Plate x.
Caroline.Then, after all, the sun which I thought so partial, confers his favours equally on all.
Mrs. B.Not so either: the inhabitants of the torrid zone have much more heat than we have, as the sun's rays fall perpendicularly twice in the course of a year, on every place within the tropics, while they shine more or less obliquely on the rest of the world, and almost horizontally at the poles; for during their long day of six months, the sun moves round their horizon without either rising or setting; the only observable difference, is that it is more elevated by a few degrees at mid-day, than at midnight.
Emily.To a person placed in the temperate zone, in the situation in which we are in England, the sun will shine neither so obliquely as it does on the poles, nor vertically as at the equator; but its rays will fall upon him more obliquely in autumn, and winter, than in summer.
Caroline.And therefore, the inhabitants of the temperate zones, will not have merely one day, and one night, in the year, as happens at the poles, nor will they have equal days, and equal nights, as at the equator; but their days and nights will vary in length, at different times of the year, according as their respective poles incline towards, or from the sun, and the difference will be greater in proportion to their distance from the equator.
Mrs. B.We shall now follow the earth through the other half of her orbit, and you will observe, that now exactly the same changes take place in the southern hemisphere, as those we have just remarked in the northern. Day commences at the south pole, when night sets in at the north pole; and in every other part of the southern hemisphere the days are longer than the nights, while, on the contrary, our nights are longer than our days. When the earth arrives at the vernal equinox, D, where the ecliptic again cuts the equator, on the 21st of March, she is situated, with respect to the sun, exactly in the same position, as in the autumnal equinox; and the only differencewith respect to the earth, is, that it is now autumn in the southern hemisphere, whilst it is spring with us.
Caroline.Then the days and nights are again every where equal.
Mrs. B.Yes, for the half of the globe which is enlightened, extends exactly from one pole to the other, the sun has just risen to the north pole, and is just setting to the south pole; but in every other part of the globe, the day and night is of twelve hours length; hence the word equinox, which is derived from the Latin, meaning equal night.
As our summer advances, the days lengthen in the northern hemisphere, and shorten in the southern, till the earth reaches the summer solstice, when the north frigid zone is entirely illumined, and the southern is in complete darkness; and we have now brought the earth again to the spot from whence we first accompanied her.
Emily.This is indeed a most satisfactory explanation of the cause of the different lengths of our days and nights, and of the variation of the seasons; and the more I learn, the more I admire the simplicity of means by which such wonderful effects are produced.
Mrs. B.I know not which is most worthy of our admiration, the causes, or the effects of the earth's revolution round the sun. The mind can find no object of contemplation more sublime, than the course of this magnificent globe, impelled by the combined powers of projection and attraction, to roll in one invariable course, around the source of light and heat: and what can be more delightful than the beneficent effects of this vivifying power on its attendant planet. It is at once the grand principle which animates and fecundates nature.
Emily.There is one circumstance in which this little ivory globe appears to me to differ from the earth; it is not quite dark on that side of it which is turned from the candle, as is the case with the earth when neither moon nor stars are visible.
Mrs. B.This is owing to the light of the candle, being reflected by the walls of the room, on every part of the globe, consequently that side of the globe, on which the candle does not directly shine, is not in total darkness. Now the skies have no walls to reflect the sun's light on that side of our earth which is in darkness.
Caroline.I beg your pardon, Mrs. B., I think that the moon, and stars, answer the purpose of walls in reflecting the sun's light to us in the night.
Mrs. B.Very well, Caroline; that is to say, the moon and planets; for the fixed stars, you know, shine by their own light.
Emily.You say, that the superior heat of the equatorial parts of the earth, arises from the rays falling perpendicularly on those regions, whilst they fall obliquely on these more northern regions; now I do not understand why perpendicular rays should afford more heat than oblique rays.
Caroline.You need only hold your hand perpendicularly over the candle, and then hold it sideways obliquely, to be sensible of the difference.
Emily.I do not doubt the fact, but I wish to have it explained.
Mrs. B.You are quite right; if Caroline had not been satisfied with ascertaining the fact, without understanding it, she would not have brought forward the candle as an illustration; the reason why you feel so much more heat if you hold your hand perpendicularly over the candle, than if you hold it sideways, is because a stream of heated vapour constantly ascends from the candle, or any other burning body, which being lighter than the air of the room, does not spread laterally but rises perpendicularly, and this led you to suppose that the rays were hotter in the latter direction. Had you reflected, you would have discovered that rays issuing from the candle sideways, are no less perpendicular to your hand when held opposite to them, than the rays which ascend when your hand is held over them.
The reason why the sun's rays afford less heat when in an oblique direction, than when perpendicular, is because fewer of them fall upon an equal portion of the earth; this will be understood better by referring toplate 10. fig. 1, which represents two equal portions of the sun's rays, shining upon different parts of the earth. Here it is evident, that the same quantity of rays fall on the space A B, as fall on the space B C; and as A B is less than B C, the heat and light will be much stronger in the former than in the latter; A B, you see, represents the equatorial regions, where the sun shines perpendicularly; and B C, the temperate and frozen climates, where his rays fall more obliquely.
Emily.This accounts not only for the greater heat of the equatorial regions, but for the greater heat of our summers, as the sun shines less obliquely in summer than in winter.
