Fig. 34.—Relation of the lunar nodes to eclipses.Fig. 34.—Relation of the lunar nodes to eclipses.
67.Relation of the lunar nodes to eclipses.—To show why the moon sometimes encounters the earth's shadow centrally and more frequently at full moon passes by without touching it at all, we resort toFig. 34, which represents a part of the orbit of the earth about the sun, with dates showing the time in each year at which the earth passes the part of its orbit thus marked. The orbit of the moon about the earth,M M', is also shown, with the new moon,M, casting its shadow toward the earth and the full moon,M', apparently immersed in the earth's shadow. But here appearances are deceptive, and the student who has madethe observations set forth inChapter IIIhas learned for himself a fact of which careful account must now be taken. The apparent paths of the moon and sun among the stars are great circles which lie near each other, but are not exactly the same; and since these great circles are only the intersections of the sky with the planes of the earth's orbit and the moon's orbit, we see that these planes are slightly inclined to each other and must therefore intersect along some line passing through the center of the earth. This line,N' N'', is shown in the figure, and if we suppose the surface of the paper to represent the plane of the earth's orbit, we shall have to suppose the moon's orbit to be tipped around this line, so that the left side of the orbit lies above and the right side below the surface of the paper. But since the earth's shadow lies in the plane of its orbit—i. e., in the surface of the paper—the full moon of March,M', must have passed below the shadow, and the new moon,M, must have cast its shadow above the earth, so that neither a lunar nor a solar eclipse could occur in that month. But toward the end of May the earth and moon have reached a position where the lineN' N''points almost directly toward the sun, in line with the shadow cones which hide it. Note that the lineN' N''remains very nearly parallel to its original position, while the earth is moving alongits orbit. The full moon will now be very near this line and therefore very close to the plane of the earth's orbit, if not actually in it, and must pass through the shadow of the earth and be eclipsed. So also the new moon will cast its shadow in the plane of the ecliptic, and this shadow, falling upon the earth, produced the total solar eclipse of May 28, 1900.
N' N''is called the line of nodes of the moon's orbit (§ 39), and the two positions of the earth in its orbit, diametrically opposite each other, at whichN' N''points exactly toward the sun, we shall call thenodesof the lunar orbit. Strictly speaking, the nodes are those points of the sky against which the moon's center is projected at the moment when in its orbital motion it cuts through the plane of the earth's orbit. Bearing in mind these definitions, we may condense much of what precedes into the proposition: Eclipses of either sun or moon can occur only when the earth is at or near one of the nodes of the moon's orbit. Corresponding to these positions of the earth there are in each year two seasons, about six months apart, at which times, and at these only, eclipses can occur. Thus in the year 1900 the earth passed these two points on June 2d and November 24th respectively, and the following list of eclipses which occurred in that year shows that all of them were within a few days of one or the other of these dates:
Total solar eclipseMay 28th.Partial lunar eclipseJune 12th.Annular (solar) eclipseNovember 21st.
68.Eclipse limits.—If the earth is exactly at the node at the time of new moon, the moon's shadow will fall centrally upon it and will produce an eclipse visible within the torrid zone, since this is that part of the earth's surface nearest the plane of its orbit. If the earth is near but not at the node, the new moon will stand a little north or southof the plane of the earth's orbit, and its shadow will strike the earth farther north or south than before, producing an eclipse in the temperate or frigid zones; or the shadow may even pass entirely above or below the earth, producing no eclipse whatever, or at most a partial eclipse visible near the north or south pole. Just how many days' motion the earth may be away from the node and still permit an eclipse is shown in the following brief table of eclipse limits, as they are called:
If at any new moon the earth isLess than 10 days awayfromanode,a central eclipse is certain.Between 10 and 16 days"""some kind of eclipse is certain.Between 16 and 19 days"""a partial eclipse is possible.More than 19 days"""no eclipse is possible.
If at any full moon the earth isLess than 4 days awayfromanode,a total eclipse is certain.Between 4 and 10 days"""some kind of eclipse is certain.Between 10 and 14 days"""a partial eclipse is possible.More than 14 days"""no eclipse is possible.
From this table of eclipse limits we may draw some interesting conclusions about the frequency with which eclipses occur.
