example under this method, we give the following:

E*