Mrs. B.This you will see exemplified infigure 2, in which the earth is represented, as it is situated on the 21st of June, and England receives less oblique, and consequently a greaternumber of rays, than at any other season; andfigure 3, shows the situation of England on the 21st of December, when the rays of the sun fall most obliquely upon her. But there is also another reason why oblique rays give less heat, than perpendicular rays; which is, that they have a greater portion of the atmosphere to traverse; and though it is true, that the atmosphere is itself a transparent body, freely admitting the passage of the sun's rays, yet it is always loaded more or less with dense and foggy vapour, which the rays of the sun cannot easily penetrate; therefore, the greater the quantity of atmosphere the sun's rays have to pass through in their way to the earth, the less heat they will retain when they reach it. This will be better understood, by referring tofig. 4.The dotted line round the earth, describes the extent of the atmosphere, and the lines which proceed from the sun to the earth, the passage of two equal portions of the sun's rays, to the equatorial and polar regions; the latter you see, from its greater obliquity, passes through a greater extent of atmosphere.
Caroline.And this, no doubt, is the reason why the sun, in the morning and in the evening, gives so much less heat, than at mid-day.
Mrs. B.The diminution of heat, morning and evening, is certainly owing to the greater obliquity of the sun's rays; and they are also affected by the other, both the cause, which I have just explained to you; the difficulty of passing through a foggy atmosphere is perhaps more particularly applicable to them, as mist and vapours are prevalent about the time of sunrise and sunset. But the diminished obliquity of the sun's rays, is not the sole cause of the heat of summer; the length of the days greatly conduces to it; for the longer the sun is above the horizon, the more heat he will communicate to the earth.
Caroline.Both the longest days, and the most perpendicular rays, are on the 21st of June; and yet the greatest heat prevails in July and August.
Mrs. B.Those parts of the earth which are once heated, retain the heat for some length of time, and the additional heat they receive, occasions an elevation of temperature, although the days begin to shorten, and the sun's rays to fall more obliquely. For the same reason, we have generally more heat at three o'clock in the afternoon, than at twelve, when the sun is on the meridian.
Emily.And pray, have the other planets the same vicissitudes of seasons, as the earth?
Mrs. B.Some of them more, some less, according as their axes deviate more or less from the perpendicular, to the plane of their orbits. The axis of Jupiter, is nearly perpendicular to the plane of his orbit; the axes of Mars, and of Saturn, are each, inclined at angles of about sixty degrees; whilst the axis of Venus is believed to be elevated only fifteen or twenty degrees above her orbit; the vicissitudes of her seasons must therefore be considerably greater than ours. For further particulars respecting the planets, I shall refer you to Bonnycastle's Introduction to Astronomy.
I have but one more observation to make to you, relative to the earth's motion; which is, that although we have but 365 days and nights in the year, she performs 366 complete revolutions on her axis, during that time.
Caroline.How is that possible? for every complete revolution must bring the same place back to the sun. It is now just twelve o'clock, the sun is, therefore, on our meridian; in twenty-four hours will it not have returned to our meridian again, and will not the earth have made a complete rotation on its axis?
Mrs. B.If the earth had no progressive motion in its orbit whilst it revolves on its axis, this would be the case; but as it advances almost a degree westward in its orbit, in the same time that it completes a revolution eastward on its axis, it must revolve nearly one degree more in order to bring the same meridian back to the sun.
Caroline.Oh, yes! it will require as much more of a second revolution to bring the same meridian back to the sun, as is equal to the space the earth has advanced in her orbit; that is, nearly a degree; this difference is, however, very little.
Mrs. B.These small daily portions of rotation, are each equal to the three hundred and sixty-fifth part of a circle, which at the end of the year amounts to one complete rotation.
Emily.That is extremely curious. If the earth then, had no other than its diurnal motion, we should have 366 days in the year.
Mrs. B.We should have 366 days in the same period of time that we now have 365; but if we did not revolve round the sun, we should have no natural means of computing years.
You will be surprised to hear, that if time is calculated by thestars instead of the sun, the irregularity which we have just noticed does not occur, and that one complete rotation of the earth on its axis, brings the same meridian back to any fixed star.
Emily.That seems quite unaccountable; for the earth advances in her orbit with regard to the fixed stars, the same as with regard to the sun.
Mrs. B.True, but then the distance of the fixed stars is so immense, that our solar system is in comparison to it but a spot, and the whole extent of the earth's orbit but a point; therefore, whether the earth remain stationary, or whether it revolved in its orbit during its rotation on its axis, no sensible difference would be produced with regard to the fixed stars. One complete revolution brings the same meridian back to the same fixed star; hence the fixed stars appear to go round the earth in a shorter time than the sun by three minutes fifty-six seconds of time.
Caroline.These three minutes fifty-six seconds is the time which the earth takes to perform the additional three hundred and sixty-fifth part of the circle, in order to bring the same meridian back to the sun.
Mrs. B.Precisely. Hence the stars gain every day three minutes fifty-six seconds on the sun, which makes them rise that portion of time earlier every day.
When time is calculated by the stars it is called sidereal time; when by the sun, solar, or apparent time.
Caroline.Then a sidereal day is three minutes fifty-six seconds shorter, than a solar day of twenty-four hours.
Mrs. B.I must also explain to you what is meant by a sidereal year.
The common year, called the solar or tropical year, containing 365 days, five hours, forty-eight minutes and fifty-two seconds, is measured from the time the sun sets out from one of the equinoxes, or solstices, till it returns to the same again; but this year is completed, before the earth has finished one entire revolution in its orbit.
Emily.I thought that the earth performed one complete revolution in its orbit, every year; what is the reason of this variation?
Mrs. B.It is owing to the spheroidal figure of the earth. The elevation about the equator produces much the same effect as if a similar mass of matter, collected in the form of a moon, revolved round the equator. When this moon acted on the earth, in conjunction with, or in opposition to the sun, variationsin the earth's motion would be occasioned, and these variations produce what is called the precession of the equinoxes.
