At e

er seen from the sun or the earth; consequently its motion will be direct. But while it is passing from h to b, it will appear to move from m, through n, o, to p, in a different direction, as seen from the earth, from that in which it appears to move, as seen from the sun ; that . is, its motion is retrograde, and directly contrary to what it was in the opposite part of its orbit. While it is passing from b to c, or from g to h, it is moving almost directly from or to the earth, and consequently it will appear nearly stationary among the stars. Venus is said to be in its superior conjunction, because it is beyond the sun ; at a it is said to be in its inferior conjunction, because it is between the sun and earth. The motions and conjunctions of Mercury are like those of Venus.

84. It is obvious also, that while the motion of Venus is direct or retrograde to us on earth, the motion of the earth will be direct or retrograde to the inhabitants of Venus ; for, while Venus passes from h to b, and is retrograde to us, the earth appears to move from r towards s, directly opposite to its motion as seen from the sun. But while Venus is moving from d to f, the earth will appear to move in the same direction as if seen from the sun, that is, from v towards ri So also while Venus appears to us stationary at and near her greatest elongation, the earth appears stationary to an inhabitant of Venus. When Venus is at a, the earth is in opposition ; that is, in a part of the heavens directly opposite to the sun. But when Venus is at e, the earth is in conjunction with the sun. Now, precisely the same motions which the earth exhibits to the inhabitants of Venus, each of the exterior planets exhibits to us.

85. It is plain also, that from the earth's situation out of the centre of the solar system, the apparent magnitudes of the other planets vary; for common experience shows, that, as objects are nearer they appear larger. Hence, when Venus is nearest the earth, as at or near a, its magnitude must appear larger, than when

As the apparent magnitudes of other planets vary to us, that of the earth varies to them.

at or near e.

ART. 2. Of Eclipses. 86. The situation of the earth with regard to the moon, or rather of the moon with regard to the earth, occasions eclipses both of the sun and moon.

Those of the sun take place when the moon, passing between the sun and earth, intercepts his rays. Those of the moon take place when the earth, coming between the sun and moon, deprive the rnoon of his light. Hence an eclipse of the sun can take place only when the moon changes, and an eclipse of the moon only when the moons full ; for at the time of an eclipse, either of the sun or moon, the sun, earth, and moon must be in the same straight line.

87. If the moon went round the earth in the same plane in which the earth goes round the sun, that is, in the ecliptic, it is plain that the sun would be eclipsed at every new moon; and the moon would be eclipsed

For at each of these times, these three bodies would be in the same straight line. But the moon's orbit does not coincide with the ecliptic, but is inclined to it at an angle of about 5° 20'. Hence, since the apparent diameter of the sun is but about į a degree, and that of the moon about the same, no eclipse will take place at new or full moon, unless the moon be within a degree of the ecliptic, that is, in or near one of its nodes. It is found that if the moon be within 16° of a node at time of change, it will be so near the ecliptic, that the sun will be more or less eclipsed ; if within 12° at time of full, the moon will be more or less eclipsed.

at every full.

N

88. It is obvious that the moon will be oftener within 161° of a node at the time of change, than within 12° at the time of full; consequently there will be more eclipses of the sun than of the moon in a course of years. As the nodes commonly come between the sun and earth but twice in a year, and the moon's orbit contains 360°, of which 161°, the limit of solar eclipses, and 12°, the limit of lunar eclipses, are but small portions, it is plain there must be many new and full moons without any eclipses.

89. Although there are more eclipses of the sun than of the moon, yet more eclipses of the moon will be visible at a particular place, as Boston, in a course of years, than of the sun. Since the sun is very much larger than either the earth or moon, the shadow of these bodies must always terminate in a point; that is, it must always be à cone. (See Pl. IV. fig. 1 and 2.) Let S be the sun, m the moon, and E the earth. The sun constantly illuminates half the earth's surface, that is, a hemisphere; and consequently he is visible to all in this hemisphere. But the moon's shadow falls upon but a part of this hemisphere; and hence the sun appears eclipsed to but a part of those to whom he is visible. Sometimes when the moon is at its greatest distance, its shadow om, terminates before it reaches the earth. In eclipses of this kind, to an inhabitant directly under the point o, the outermost edge of the sun's disk is seen, forming a bright ring round the moon; from which circumstance these eclipses are called annular, from annulus, a Latin word for ring. ***

(360 • 24) = 15° every hour. Hence, when it is noon at a particular place, as Boston, it will be 1 o'clock at all places on a meridian 15° east of that of Boston, and 11 o'clock at all places on a meridian 15° west of that of Boston. If the distance of two meridians be 30°, the difference of time is 2 hours, and so on.

74. Hence it is plain that as places differ in longitude, that is, are situated on different meridians, the clocks and watches of those places will show different hours at the same instant of absolute time ; a difference of 15° always producing a difference of 1 hour in time. For example, Paris is 21° east longitude from London. This difference, at the rate of 1 hour for 15°, produces a difference of time of 9 minutes 22 seconds. Hence the clocks at Paris are 9 minutes 22 seconds faster than those of London ; so that when it is noon at London it is 9 minutes 22 seconds past noon at Paris. So also the difference of longitude between London and Boston is 71° 4'; consequently the difference of time by the clocks at Boston and London is 4 hours 44 minutes 16 seconds. Hence when it is noon at Boston, it wants 15 minutes 44 seconds of 5 o'clock at London ; and when it is noon at London it is 15 minutes 44 seconds after 7 in the morning at Boston.

75. Hence, if the difference of time, as shown by the clocks of two places, is known, the difference of longitude between them can be ascertained. Suppose I have a watch of such workmanship, and so well regulated, that it would always show the exact time at London; by this I can find my longitude. For by observing the precise time when the sun comes to the meridian where I am, I know it is 12 o'clock where I am ; and by looking at my watch, I know what the time is at London. Then, by allowing 1 hour for 15°, I know my longitude.

*76. To illustrate this, suppose I am sailing in the

Mediterranean sea, and wish to know my longitude. When the sun is exactly south, and I know it to be noon where I am, I find by my watch that it wants 20 minutes of 11 o'clock at London. The difference in time is 1 hour 20 minutes. I am, therefore, on a meridian 20° from that of London; and eastward, because it is noon where I am before it is at London. Again, suppose I sail from London for the West Indies.

ter a boisterous passage, during which no observations of the heavenly bodies could be taken, and it was impossible to keep the ship's reckoning I fall upon a coast, but know not whether it be that of an island or of the American continent. When the sun is in the meridian, I find by my watch, that it is a trifle more than 7 minutes past 5 at London. By turning this difference of 5 hours 7 minutes into degrees, I find I am in longitude about 76° 45', and this must be west, because it is noon where I am later than at London. But in this case when I have found my longitude, I have not determined the coast. For by reference to a chart or a map, I find I

may

be either on the coast of the southern part of the United States, of the Island Cuba, of Jamaica, or of the northern coast of South America. But by taking the sun's altitude at the same time, and thus finding my latitude, say 22° 30' north, I ascertain which of these several coasts I am on ; viz. that of Cuba.

77. The principal difficulty in ascertaining longitude by this method is, that no timepieces have yet been constructed, and none probably can be, which will measure time accurately, and without variation. Clocks, which move by, weights and are regulated by pendulums, are most uniform in their movements. But the constant motion of the vessel entirely precludes their use at sea. Incredible pains have been taken to render watches and chronometers accurate measurers of