69.Number of eclipses in a year.—Whenever the earth passes a node of the moon's orbit a new moon must occur at some time during the 2 × 16 days that the earth remains inside the limits where some kind of eclipse is certain, and there must therefore be an eclipse of the sun every time the earth passes a node of the moon's orbit. But, since there are two nodes past which the earth moves at least once in each year, there must be at least two solar eclipses every year. Can there be more than two? On the average, will central or partial eclipses be the more numerous?
A similar line of reasoning will not hold true for eclipses of the moon, since it is quite possible that no fullmoon should occur during the 20 days required by the earth to move past the node from the western to the eastern limit. This omission of a full moon while the earth is within the eclipse limits sometimes happens at both nodes in the same year, and then we have a year with no eclipse of the moon. The student may note in the list of eclipses for 1900 that the partial lunar eclipse of June 12th occurred 10 days after the earth passed the node, and was therefore within the doubtful zone where eclipses may occur and may fail, and corresponding to this position the eclipse was a very small one, only a thousandth part of the moon's diameter dipping into the shadow of the earth. By so much the year 1900 escaped being an illustration of a year in which no lunar eclipse occurred.
A partial eclipse of the moon will usually occur about a fortnight before or after a total eclipse of the sun, since the full moon will then be within the eclipse limit at the opposite node. A partial eclipse of the sun will always occur about a fortnight before or after a total eclipse of the moon.
Fig. 35.—The eclipse of May 28, 1900.Fig. 35.—The eclipse of May 28, 1900.
70.Eclipse maps.—It is the custom of astronomers to prepare, in advance of the more important eclipses, maps showing the trace of the moon's shadow across the earth, and indicating the times of beginning and ending of the eclipses, as is shown inFig. 35. While the actual construction of such a map requires much technical knowledge, the principles involved are simple enough: the straight line passed through the center of sun and moon is the axis of the shadow cone, and the map contains little more than a graphical representation of when and where this cone meets the surface of the earth. Thus in the map, the "Path of Total Eclipse" is the trace of the shadow cone across the face of the earth, and the width of this path shows that the earth encountered the shadow considerably inside the vertex of the cone. The general direction of the path is from west to east, and the slight sinuousities which it presents are for the most part due to unavoidable distortion of the map caused by the attempt to represent the curved surface of the earth upon the flat surface of the paper. On either side of the Path of Total Eclipse is the region within which the eclipse was only partial, and the broken lines marked Begins at 3h., Ends at 3h., show the intersection of the penumbral cone with the surface of the earth at 3P. M., Greenwich time. These two lines inclose every part of the earth's surface from which at that time any eclipse whatever could be seen, and at this moment the partial eclipse was just beginning at every point on the eastern edge of the penumbra and just ending at every point on the western edge, while at the center of the penumbra, on the Path of Total Eclipse, lay the shadow of the moon, an oval patch whose greatest diameter was but little more than 60 miles in length, and within which lay every part of the earth where the eclipse was total at that moment.
The position of the penumbra at other hours is also shown on the map, although with more distortion, because it then meets the surface of the earth more obliquely, and from these lines it is easy to obtain the time of beginning and end of the eclipse at any desired place, and to estimate by the distance of the place from the Path of Total Eclipse how much of the sun's face was obscured.
Let the student make these "predictions" for Washington, Chicago, London, and Algiers.
The points in the map marked First Contact, Last Contact, show the places at which the penumbral cone first touched the earth and finally left it. According to computations made as a basis for the construction of the map the Greenwich time of First Contact was 0h. 12.5m. and of Last Contact 5h. 35.6m., and the difference between these two times gives the total duration of the eclipse upon the earth—i. e., 5 hours 23.1 minutes.
Fig. 36.—Central eclipses for the first two decades of the twentieth century. Oppolzer.Fig. 36.—Central eclipses for the first two decades of the twentieth century.Oppolzer.
71.Future eclipses.—An eclipse map of a different kind is shown inFig. 36, which represents the shadow paths ofall the central eclipses of the sun, visible during the period 1900-1918A. D., in those parts of the earth north of the south temperate zone. Each continuous black line shows the path of the shadow in a total eclipse, from its beginning, at sunrise, at the western end of the line to its end, sunset, at the eastern end, the little circle near the middle of the line showing the place at which the eclipse was total at noon. The broken lines represent similar data for the annular eclipses. This map is one of a series prepared by the Austrian astronomer, Oppolzer, showing the path of every such eclipse from the year 1200B. C.to 2160A. D., a period of more than three thousand years.