Plate xi.
Emily.What does that mean? I thought the equinoctial points, were fixed points in the heavens, in which the equator cuts the ecliptic.
Mrs. B.These points are not quite fixed, but have an apparently retrograde motion, among the signs of the zodiac; that is to say, instead of being at every revolution in the same place, they move backwards. Thus if the vernal equinox is at A, (fig. 1. plate XI.) the autumnal one, will be at B, instead of C, and the following vernal equinox, at D, instead of at A, as would be the case if the equinoxes were stationary, at opposite points of the earth's orbit.
Caroline.So that when the earth moves from one equinox to the other, though it takes half a year to perform the journey, it has not travelled through half its orbit.
Mrs. B.And, consequently, when it returns again to the first equinox, it has not completed the whole of its orbit. In order to ascertain when the earth has performed an entire revolution in its orbit, we must observe when the sun returns in conjunction with any fixed star; and this is called a sidereal year. Supposing a fixed star situated at E, (fig. 1. plate XI.) the sun would not appear in conjunction with it, till the earth had returned to A, when it would have completed its orbit.
Emily.And how much longer is the sidereal, than the solar year?
Mrs. B.Only twenty minutes; so that the variation of the equinoctial points is very inconsiderable. I have given them a greater extent in the figure, in order to render them sensible.
In regard to time, I must further add, that the earth's diurnal motion on an inclined axis, together with its annual revolution in an elliptic orbit, occasions so much complication in its motion, as to produce many irregularities; therefore the true time cannot be measured by the apparent place of the sun. A perfectly correct clock, would in some parts of the year be before the sun, and in other parts after it. There are but four periods in which the sun and a perfect clock would agree, which is the 15th of April, the 16th of June, the 23d of August, and the 24th of December.
Emily.And is there any considerable difference between solar time, and true time?
Mrs. B.The greatest difference amounts to between fifteen and sixteen minutes. Tables of equation are constructed for the purpose of pointing out, and correcting these differences between solar time and equal or mean time, which is the denomination given by astronomers, to true time.
Questions1.(Pg.92) What does the line A B, (fig. 2 plate 8.) represent, and what are its extremities called?2.(Pg.92) What is meant by the equator, and how is it situated?3.(Pg.92) There are two hemispheres; how are they named and distinguished?4.(Pg.92) What are the circles near the poles called?5.(Pg.92) What do the lines I K, and L M, represent?6.(Pg.92) What circle is in part represented by the line L K?7.(Pg.92) Against what mistake must you guard respecting this line?8.(Pg.92) What is meant by a plane, and how could one be represented?9.(Pg.93) Describe what is intended by the plane of the earth's orbit.10.(Pg.93) Extending this plane to the fixed stars, what circle would it form, and among what particular stars would it be found?11.(Pg.93) What isfig. 1. plate 9, designed to represent?12.(Pg.93) The ecliptic does not properly belong to the earth, for what purpose then is it described on the terrestrial globe?13.(Pg.93) What does the obliquity of the ecliptic to the equator serve to show?14.(Pg.93) Within what limits do you find the torrid zone?15.(Pg.93) What two zones are there between the torrid, and the two frigid zones?16.(Pg.93) Where are the frigid zones situated?17.(Pg.93) What is meant by the term zone; and are the frigid zones properly so called?18.(Pg.93) How do meridian lines extend, and what is meant by the meridian of a place?19.(Pg.93) What is said of the meridian to which the sun is opposite, and where is it then midnight?20.(Pg.94) What hour is it then, at places exactly half way between these meridians?21.(Pg.94) How are greater and lesser circles distinguished?22.(Pg.94) What part of a circle is a degree, and how are these further divided?23.(Pg.94) What is the diameter, and what the circumference of a circle, and what proportion do they bear to each other?24.(Pg.94) What part of a circle is a meridian?25.(Pg.94) How many degrees are there between the equator and the poles?26.(Pg.94) Into what parts, besides degrees, is the ecliptic divided?27.(Pg.94) How are degrees of latitude measured, and to what number do they extend?28.(Pg.94) On what circles are degrees of longitude measured, and to what number do they extend?29.(Pg.94) What is a parallel of latitude?30.(Pg.95) Degrees of longitude vary in length; what is the cause of this?31.(Pg.95) What is the length of a degree of latitude, and why do not these vary?32.(Pg.95) What causes the equator to be somewhat larger than a great circle passing through the poles, and what effect has this on degrees of longitude measured on the equator?33.(Pg.95) What is the cause of this form being given to the earth?34.(Pg.96) What would have been a consequence of the centrifugal force, had the earth been a perfect sphere?35.(Pg.96) A body situated at the poles, is attracted more forcibly than if placed at the equator, what is the reason?36.(Pg.97) What effect would be produced upon the gravity of a body, were it placed beneath the surface of the earth, and what supposing it at its centre?37.(Pg.97) What two circumstances combine, to lessen the weight of a body on the equator?38.(Pg.97) Why could not this be proved by weighing a body at the poles, and at the equator?39.(Pg.98) What is a pendulum?40.(Pg.98) What causes it to vibrate?41.(Pg.98) Why are not its vibrations perpetual?42.(Pg.98) Two pendulums of the same length, will not, in different latitudes, perform their vibrations in equal times, what is the cause of this?43.