PRACTICAL ASTRONOMY

AND

GEODESY.

CHAPTER I.

THE EARTH.-PHENOMENA OF THE CELESTIAL BODIES. FORM OF THE EARTH, AND ROTATION ON ITS AXIS. APPARENT MOVEMENT OF THE STARS. REVOLUTION OF THE MOON ABOUT THE EARTH. HYPOTHESIS OF THE EARTH'S ANNUAL MOTION. PHASES OF THE MOON.—APPARENT MOVEMENTS OF THE PLANETS. THE CIRCLES OF THE SPHERE.

1. THAT the surface of the earth is of a form nearly spherical may be readily inferred from the appearance presented at any point on the ocean by a ship when receding from thence; for, on observing that the line which bounds the view on all sides is accurately or nearly the circumference of a circle, and that when a ship has reached any part of this line she seems to sink into the water, the spectator recognizes the fact that she is moving on a surface to which the visual rays from that circumference are tangents. These rays may be imagined to constitute the surface of a cone of which the eye of the spectator is the vertex; and the solid with which, at every part of its surface, a cone is in contact on the periphery of a line which is accurately or nearly a circle (that is, the solid whose section when cut any where by a plane is accurately or nearly a circle) is (Geom. 1. Prop. Cylind.) accurately or nearly a sphere. The like inference may be drawn from the appearance presented on all sides of a spectator on land, the curve line which bounds his view being the circumference of a circle except where inequalities of the ground destroy its regularity.

2. The plane of the circle which terminates the view of a spectator is designated his visible or sensible horizon. A plane

B

to

conceived to pass through the spectator and the sun at noon, perpendicularly to the horizon, is called his meridian; and, on the supposition that the earth is a sphere or spheroid, this plane will pass through its centre. Its intersection with the surface of the earth or with a horizontal plane, which, to the extent of a few yards in every direction about the spectator, may be considered as coincident with that surface, is called a meridian line of this line, the extremity which is nearest to the Arctic regions of the earth is called the north point, and that which is opposite to it, the south point. A line imagined to pass through the spectator perpendicularly to the plane of the horizon, and to be produced above and below it towards the heavens, is denominated a vertical line; its upper and lower extremities are designated, respectively, the zenith and nadir. Every plane which may be conceived to pass through this line is said to be a vertical plane, but that which is at right angles to the plane of the meridian is called the prime vertical: it cuts the plane of the horizon in a line whose extremities are called the east and west points; the former being that which is on the right hand of the spectator when he looks towards the Arctic regions of the earth, and the latter, that which is on his left hand when in the same position. 3. Now, if a spectator were at any season of the year land on the shores of Spitzbergen, the stars which are visible would appear to describe about him circles nearly parallel to his horizon. In the British Isles certain stars towards the north indicate by their movements that they describe during a day and a night the circumferences of circles whose planes are very oblique to the horizon and wholly above it, while others describe arcs which are easily seen to become smaller portions of a circumference as they rise more remotely from the northern part of the horizon; and a few may be observed which rise and set near the southern point, describing, during the time they are visible, curves which ascend but little above that plane. About the mouth of the Amazon, and in the islands of the Indian Ocean, the spectator would see the stars rise and set perpendicularly to the horizon, each of them describing half the circumference of a circle above it. If the spectator were to transfer himself to the southern regions of the earth he would see phenomena similar to those above mentioned exhibited by the stars which are situated in that part of the heavens; while on directing his eye towards the north, the stars which before were seen to ascend to considerable heights above the southern part of the horizon, would be either invisible or would be seen but for a short time, the places of rising and setting being near the northern point.

4. These circumstances indicate a general revolution of all the stars about an axis passing through the earth perpendicularly to the planes of the circular arcs apparently described by them: but it is very improbable that so many different bodies should perform the revolution in the same time, preserving their apparent distances unchanged; and, on the ground that the like phenomena would result from a rotation of the earth about the same axis, the latter hypothesis is adopted by astronomers. In the present age a certain star (a Polaris) nearly indicates the northern extremity of the axis in the heavens, and an arc supposed to be traced through two bright stars (y and a of the southern cross) tends directly towards the opposite extremity.

5. The stars appearing to be at the same distance from the spectator, they are, for convenience, imagined to be attached to the concave surface of a hollow sphere of which his eye is the centre; and hence the general movement of the stars about the earth is sometimes called the diurnal rotation of the celestial sphere. The sun appears daily to rise and set: the moon also, when visible, exhibits the like phenomena; but these two celestial bodies, and certain stars which are not always visible, have proper movements which prove them to be quite distinct from the other bodies of the universe.