If we examine the dates of the eclipses shown in this map we shall find that they are not limited to the particular seasons, May and November, in which those of the year 1900 occurred, but are scattered through all the months of the year, from January to December. This shows at once that the line of nodes,N' N'', ofFig. 34, does not remain in a fixed position, but turns round in the plane of the earth's orbit so that in different years the earth reaches the node in different months. The precession has already furnished us an illustration of a similar change, the slow rotation of the earth's axis, producing a corresponding shifting of the line in which the planes of the equator and ecliptic intersect; and in much the same way, through the disturbing influence of the sun's attraction, the lineN' N''is made to revolve westward, opposite to the arrowheads inFig. 34, at the rate of nearly 20° per year, so that the earth comes to each node about 19 days earlier in each year than in the year preceding, and the eclipse season in each year comes on the average about 19 days earlier than in the year before, although there is a good deal of irregularity in the amount of change in particular years.
72.Recurrence of eclipses.—Before the beginning of the Christian era astronomers had found out a rough-and-ready method of predicting eclipses, which is still of interest and value. The substance of the method is that if we start with any eclipse whatever—e. g., the eclipse of May 28, 1900—and reckon forward or backward from that date a period of 18 years and 10 or 11 days, we shall find another eclipse quite similar in its general characteristics to the one with which we started. Thus, from the map of eclipses (Fig. 36), we find that a total solar eclipse will occur on June 8, 1918, 18 years and 11 days after the one illustrated inFig. 35. This period of 18 years and 11 days is calledsaros, an ancient word which means cycle or repetition, and sinceevery eclipse is repeated after the lapse of a saros, we may find the dates of all the eclipses of 1918 by adding 11 days to the dates given in the table of eclipses for 1900 (§ 67), and it is to be especially noted that each eclipse of 1918 will be like its predecessor of 1900 in character—lunar, solar, partial, total, etc. The eclipses of any year may be predicted by a similar reference to those which occurred eighteen years earlier. Consult a file of old almanacs.
The exact length of a saros is 223 lunar months, each of which is a little more than 29.5 days long, and if we multiply the exact value of this last number (see§ 60) by 223, we shall find for the product 6,585.32 days, which is equal to 18 years 11.32 days when there are four leap years included in the 18, or 18 years 10.32 days when the number of leap years is five; and in applying the saros to the prediction of eclipses, due heed must be paid to the number of intervening leap years. To explain why eclipses are repeated at the end of the saros, we note that the occurrence of an eclipse depends solely upon the relative positions of the earth, moon, and node of the moon's orbit, and the eclipse will be repeated as often as these three come back to the position which first produced it. This happens at the end of every saros, since the saros is, approximately, the least common multiple of the length of the year, the length of the lunar month, and the length of time required by the line of nodes to make a complete revolution around the ecliptic. If the saros were exactly a multiple of these three periods, every eclipse would be repeated over and over again for thousands of years; but such is not the case, the saros is not an exact multiple of a year, nor is it an exact multiple of the time required for a revolution of the line of nodes, and in consequence the restitution which comes at the end of the saros is not a perfect one. The earth at the 223d new moon is in fact about half a day's motion farther west, relative to the node,than it was at the beginning, and the resulting eclipse, while very similar, is not precisely the same as before. After another 18 years, at the second repetition, the earth is a day farther from the node than at first, and the eclipse differs still more in character, etc. This is shown inFig. 37, which represents the apparent positions of the disks of the sun and moon as seen from the center of the earth at the end of each sixth saros, 108 years, where the upper row of figures represents the number of repetitions of the eclipse from the beginning, marked0, to the end,72. The solar eclipse limits, 10, 16, 19 days, are also shown, and all those eclipses which fall between the 10-day limits will be central as seen from some part of the earth, those between 16 and 19 partial wherever seen, while between 10 and 16 they may be either total or partial. Compare the figure with the following description given by Professor Newcomb: "A series of such eclipses commences with a very small eclipse near one pole of the earth. Gradually increasing for about eleven recurrences, it will become central near the same pole. Forty or more central eclipses will then recur, the central line moving slowly toward the other pole. The series will then become partial, and finally cease. The entire duration of the series will be more than a thousand years. A new series commences, on the average, at intervals of thirty years."