(Pg.98) To what use has this property of the pendulum been applied?44.(Pg.99) What change must be made in pendulums situated at the equator and at the poles, to render their vibrations equal?45.(Pg.99) What do the vibrations of a pendulum resemble, and why will it vibrate more rapidly if shortened?46.(Pg.99) In the revolution of the earth round the sun, what is the position of its axis?47.(Pg.99) How much is the axis of the earth inclined, and with what line does it form this angle?48.(Pg.99) What is represented byfig. 2, plate 9?49.(Pg.100) How is the north pole inclined in the middle of our summer, and what effect has this on the north frigid zone?50.(Pg.100) In what direction does the north pole always point?51.(Pg.100) What is shown by the position of the earth at B, in the figure?52.(Pg.100) How does the sun then shine at the poles, and what is the effect on the days and nights?53.(Pg.101) When the earth has passed the autumnal equinox, what changes take place at the poles, and also in the whole northern and southern hemispheres?54.(Pg.101) Why is the heat greatest within the torrid zone?55.(Pg.101) How does the sun appear at the poles, during the period of day there?56.(Pg.101) In what will the days and nights differ in the temperate zone, from those at the poles, and at the equator?57.(Pg.102) Trace the earth from the winter solstice to the vernal equinox, and inform me what changes take place.58.(Pg.102) What takes place at the time of the vernal equinox, and what is meant by the term?59.(Pg.102) In proceeding from the vernal equinox to the summer solstice, what changes take place?60.(Pg.103) From what cause arises the superior heat of the equatorial regions?61.(Pg.103) Why should oblique rays afford less heat than those which are perpendicular?62.(Pg.103) How is this explained byfig. 1. plate 10?63.(Pg.103) How do you account for the superior heat of summer, and how is this exemplified infig. 2 and 3, plate 10?64.(Pg.104) What other cause lessens the intensity of oblique rays?65.(Pg.104) How is this explained byfig. 4?66.(Pg.104) What causes conspire to lessen the solar heat in the morning and evening?67.(Pg.104) The greatest heat of summer is after the solstice, and the greatest heat of the day, after 12 o'clock, although the sun's rays are then most direct, how is this accounted for?68.(Pg.105) Is there any change of seasons in the other planets?69.(Pg.105) What is said respecting the axes of Jupiter, of Mars, and of Saturn?70.(Pg.105) In 365 days, how many times does the earth revolve on its axis?71.(Pg.105) How is this accounted for?72.(Pg.105) Do the fixed stars require the same time as the sun, to return to the same meridian?73.(Pg.106) How is this accounted for?74.(Pg.106) What is meant by the solar and the sidereal day?75.(Pg.106) What is the difference in time between them?76.(Pg.106) What is the length of the tropical year?77.(Pg.107) The solar year is completed before the earth has made a complete revolution in its orbit, by what is this caused?78.(Pg.107) What is this called, and what is represented respecting it byfig. 1, plate 11?79.(Pg.107) By what means can we ascertain the period of a complete revolution of the earth in its orbit, as illustrated by the fixed star E, infig. 1?80.(Pg.107) What difference is there in the length of the solar and sidereal year?81.(Pg.107) Why can we not always ascertain the true time by the apparent place of the sun?82.(Pg.108) What would be the greatest difference between solar, and true time, as indicated by a perfect clock?
Questions
1.(Pg.92) What does the line A B, (fig. 2 plate 8.) represent, and what are its extremities called?
2.(Pg.92) What is meant by the equator, and how is it situated?
3.(Pg.92) There are two hemispheres; how are they named and distinguished?
4.(Pg.92) What are the circles near the poles called?
5.(Pg.92) What do the lines I K, and L M, represent?
6.(Pg.92) What circle is in part represented by the line L K?
7.(Pg.92) Against what mistake must you guard respecting this line?
8.(Pg.92) What is meant by a plane, and how could one be represented?
9.(Pg.93) Describe what is intended by the plane of the earth's orbit.
10.(Pg.93) Extending this plane to the fixed stars, what circle would it form, and among what particular stars would it be found?
11.(Pg.93) What isfig. 1. plate 9, designed to represent?
12.(Pg.93) The ecliptic does not properly belong to the earth, for what purpose then is it described on the terrestrial globe?
13.(Pg.93) What does the obliquity of the ecliptic to the equator serve to show?
14.(Pg.93) Within what limits do you find the torrid zone?
15.(Pg.93) What two zones are there between the torrid, and the two frigid zones?
16.(Pg.93) Where are the frigid zones situated?
17.(Pg.93) What is meant by the term zone; and are the frigid zones properly so called?
18.(Pg.93) How do meridian lines extend, and what is meant by the meridian of a place?
19.(Pg.93) What is said of the meridian to which the sun is opposite, and where is it then midnight?
20.(Pg.94) What hour is it then, at places exactly half way between these meridians?
21.(Pg.94) How are greater and lesser circles distinguished?
22.(Pg.94) What part of a circle is a degree, and how are these further divided?
23.(Pg.94) What is the diameter, and what the circumference of a circle, and what proportion do they bear to each other?
24.(Pg.94) What part of a circle is a meridian?
25.(Pg.94) How many degrees are there between the equator and the poles?
26.(Pg.94) Into what parts, besides degrees, is the ecliptic divided?
27.(Pg.94) How are degrees of latitude measured, and to what number do they extend?
28.(Pg.94) On what circles are degrees of longitude measured, and to what number do they extend?
29.(Pg.94) What is a parallel of latitude?
30.(Pg.95) Degrees of longitude vary in length; what is the cause of this?
31.(Pg.95) What is the length of a degree of latitude, and why do not these vary?