6. At a certain season, in any part of the world, a very distinguishable cluster of stars, which may have been observed to rise very near the eastern part of the horizon, will be on the meridian of the observer a short time before the rising of the sun on continuing to observe the cluster, its apparent elongation from the sun will constantly increase, and, in two or three months from the time of the first observation, it will appear at morning dawn to be setting in the west. During several months it will not be visible, but it will afterwards appear near the east a little while before the sun is there; and at the end of one year from the first observation it will be again seen on the meridian near the time of his rising. The like phenomena are exhibited by all the stars which rise in or near the east; and from this change in the sun's position with respect to such stars, it may be inferred either that those stars, and with them all the others, have been carried towards the west independently of the diurnal movement, or that the sun has, during the year, moved eastward about the earth. The moon is observed to change her place in like manner; for if on any night her distance eastward from some star be remarked, on the following night the distance in that direction will be sensibly increased: the distance

will go on continually increasing and, in about a month, the moon will be in the same position as at first with respect to the star. That an annual and monthly, as well as a diurnal revolution of all the stars should take place simultaneously, is highly improbable; and it may therefore be inferred that the moon revolves about the earth from west to east: the phenomena above mentioned may seem to indicate a like movement of the sun; but since they will be the same whether the sun revolve about the earth in one year, or the earth about the sun in the same time, the latter hypothesis, which alone is consistent with the laws of general attraction among the great bodies of the universe, may be immediately adopted.

7. It is well known that the sun's angular elevation above the horizon at noon experiences, from mid-winter to midsummer, a continual increase, and, from mid-summer to midwinter, a continual decrease. Now, by observing what groups of stars appear to rise and set very near the sun during a year, the trace of his apparent route in the heavens may be distinguished; and hence it may be readily ascertained in what groups the sun is at the times when his elevations above the horizon are the least and the greatest. These groups, or constellations, are on opposite sides of the celestial sphere with respect to the earth; and it may be perceived that a mean between the greatest and least elevations of the sun at noon is nearly equal to the elevation of that luminary at the noon of the day which is the middle of the interval between mid-winter and mid-summer, or between mid-summer and mid-winter: it may be observed also, that the greatest elevation of any star, which, rising in the east and setting in the west, appears to describe daily about the earth a path whose plane is perpendicular to the axis of the diurnal rotation, is equal to that mean elevation of the sun; and it may from these circumstances be presumed, that the path of the sun in his apparent yearly revolution about the earth, or the path of the earth about the sun, is a plane curve having a certain inclination to the plane last mentioned. The angular elevations of the points which the moon appears to occupy in the celestial sphere are sometimes greater than the greatest, and sometimes less than the least elevations of the sun; and it may from thence be inferred that the moon's orbit has a certain inclination to that in which the earth revolves about the sun.

8. Since the angular distance of the sun below the plane passing through the earth perpendicularly to the axis of rotation. is at noon, on the day of mid-winter, equal to the angular

distance of the sun above that plane at noon on the day of midsummer, and that on the two days of the year which are equally distant from those days the sun is in the plane perpendicular to the axis of rotation; it follows, if the earth be supposed to revolve annually about the sun, that the axis of the diurnal rotation must on. those four days be in positions parallel to one another; also, since the changes in the angular distance of the sun from that plane take place gradually, it may be inferred that the axis of rotation continues always strictly or nearly parallel to itself.

9. If the moon be at first observed near the west about the time that the sun is setting, her angular distance from that luminary will on every succeeding evening be found to have increased, and at the end of about fourteen days, she may be observed rising near the east, when the sun is on the western side of the horizon: she is then said to be in opposition to the sun from that time, she appears to approach the sun towards the east, the intervals between the times at which the two luminaries rise continually diminishing; and, at the end of about a month from the first observation, the moon is in conjunction with the sun. After remaining invisible for a few days, she re-appears in the west at a small distance from the setting sun, and the like phenomena are repeated.

10. During this revolution of the moon about the earth the form exhibited by the outline of her face gradually changes. At the time of new moon, when, in the western part of the horizon, she first emerges from the sun's rays, she assumes the form of a slender crescent of light, and this crescent daily increases in breadth, till, at the time of opposition, it becomes a complete circle: afterwards the breadth diminishes till the moon is about to become invisible from her proximity to the sun in the east, when the figure is again that of a slender crescent. These phases are exactly such as are presented by a globular body enlightened on half its surface by the sun, the circle bounding the light and shadow being in different positions with respect to the observer; and hence it is inferred that the figure of the moon is exactly or nearly that of a sphere.

It happens occasionally that, at the time of opposition, the centre of the moon is exactly or nearly in the direction of a line drawn from the centre of the sun through that of the earth, and produced towards her; and then, the shadow of the earth falling on the moon, the inhabitants of the side of the earth which is nearest to her observe her to be eclipsed, or deprived of the light which she would have received from the sun it happens also, occasionally, that at the time of