Fig. 37.—Graphical illustration of the saros.Fig. 37.—Graphical illustration of the saros.
A similar figure may be constructed to represent the recurrence of lunar eclipses; but here, in consequence of the smallereclipse limits, we shall find that a series is of shorter duration, a little over eight centuries as compared with twelve centuries, which is the average duration of a series of solar eclipses.
One further matter connected with the saros deserves attention. During the period of 6,585.32 days the earth has 6,585 times turned toward the sun the same face upon which the moon's shadow fell at the beginning of the saros, but at the end of the saros the odd 0.32 of a day gives the earth time to make about a third of a revolution more before the eclipse is repeated, and in consequence the eclipse is seen in a different region of the earth, on the average about 116° farther west in longitude. Compare inFig. 36the regions in which the eclipses of 1900 and 1918 are visible.
Is this change in the region where the repeated eclipse is visible, true of lunar eclipses as well as solar?
73.Use of eclipses.—At all times and among all peoples eclipses, and particularly total eclipses of the sun, have been reckoned among the most impressive phenomena of Nature. In early times and among uncultivated people they were usually regarded with apprehension, often amounting to a terror and frenzy, which civilized travelers have not scrupled to use for their own purposes with the aid of the eclipse predictions contained in their almanacs, threatening at the proper time to destroy the sun or moon, and pointing to the advancing eclipse as proof that their threats were not vain. In our own day and our own land these feelings of awe have not quite disappeared, but for the most part eclipses are now awaited with an interest and pleasure which, contrasted with the former feelings of mankind, furnish one of the most striking illustrations of the effect of scientific knowledge in transforming human fear and misery into a sense of security and enjoyment.
But to the astronomer an eclipse is more than a beautiful illustration of the working of natural laws; it is invarying degree an opportunity of adding to his store of knowledge respecting the heavenly bodies. The region immediately surrounding the sun is at most times closed to research by the blinding glare of the sun's own light, so that a planet as large as the moon might exist here unseen were it not for the occasional opportunity presented by a total eclipse which shuts off the excessive light and permits not only a search for unknown planets but for anything and everything which may exist around the sun. More than one astronomer has reported the discovery of such planets, and at least one of these has found a name and a description in some of the books, but at the present time most astronomers are very skeptical about the existence of any such object of considerable size, although there is some reason to believe that an enormous number of little bodies, ranging in size from grains of sand upward, do move in this region, as yet unseen and offering to the future problems for investigation.
But in other directions the study of this region at the times of total eclipse has yielded far larger returns, and in the chapter on the sun we shall have to consider the marvelous appearances presented by the solar prominences and by the corona, an appendage of the sun which reaches out from his surface for millions of miles but is never seen save at an eclipse. Photographs of the corona are taken by astronomers at every opportunity, and reproductions of some of these may be found inChapter X.
Annular eclipses and lunar eclipses are of comparatively little consequence, but any recorded eclipse may become of value in connection with chronology. We date our letters in a particular year of the twentieth century, and commonly suppose that the years are reckoned from the birth of Christ; but this is an error, for the eclipses which were observed of old and by the chroniclers have been associated with events of his life, when examined by the astronomers are found quite inconsistent with astronomic theory.They are, however, reconciled with it if we assume that our system of dates has its origin four years after the birth of Christ, or, in other words, that Christ was born in the year 4B. C.A mistake was doubtless made at the time the Christian era was introduced into chronology. At many other points the chance record of an eclipse in the early annals of civilization furnishes a similar means of controlling and correcting the dates assigned by the historian to events long past.
74.Two familiar instruments.—In previous chapters we have seen that a clock and a divided circle (protractor) are needed for the observations which an astronomer makes, and it is worth while to note here that the geography of the sky and the science of celestial motions depend fundamentally upon these two instruments. The protractor is a simple instrument, a humble member of the family of divided circles, but untold labor and ingenuity have been expended on this family to make possible the construction of a circle so accurately divided that with it angles may be measured to the tenth of a second instead of to the tenth of a degree—i. e., 3,600 times as accurate as the protractor furnishes.