32.(Pg.95) What causes the equator to be somewhat larger than a great circle passing through the poles, and what effect has this on degrees of longitude measured on the equator?
33.(Pg.95) What is the cause of this form being given to the earth?
34.(Pg.96) What would have been a consequence of the centrifugal force, had the earth been a perfect sphere?
35.(Pg.96) A body situated at the poles, is attracted more forcibly than if placed at the equator, what is the reason?
36.(Pg.97) What effect would be produced upon the gravity of a body, were it placed beneath the surface of the earth, and what supposing it at its centre?
37.(Pg.97) What two circumstances combine, to lessen the weight of a body on the equator?
38.(Pg.97) Why could not this be proved by weighing a body at the poles, and at the equator?
39.(Pg.98) What is a pendulum?
40.(Pg.98) What causes it to vibrate?
41.(Pg.98) Why are not its vibrations perpetual?
42.(Pg.98) Two pendulums of the same length, will not, in different latitudes, perform their vibrations in equal times, what is the cause of this?
43.(Pg.98) To what use has this property of the pendulum been applied?
44.(Pg.99) What change must be made in pendulums situated at the equator and at the poles, to render their vibrations equal?
45.(Pg.99) What do the vibrations of a pendulum resemble, and why will it vibrate more rapidly if shortened?
46.(Pg.99) In the revolution of the earth round the sun, what is the position of its axis?
47.(Pg.99) How much is the axis of the earth inclined, and with what line does it form this angle?
48.(Pg.99) What is represented byfig. 2, plate 9?
49.(Pg.100) How is the north pole inclined in the middle of our summer, and what effect has this on the north frigid zone?
50.(Pg.100) In what direction does the north pole always point?
51.(Pg.100) What is shown by the position of the earth at B, in the figure?
52.(Pg.100) How does the sun then shine at the poles, and what is the effect on the days and nights?
53.(Pg.101) When the earth has passed the autumnal equinox, what changes take place at the poles, and also in the whole northern and southern hemispheres?
54.(Pg.101) Why is the heat greatest within the torrid zone?
55.(Pg.101) How does the sun appear at the poles, during the period of day there?
56.(Pg.101) In what will the days and nights differ in the temperate zone, from those at the poles, and at the equator?
57.(Pg.102) Trace the earth from the winter solstice to the vernal equinox, and inform me what changes take place.
58.(Pg.102) What takes place at the time of the vernal equinox, and what is meant by the term?
59.(Pg.102) In proceeding from the vernal equinox to the summer solstice, what changes take place?
60.(Pg.103) From what cause arises the superior heat of the equatorial regions?
61.(Pg.103) Why should oblique rays afford less heat than those which are perpendicular?
62.(Pg.103) How is this explained byfig. 1. plate 10?
63.(Pg.103) How do you account for the superior heat of summer, and how is this exemplified infig. 2 and 3, plate 10?
64.(Pg.104) What other cause lessens the intensity of oblique rays?
65.(Pg.104) How is this explained byfig. 4?
66.(Pg.104) What causes conspire to lessen the solar heat in the morning and evening?
67.(Pg.104) The greatest heat of summer is after the solstice, and the greatest heat of the day, after 12 o'clock, although the sun's rays are then most direct, how is this accounted for?
68.(Pg.105) Is there any change of seasons in the other planets?
69.(Pg.105) What is said respecting the axes of Jupiter, of Mars, and of Saturn?
70.(Pg.105) In 365 days, how many times does the earth revolve on its axis?
71.(Pg.105) How is this accounted for?
72.(Pg.105) Do the fixed stars require the same time as the sun, to return to the same meridian?
73.(Pg.106) How is this accounted for?
74.(Pg.106) What is meant by the solar and the sidereal day?
75.(Pg.106) What is the difference in time between them?
76.(Pg.106) What is the length of the tropical year?
77.(Pg.107) The solar year is completed before the earth has made a complete revolution in its orbit, by what is this caused?
78.(Pg.107) What is this called, and what is represented respecting it byfig. 1, plate 11?
79.(Pg.107) By what means can we ascertain the period of a complete revolution of the earth in its orbit, as illustrated by the fixed star E, infig. 1?
80.(Pg.107) What difference is there in the length of the solar and sidereal year?
81.(Pg.107) Why can we not always ascertain the true time by the apparent place of the sun?
82.(Pg.108) What would be the greatest difference between solar, and true time, as indicated by a perfect clock?
OF THE MOON'S MOTION. PHASES OF THE MOON. ECLIPSES OF THE MOON. ECLIPSES OF JUPITER'S MOONS. OF LATITUDE AND LONGITUDE. OF THE TRANSITS OF THE INFERIOR PLANETS. OF THE TIDES.
MRS. B.
We shall, to-day, confine our attention to the moon, which offers many interesting phenomena.
The moon revolves round the earth in the space of about twenty-nine days and a half; in an orbit, the plane of which is inclined upwards of five degrees to that of the earth; she accompanies us in our revolution round the sun.
Emily.Her motion then must be of a complicated nature; for as the earth is not stationary, but advances in her orbit, whilst the moon goes round her, the moon, in passing round the sun, must proceed in a sort of scolloped circle.
Mrs. B.That is true; and there are also other circumstances which interfere with the simplicity, and regularity of the moon's motion, but which are too intricate for you to understand at present.
The moon always presents the same face to us, by which it is evident that she turns but once upon her axis, while she performsa revolution round the earth; so that the inhabitants of the moon have but one day, and one night, in the course of a lunar month.
Caroline.We afford them, however, the advantage of a magnificent moon to enlighten their long nights.
