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my have determined that the mean diameter of the Earth, from the 45th degree of north latitude, to the opposite degree of south latitude, is accurately 7912 miles.
If the Earth were an exact sphere, its diameter might be determined by its curvature, from a single measurement. Thus, in the adjoining figure, we have A B equal to 1 mile, and B D equal to 8 inches, to find A E, or B E, which does not sensibly differ from A E, since B D is only 8 inches. Now it is a proposition of Euclid (B. 3, prop. 36), that, when from a point without a circle, two lines be drawn, one cutting and the other touching it, the touching line (B A) is a mean proportional between the cutting line (B E) and that part of it (B D) without the circle. BD: BA: BE or A E very nearly.
That is, 1 mile being equal to 63,360 inches,
8: 43,360: 63,360: 50,181,120 inches, or 7920 miles. This is very nearly what the most elaborate calculations make the Earth's equatorial diameter.
386. The Earth, considered as a planet, occupies a favored rank in the Solar System. It pleased the All-wise Creator to assign its position among the heavenly bodies, where nearly all the sister planets are visible to the naked eye. It is situated next to Venus, and is the third planet from the Sun.
To the scholar who for the first time takes up a book on astronomy, it will no doubt seem strange to find the Earth classed with the heavenly bodies. For what can appear more unlike, than the Earth, with her vast and seemingly immeasurable extent, and the stars, which appear but as points? The Earth is dark and opaque, the celestial bodies are brilliant. We perceive in it no motion; while in them we observe a continual change of place, as we view them at different hours of the day or night, or at different seasons of the year.
387. It moves round the Sun from west to east, in 365 days, 5 hours, 48 minutes, and 48 seconds; and turns the same way, on its axis, in 23 hours, 56 minutes, and 4 seconds. The former is called its annual motion, and causes the vicissitudes of the seasons. The latter is called its diurnal motion, and produces the succession of day and night.
The Earth's mean distance from the Sun is about 95,000,000 of miles. It consequently moves in its orbit at the mean rate of 68,000 miles an hour. Its equatorial diameter being 7924 miles, it turns on its axis at the rate of 1040 miles an hour.
Thus, the Earth on which we stand, and which has served for ages as the unshaken foundation of the firmest structures, is every moment turning swiftly on its center, and, at the same time, moving onwards with great rapidity through the empty space.
This compound motion is to be understood of the whole Earth, with all that it holds within its substance, or sustains upon its surface-of the solid mass beneath, of the ocean which flows around it, of the air that rests upon it, and of the clouds which float above it in the air.
886. What said of the position of the earth in the system? What remark as to classifying the earth as a planet? 387. State the time of the earth's revolution around the Sun? On her own axis? What are they called, respectively? What is the earth's mean distance from the sun? Its mean rate of motion in its orbit? Hourly motion of bodies at the equator? What twofold motion there? Includes what?
388. That the Earth, in common with all the planets, revolves around the Sun as a center, is a fact which rests upon the clearest demonstrations of philosophy. That it revolves, like them, upon its own axis, is a truth which every rising and setting sun illustrates, and which very many phenomena concur to establish. Either the Earth moves around its axis every day, or the whole universe moves around it in the same time. There is no third opinion that can be formed on this point. Either the Earth must revolve on its axis every twenty-four hours, to produce the alternate succession of day and night, or the Sun, Moon, planets, comets, fixed stars, and the whole frame of the universe itself, must move around the Earth, in the same time.
389. To suppose the latter case to be the fact, would be to cast a reflection on the wisdom of the Supreme Architect, whose laws are universal harmony. As well might the beetle, that in a moment turns on its ball, imagine the heavens and the earth had made a revolution in the same instant. It is evident, that in proportion to the distance of the celestial bodies from the Earth, must, on this supposition, be the rapidity of their movements. The Sun, then, would move at the rate of more than 400,000 miles in a minute; the nearest stars, at the inconceivable velocity of 1,400,000,000 of miles in a second; and the most distant luminaries, with a degree of swiftness which no numbers could express, and all this, to save the little globe we tread upon, from turning safely on its axis, once in twenty-four hours.