The building of a good clock is equally important and has cost a like amount of labor and pains, so that it is a far cry from Galileo and his discovery that a pendulum "keeps time" to the modern clock with its accurate construction and elaborate provision against disturbing influences of every kind. Every such timepiece, whether it be of the nutmeg variety which sells for a dollar, or whether it be the standard clock of a great national observatory, is made up of the same essential parts that fall naturally into four classes, which we may compare with the departments of a well-ordered factory: I. A timekeeping department, the pendulum or balance spring, whose oscillations must all be of equal duration. II. A power department, the weights ormainspring, which, when wound, store up the power applied from outside and give it out piecemeal as required to keep the first department running. III. A publication department, the dial and hands, which give out the time furnished by Department I. IV. A transportation department, the wheels, which connect the other three and serve as a means of transmitting power and time from one to the other. The case of either clock or watch is merely the roof which shelters it and forms no department of its industry. Of these departments the first is by far the most important, and its good or bad performance makes or mars the credit of the clock. Beware of meddling with the balance wheel of your watch.
75.Radiant energy.—But we have now to consider other instruments which in practice supplement or displace the simple apparatus hitherto employed. Among the most important of these modern instruments are the telescope, the spectroscope, and the photographic camera; and since all these instruments deal with the light which comes from the stars to the earth, we must for their proper understanding take account of the nature of that light, or, more strictly speaking, we must take account of the radiant energy emitted by the sun and stars, which energy, coming from the sun, is translated by our nerves into the two different sensations of light and heat. The radiant energy which comes from the stars is not fundamentally different from that of the sun, but the amount of energy furnished by any star is so small that it is unable to produce through our nerves any sensible perception of heat, and for the same reason the vast majority of stars are invisible to the unaided eye; they do not furnish a sufficient amount of energy to affect the optic nerves. A hot brick taken into the hand reveals its presence by the two different sensations of heat and pressure (weight); but as there is only one brick to produce the two sensations, so there is only one energy to produce through its action upon different nerves the two sensationsof light and heat, and this energy is calledradiantbecause it appears to stream forth radially from everything which has the capacity of emitting it. For the detailed study of radiant energy the student is referred to that branch of science called physics; but some of its elementary principles may be learned through the following simple experiment, which the student should not fail to perform for himself:
Drop a bullet or other similar object into a bucket of water and observe the circular waves which spread from the place where it enters the water. These waves are a form of radiant energy, but differing from light or heat in that they are visibly confined to a single plane, the surface of the water, instead of filling the entire surrounding space. By varying the size of the bucket, the depth of the water, the weight of the bullet, etc., different kinds of waves, big and little, may be produced; but every such set of waves may be described and defined in all its principal characteristics by means of three numbers—viz., the vertical height of the waves from hollow to crest; the distance of one wave from the next; and the velocity with which the waves travel across the water. The last of these quantities is called the velocity of propagation; the second is called the wave length; one half of the first is called the amplitude; and all these terms find important applications in the theory of light and heat.
The energy of the falling bullet, the disturbance which it produced on entering the water, was carried by the waves from the center to the edge of the bucket but not beyond, for the wave can go only so far as the water extends. The transfer of energy in this way requires a perfectly continuous medium through which the waves may travel, and the whole visible universe is supposed to be filled with something calledether, which serves everywhere as a medium for the transmission of radiant energyjust as the water in the experiment served as a medium for transmitting in waves the energy furnished to it by the falling bullet. The student may think of this energy as being transmitted in spherical waves through the ether, every glowing body, such as a star, a candle flame, an arc lamp, a hot coal, etc., being the origin and center of such systems of waves, and determining by its own physical and chemical properties the wave length and amplitude of the wave systems given off.
The intensity of any light depends upon the amplitude of the corresponding vibration, and its color depends upon the wave length. By ingenious devices which need not be here described it has been found possible to measure the wave length corresponding to different colors—e. g., all of the colors of the rainbow, and some of these wave lengths expressed in tenth meters are as follows: A tenth meter is the length obtained by dividing a meter into 1010equal parts. 1010= 10,000,000,000.
Color.Wave length.Extremelimitof visible violet3,900Middleof theviolet4,060""blue4,730""green5,270""yellow5,810""orange5,970""red7,000Extremelimitof visible red7,600
PLATE I. THE NORTHERN CONSTELLATIONSPLATE I. THE NORTHERN CONSTELLATIONS
The phrase "extreme limit of visible violet" or red used above must be understood to mean that in general the eye is not able to detect radiant energy having a wave length less than 3,900 or greater than 7,600 tenth meters. Radiant energy, however, exists in waves of both greater and shorter length than the above, and may be readily detected by apparatus not subject to the limitations of the human eye—e. g., a common thermometer will show a rise of temperature when its bulb is exposed to radiant energy of wave length much greater than 7,600 tenth meters, anda photographic plate will be strongly affected by energy of shorter wave length than 3,900 tenth meters.