Mrs. B.That advantage is put partial; for since we always see the same hemisphere of the moon, the inhabitants of that hemisphere alone, can perceive us.
Caroline.One half of the moon then enjoys our light, while the other half has constantly nights of darkness. If there are any astronomers in those regions, they would doubtless be tempted to visit the other hemisphere, in order to behold so grand a luminary as we must appear to them. But, pray, do they see the earth under all the changes, which the moon exhibits to us?
Mrs. B.Exactly so. These changes are called the phases of the moon, and require some explanation. Infig. 2, plate 11, let us say, that S represents the sun, E the earth, and A B C D E F G H, the moon, in different parts of her orbit. When the moon is at A, her dark side being turned towards the earth, we shall not see her as ata; but her disappearance is of very short duration, and as she advances in her orbit, we perceive her under the form of a new moon: when she has gone through one eighth of her orbit at B, one quarter of her enlightened hemisphere will be turned towards the earth, and she will then appear horned as atb; when she has performed one quarter of her orbit, she shows us one half of her enlightened side, as atc, and this is called her first quarter; atdshe is said to be gibbous, and atethe whole of the enlightened side appears to us, and the moon is at full. As she proceeds in her orbit, she becomes again gibbous, and her enlightened hemisphere turns gradually away from us, until she arrives at G, which is her third quarter; proceeding thence she completes her orbit and disappears, and then again resumes her form of a new moon, and passes successively, through the same changes.
When the moon is new, she is said to be in conjunction with the sun, as they are then both in the same direction from the earth; at the time of full moon, she is said to be in opposition, because she and the sun, are at opposite sides of the earth; at the time of her first and third quarters, she is said to be in her quadratures,because she is then one-fourth of a circle, or 90°, from her conjunction, or the period of new moon.
Emily.Are not the eclipses of the sun produced by the moon passing between the sun and the earth?
Mrs. B.Yes; when the moon passes between the sun and the earth, she intercepts his rays, or, in other words, casts a shadow on the earth, then the sun is eclipsed, and daylight gives place to darkness, while the moon's shadow is passing over us.
When, on the contrary, the earth is between the sun and the moon, it is we who intercept the sun's rays, and cast a shadow on the moon; she is then said to be eclipsed, and disappears from our view.
Emily.But as the moon goes round the earth every month, she must be, once during that time, between the earth and the sun; and the earth must likewise be once between the sun and the moon, and yet we have not a solar and a lunar eclipse every month?
Mrs. B.I have already informed you, that the orbits of the earth and moon are not in the same plane, but cross or intersect each other; and the moon generally passes either above or below that of the earth, when she is in conjunction with the sun, and does not therefore intercept its rays, and produce an eclipse; for this can take place only when the moon is in, or near her nodes, which is the name given to those two points in which her orbit crosses that of the earth; eclipses cannot happen at any other time, because it is then only, that they are both in a right line with the sun.
Emily.And a partial eclipse of the moon takes place, I suppose, when, in passing by the earth, she is not sufficiently above or below the shadow, to escape it entirely?
Mrs. B.Yes, one edge of her disk then dips into the shadow, and is eclipsed; but as the earth is larger than the moon, when eclipses happen precisely at the nodes, they are not only total, but last for upwards of three hours.
Plate xii.
A total eclipse of the sun rarely occurs, and when it happens, the total darkness is confined to one particular part of the earth, the diameter of the shadow not exceeding 180 miles; evidently showing that the moon is smaller than the sun, since she cannotentirely hide it from the earth. Infig. 1, plate 12, you will find a solar eclipse described; S is the sun, M the moon, and E the earth; and the moon's shadow, you see, is not large enough to cover the earth. The lunar eclipses, on the contrary, are visible from every part of the earth, where the moon is above the horizon; and we discover, by the length of time which the moon is passing through the earth's shadow, that it would be sufficient to eclipse her totally, were she many times her actual size; it follows, therefore, that the earth is much larger than the moon.
Infig. 2, S represents the sun, which pours forth rays of light in straight lines, in every direction. E is the earth, and M the moon. Now a ray of light coming from one extremity of the sun's disk, in the direction A B, will meet another, coming from the opposite extremity, in the direction C B; the shadow of the earth cannot therefore extend beyond B; as the sun is larger than the earth, the shadow of the latter is conical, or in the figure of a sugar loaf; it gradually diminishes, and is much smaller than the earth where the moon passes through it, and yet we find the moon to be, not only totally eclipsed, but to remain for a considerable length of time in darkness, and hence we are enabled to ascertain its real dimensions.
Emily.When the moon eclipses the sun to us, we must be eclipsed to the moon?
Mrs. B.Certainly; for if the moon intercepts the sun's rays, and casts a shadow on us, we must necessarily disappear to the moon, but only partially, as infig. 1.
Caroline.There must be a great number of eclipses in the distant planets, which have so many moons?
Mrs. B.Yes, few days pass without an eclipse taking place; for among the number of satellites, one or the other of them are continually passing either between their primary and the sun; or between the planet, and each other. Astronomers are so well acquainted with the motion of the planets, and their satellites, that they have calculated not only the eclipses of our moon, but those of Jupiter, with such perfect accuracy, that it has afforded a means of ascertaining the longitude.
Caroline.But is it not very easy to find both the latitude and longitude of any place by a map or globe?
Mrs. B.If you know where you are situated, there is no difficulty in ascertaining the latitude or longitude of the place, by referring to a map; but supposing that you had been a lengthof time at sea, interrupted in your course by storms, a map would afford you very little assistance in discovering where you were.