390. The idea of the heavens revolving about the Earth, is encumbered with innumerable other difficulties. We will mention only one more. It is estimated on good authority, that there are visible, by means of glasses, no less than 100,000,000 of stars, scattered at all possible distances in the heavens above, beneath, and around us. Now, is it in the least degree probable, that the velocities of all these bodies should be so regulated, that, though describing circles so very different in dimensions, they should complete their revolutions in exactly the same time? In short, there is no more reason to suppose that the heavens revolve around the Earth, than there is to suppose that they revolve around each of the other planets, separately, and at the same time; since the same apparent revolution is common to them all, for they all appear to revolve upon their axis, in different periods.
888. What two motions has the earth? What proof of her diurnal revolution? Why not suppose the heavens revolve around us? 390. What further proof?
391. The rotation of the Earth determines the length of the day, and may be regarded as one of the most important elements in astronomical science. It serves as an universal measure of time, and forms the standard of comparison for the revolutions of the celestial bodies, for all ages, past and to come. Theory and observation concur in proving, that among the innumerable vicissitudes that prevail throughout creation, the period of the Earth's diurnal rotation is immutable.
SOLAR AND SIDEREAL TIME.
392. The Earth performs one complete revolution on its axis in 23 hours, 56 minutes, and 4.09 seconds, of solar time. This is called a sidereal day, because, in that time, the stars appear to complete one revolution around the Earth.
But, as the Earth advances almost a degree eastward in its orbit, in the time that it turns eastward around its axis, it is plain that just one rotation never brings the same meridian around from the Sun to the Sun again; so that the Earth requires as much more than one complete revolution on its axis to complete a solar day, as it has gone forward in that time.
To the man at A the Sun (S) is exactly on the meridian, or it is twelve o'clock, noon. The Earth passes on from B to D, and at the same time revolves on her axis. When she reaches D, the man who has stood on the same meridian has made a complete revolution, as determined by the star G (which was also on his meridian at twelve o'clock the day before); but the Sun is now east of the meridian, and he must wait four minutes for the Earth to roll a little further eastward, and bring the Sun again over his north and south line. If the Earth was not revolving around the Sun, her solar and sidereal days would be the same; but as it is, she has to perform a little more than one complete revolution each solar day, to bring the Sun on the meridian.
393. It is obvious, therefore, that in every natural or solar day, the Earth performs one complete revolution on its axis, and the 365th part of another revolution. Consequently, in 365 days, the Earth turns 366 times around its axis. And as every
891. What relation has the earth's diurnal revolution to time? What said of its reguLarity? 892. What is the time required for a complete revolution? Explain the difference between solar and sidereal time? 893. Is a solar day more than a complete revolution of the earth on her axis? To what does this excess amount in a year?
revolution of the earth on its axis completes a sidereal day, there must be 366 sidereal days in a year. And, generally, since the rotation of any planet about its axis is the length of a sidereal day at that planet, the number of sidereal days will always exceed the number of solar days by one, let that number be what it may, one revolution being always lost in the course of an annual revolution. This difference between the sidereal and solar days may be illustrated by referring to a watch or clock. When both hands set out together, at 12 o'clock for instance, the minute hand must travel more than a whole circle before it will overtake the hour hand, that is, before they will come into conjunction again.
394. In the same manner, if a man travel around the Earth eastwardly, no matter in what time, he will reckon one day more, on his arrival at the place whence he set out, than they do who remain at rest; while the man who travels around the Earth westwardly will have one day less. From which it is manifest, that if two persons start from the same place at the same time, but go in contrary directions, the one traveling eastward and the other westward, and each goes completely around the globe, although they should both arrive again at the very same hour at the same place from which they set out, yet they will disagree two whole days in their reckoning. Should the day of their return, to the man who traveled westwardly, be Monday, to the man who travelled eastwardly, it would be Wednesday; while to those who remained at the place itself, it would be Tuesday.