Caroline.Under such circumstances, I confess I should be equally at a loss to discover either latitude, or longitude.
Mrs. B.The latitude is usually found by taking the altitude of the sun at mid-day; that is to say, the number of degrees that it is elevated above the horizon, for the sun appears more elevated as we approach the equator, and less as we recede from it.
Caroline.But unless you can see the sun, how can you take its altitude?
Mrs. B.When it is too cloudy to see the sun, the latitude is sometimes found at night, by the polar star; the north pole of the earth, points constantly towards one particular part of the heavens, in which a star is situated, called the Polar star: this star is visible on clear nights, from every part of the northern hemisphere; the altitude of the polar star, is therefore the same number of degrees, as that of the pole; the latitude may also be determined by observations made on any of the fixed stars: the situation therefore of a vessel at sea, with regard to north and south, is easily ascertained. The difficulty is, respecting east and west, that is to say, its longitude. As we have no eastern poles from which we can reckon our distance, some particular spot, or line, must be fixed upon for that purpose. The English, reckon from the meridian of Greenwich, where the royal observatory is situated; in French maps, you will find that the longitude is reckoned from the meridian of Paris.
The rotation of the earth on its axis in 24 hours from west to east, occasions, you know, an apparent motion of the sun and stars in a contrary direction, and the sun appears to go round the earth in the space of 24 hours, passing over fifteen degrees, or a twenty-fourth part of the earth's circumference every hour; therefore, when it is twelve o'clock in London, it is one o'clock in any place situated fifteen degrees to the east of London, as the sun must have passed the meridian of that place, an hour before he reaches that of London. For the same reason it is eleven o'clock in any place situated fifteen degrees to the west of London, as the sun will not come to that meridian till an hour later.
If then the captain of a vessel at sea, could know precisely what was the hour at London, he could, by looking at his watch,and comparing it with the hour at the spot in which he was, ascertain the longitude.
Emily.But if he had not altered his watch, since he sailed from London, it would indicate the hour it then was in London.
Mrs. B.True; but in order to know the hour of the day at the spot in which he is, the captain of a vessel regulates his watch by the sun when it reaches the meridian.
Emily.Then if he had two watches, he might keep one regulated daily, and leave the other unaltered; the former would indicate the hour of the place in which he was situated, and the latter the hour at London; and by comparing them together, he would be able to calculate his longitude.
Mrs. B.You have discovered, Emily, a mode of finding the longitude, which I have the pleasure to tell you, is universally adopted: watches of a superior construction, called chronometers, or time-keepers, are used for this purpose, and are now made with such accuracy, as not to vary more than four or five seconds in a whole year; but the best watches are liable to imperfections, and should the time-keeper go too fast or too slow, there would be no means of ascertaining the error; implicit reliance, cannot consequently be placed upon them.
Recourse, therefore, is sometimes had to the eclipses of Jupiter's satellites. A table is made, of the precise time at which the several moons are eclipsed to a spectator at London; when they appear eclipsed to a spectator in any other spot, he may, by consulting the table, know what is the hour at London; for the eclipse is visible at the same moment, from whatever place on the earth it is seen. He has then only to look at his watch, which he regulates by the sun, and which therefore points out the hour of the place in which he is, and by observing the difference of time there, and at London, he may immediately determine his longitude.
Let us suppose, that a certain moon of Jupiter is always eclipsed at six o'clock in the evening; and that a man at sea consults his watch, and finds that it is ten o'clock at night, where he is situated, at the moment the eclipse takes place, what will be his longitude?
Emily.That is four hours later than in London: four times fifteen degrees, make 60; he would, therefore, be sixty degrees east of London, for the sun must have passed his meridian before it reaches that of London.
Mrs. B.For this reason the hour is always later than inLondon, when the place is east longitude, and earlier when it is west longitude. Thus the longitude can be ascertained whenever the eclipses of Jupiter's moons are visible.
Caroline.But do not the primary planets, sometimes eclipse the sun from each other, as they pass round in their orbits?
Mrs. B.They must of course sometimes pass between each other and the sun, but as their shadows never reach each other, they hide so little of his light, that the term eclipse is not in this case used; this phenomenon is called a transit. The primary planets do not any of them revolve in the same plane, and the times of their revolution round the sun is considerable, it therefore but rarely happens that they are at the same time, in conjunction with the sun, and in their nodes. It is evident also, that a planet must be inferior (that is within the orbit of another) in order to its apparently passing over the disk of the sun. Mercury, and Venus, have sometimes passed in a right line between us, and the sun, but being at so great a distance from us, their shadows did not extend so far as the earth; no darkness was therefore produced on any part of our globe; but the planet appeared like a small black spot, passing across the sun's disk.
It was by the last transit of Venus, that astronomers were enabled to calculate, with some degree of accuracy, the distance of the earth from the sun, and the dimensions of the latter.
Emily.I have heard that the tides are affected by the moon, but I cannot conceive what influence it can have on them.
Mrs. B.They are produced by the moon's attraction, which draws up the waters of that part of the ocean over which the moon passes, so as to cause it to stand considerably higher than the surrounding parts.
Caroline.Does attraction act on water more powerfully than on land? I should have thought it would have been just the contrary, for land is certainly a more dense body than water?
Mrs B.Tides do not arise from water being more strongly attracted than land, for this certainly is not the case; but the cohesion of fluids, being much less than that of solid bodies, they more easily yield to the power of gravity; in consequence of which, the waters immediately below the moon, are drawn up by it, producing a full tide, or what is commonly called, high water, at the spot where it happens. So far, the theory of the tides is not difficult to understand.
Caroline.On the contrary, nothing can be more simple; the waters, in order to rise up under the moon, must draw the watersfrom the opposite side of the globe, and occasion ebb-tide, or low water, in those parts.
Mrs. B.You draw your conclusion rather too hastily, my dear; for according to your theory, we should have full tide only once in about twenty-four hours, that is, every time that we were below the moon, while we find that in this time we have two tides, and that it is high water with us, and with our antipodes, at the same time.
Caroline.Yet it must be impossible for the moon to attract the sea in opposite parts of the globe, and in opposite directions, at the same time.
Mrs. B.This opposite tide, is rather more difficult to explain, than that which is immediately beneath the moon; with a little attention, however, I hope I shall be able to make you understand the explanation which has been given of it, by astronomers. It must be confessed, however, that the theory upon this subject, is attended with some difficulties. You recollect that the earth and the moon mutually attract each other, but do you suppose that every part of the earth is equally attracted by the moon?
Emily.Certainly not; you have taught us that the force of attraction decreases, with the increase of distance, and therefore that part of the earth which is farthest from the moon, must be attracted less powerfully, than that to which she is nearest.
Mrs. B.This fact will aid us in the explanation which I am about to give to you.
In order to render the question more simple, let us suppose the earth to be every where covered by the ocean, as represented in (fig. 3. pl. 12.) M is the moon, A B C D the earth. Now the waters on the surface of the earth, about A, being more strongly attracted than any other part, will be elevated: the attraction of the moon at B and C being less, and at D least of all. The high tide at A, is accounted for from the direct attraction of the moon; to produce this the waters are drawn from B and C, where it will consequently be low water. At D, the attraction of the moon being considerably decreased, the waters are left relatively high, which height is increased, by the centrifugal force of the earth being greater at D than at A, in consequence of its greater distance from the common centre of gravity X, between the earth and the moon.
Emily.The tide A, then, is produced by the moon's attraction, and the tide D, is produced by the centrifugal force, andincreased by the feebleness of the moon's attraction, in those parts.
Caroline.And when it is high water at A and D, it is low water at B and C: now I think I comprehend the nature of the tides, though I confess it is not quite so easy as I at first thought.
But, Mrs. B., why does not the sun produce tides, as well as the moon; for its attraction is greater than that of the moon?
Mrs. B.It would be at an equal distance, but our vicinity to the moon, makes her influence more powerful. The sun has, however, a considerable effect on the tides, and increases or diminishes them as it acts in conjunction with, or in opposition to the moon.
Emily.I do not quite understand that.
Mrs. B.The moon is a month in going round the earth; twice during that time, therefore, at full and at change, she is in the same direction as the sun; both, then act in conjunction on the earth, and produce very great tides, called spring tides, as represented infig. 4, at A and B; but when the moon is at the intermediate parts of her orbit, that is in her quadratures, the sun, instead of affording assistance, weakens her power, by acting in opposition to it; and smaller tides are produced, called neap tides, as represented at M, infig. 5.
Emily.I have often observed the difference of these tides, when I have been at the sea side.
But since attraction is mutual between the moon and the earth, we must produce tides in the moon; and these must be more considerable in proportion as our planet is larger. And yet the moon does not appear of an oval form.
Mrs. B.You must recollect, that in order to render the explanation of the tides clearer, we suppose the whole surface of the earth to be covered with the ocean; but that is not really the case, either with the earth or the moon, and the land which intersects the water, destroys the regularity of the effect. Thus, in flowing up rivers, in passing round points of land, and into bays and inlets, the water is obstructed, and high water must happen much later, than would otherwise be the case.
Caroline.True; we may, however, be certain that whenever it is high water, the moon is immediately over our heads.
Mrs. B.Not so either; for as a similar effect is produced on that part of the globe immediately beneath the moon, and on that part most distant from it, it cannot be over the heads of the inhabitantsof both those situations, at the same time. Besides, as the orbit of the moon is very nearly parallel to that of the earth, she is never vertical, but to the inhabitants of the torrid zone.
Caroline.In the torrid zone, then, I hope you will grant that the moon is immediately over, or opposite the spots where it is high water?
Mrs. B.I cannot even admit that; for the ocean naturally partaking of the earth's motion, in its rotation from west to east, the moon, in forming a tide, has to contend against the eastern motion of the waves. All matter, you know, by its inertia, makes some resistance to a change of state; the waters, therefore, do not readily yield to the attraction of the moon, and the effect of her influence is not complete, till three hours after she has passed the meridian, where it is full tide.
When a body is impelled by any force, its motion may continue, after the impelling force ceases to act: this is the case with all projectiles. A stone thrown from the hand, continues its motion for a length of time, proportioned to the force given to it: there is a perfect analogy between this effect, and the continued rise of the water, after the moon has passed the meridian at any particular place.
Emily.Pray what is the reason that the tide is three-quarters of an hour later every day?
Mrs. B.Because it is twenty-four hours and three-quarters before the same meridian, on our globe, returns beneath the moon. The earth revolves on its axis in about twenty-four hours; if the moon were stationary, therefore, the same part of our globe would, every twenty-four hours, return beneath the moon; but as during our daily revolution, the moon advances in her orbit, the earth must make more than a complete rotation, in order to bring the same meridian opposite the moon: we are three-quarters of an hour in overtaking her. The tides, therefore, are retarded, for the same reason that the moon rises later by three-quarters of an hour, every day.
We have now, I think, concluded the observations I had to make to you on the subject of astronomy; at our next interview, I shall attempt to explain to you the elements of hydrostatics.