395. Nor is it necessary, in order to produce the gain or loss of a day, that the journey be performed either on the equator, or on any parallel of latitude: it is sufficient for the purpose, that all the meridians of the Earth be passed through, eastward or westward. The time, also, occupied in the journey, is equally unimportant; the gain or loss of a day being the same, whether the Earth be traveled around in 24 years, or in as many hours.
396. It is also evident, that if the Earth turned around its axis but once in a year, and if the revolution was performed the same way as its revolution around the Sun, there would be perpetual day on one side of it, and perpetual night on the other.
Hence what general rule? What illustration referred to? 894. What effect has traveling east or west, upon time? Hence what result? 895. Is it important that the supposed journeys be performed in a short period? 896. How would it be if the Earth revolved on her axis but once a year?
From these facts the pupil will readily comprehend the principles involved in a curious problem which appeared a few years ago. It was gravely reported by an American ship, that, in sailing over the ocean, it chanced to find six Sundays in February. The fact was insisted on, and a solution demanded. There is nothing absurd in this. The man who travels around the earth eastwardly, will see the Sun go down a little earlier every succeeding day, than if he had remained at rest; or earlier than they do who live at the place from which he set out. The faster he travels towards the rising sun, the sooner will it appear above the horizon in the morning, and so much sooner will it set in the evening. What he thus gains in time, will bear the same proportion to a solar day, as the distance traveled does to the circumference of the Earth. As the globe is 360 degrees in circumference, the Sun will appear to move over one twenty-fourth part of its surface, or 14° every hour, which is 4 minutes to one degree. Consequently, the Sun will rise, come to the meridian, and set, 4 minutes sooner, at a place 1° east of us, than it will with us; at the distance of 2° the Sun will rise and set 8 minutes sooner; at the distance of 8°, 12 minutes sooner, and so on.
Now the man who travels one degree to the east, the first day will have the Sun on his meridian 4 minutes sooner than we do who are at rest; and the second day 8 minutes sooner, and on the third day 12 minutes sooner, and so on; each successive day being completed 4 minutes earlier than the preceding, until he arrives again at the place from which he started: when this continual gain of 4 minutes a day will have amounted to a whole day in advance of our time: he having seen the Sun rise and set once more than we have. Consequently, the day on which he arrives at home, whatever day of the week it may be, is one day in advance of ours, and he must needs live that day over again, by calling the next day by the same name, in order to make the accounts harmonize.
If this should be the last day of February in a bissextile year, it would also be the same day of the week that the first was, and be six times repeated, and if it should happen on Sunday, he would, under these circumstances, have six Sundays in February. Again whereas the man who travels at the rate of one degree to the east, will have all his days 4 minutes shorter than ours, so, on the contrary, the man who travels at the same rate towards the west, will have all his days 4 minutes longer than ours. When he has finished the circuit of the Earth, and arrived at the place from which he first set out, he will have seen the Sun rise and set once less than we have. Consequently, the day he gets home will be one day after the time at that place; for which reason, if he arrives at home on Saturday, according to his own account, he will have to call the next day Monday; Sunday having gone by before he reached home. Thus, on whatever day of the week January should end, in common years, he would find the same day repeated only three times in February. If January ended on Sunday, he would, under these circumstances, find only three Sundays in February.
397. The Earth's motion about its axis being perfectly equable and uniform in every part of its annual revolution, the sidereal days are always of the same length, but the solar or natural days vary very considerably at different times of the year. This variation is owing to two distinct causes, the inclination of the Earth's axis to its orbit, and the inequality of its motion around the Sun. From these two causes it is, that the time shown by a well-regulated clock and that of a true sun-dial are scarcely ever the The difference between them, which sometimes amounts to 16 minutes, is called the Equation of Time, or the equation of solar days.
What curious facts accounted for? What supposition of a man traveling eastward one degree a day? What effect upon the time of the Sun's passing the meridian? Upon the length of his day? What change of name may it require? 397. Are the solar and sidereal days alike uniform as to length? Why do solar days vary in length? Why do not a dial and clock agree? What is the Equation of Time?