76.Reflection and condensation of waves.—When the waves produced by dropping a bullet into a bucket of water meet the sides of the bucket, they appear to rebound and are reflected back toward the center, and if the bullet is dropped very near the center of the bucket the reflected waves will meet simultaneously at this point and produce there by their combined action a wave higher than that which was reflected at the walls of the bucket. There has been a condensation of energy produced by the reflection, and this increased energy is shown by the greater amplitude of the wave. The student should not fail to notice that each portion of the wave has traveled out and back over the radius of the bucket, and that they meet simultaneously at the center because of this equality of the paths over which they travel, and the resulting equality of time required to go out and back. If the bullet were dropped at one side of the center, would the reflected waves produceat any pointa condensation of energy?
If the bucket were of elliptical instead of circular cross section and the bullet were dropped at one focus of the ellipse there would be produced a condensation of reflected energy at the other focus, since the sum of the paths traversed by each portion of the wave before and after reflection is equal to the sum of the paths traversed by every other portion, and all parts of the wave reach the second focus at the same time. Upon what geometrical principle does this depend?
The condensation of wave energy in the circular and elliptical buckets are special cases under the general principle that such a condensation will be produced at any point which is so placed that different parts of the wave front reach it simultaneously, whether by reflection or by some other means, as shown below.
The student will note that for the sake of greater precisionwe here saywave frontinstead of wave. If in any wave we imagine a line drawn along the crest, so as to touch every drop which at that moment is exactly at the crest, we shall have what is called a wave front, and similarly a line drawn through the trough between two waves, or through any set of drops similarly placed on a wave, constitutes a wave front.
77.Mirrors and lenses.—That form of radiant energy which we recognize as light and heat may be reflected and condensed precisely as are the waves of water in the exercise considered above, but owing to the extreme shortness of the wave length in this case the reflecting surface should be very smooth and highly polished. A piece of glass hollowed out in the center by grinding, and with a light film of silver chemically deposited upon the hollow surface and carefully polished, is often used by astronomers for this purpose, and is called a concave mirror.
The radiant energy coming from a star or other distant object and falling upon the silvered face of such a mirror is reflected and condensed at a point a little in front of the mirror, and there forms an image of the star, which may be seen with the unaided eye, if it is held in the right place, or may be examined through a magnifying glass. Similarly, an image of the sun, a planet, or a distant terrestrial object is formed by the mirror, which condenses at its appropriate place the radiant energy proceeding from each and every point in the surface of the object, and this, in common phrase, produces an image of the object.
Another device more frequently used by astronomers for the production of images (condensation of energy) is a lens which in its simplest form is a round piece of glass, thick in the center and thin at the edge, with a cross section, such as is shown atA BinFig. 38. If we supposeE G Dto represent a small part of a wave front coming from a very distant source of radiant energy, such as a star, this wave front will be practically a plane surface representedby the straight lineE D, but in passing through the lens this surface will become warped, since light travels slower in glass than in air, and the central part of the beam,G, in its onward motion will be retarded by the thick center of the lens, more thanEorDwill be retarded by the comparatively thin outer edges ofA B. On the right of the lens the wave front therefore will be transformed into a curved surface whose exact character depends upon the shape of the lens and the kind of glass of which it is made. By properly choosing these the new wave front may be made a part of a sphere having its center at the pointFand the whole energy of the wave front,E G D, will then be condensed atF, because this point is equally distant from all parts of the warped wave front, and therefore is in a position to receive them simultaneously. The distance ofFfromA Bis called the focal length of the lens, andFitself is called the focus. The significance of this last word (Latin,focus= fireplace) will become painfully apparent to the student if he will hold a common reading glass between his hand and the sun in such a way that the focus falls upon his hand.
Fig. 38.—Illustrating the theory of lenses.Fig. 38.—Illustrating the theory of lenses.
All the energy transmitted by the lens in the directionG Fis concentrated upon a very small area atF, and an image of the object—e. g., a star, from which the light came—is formed here. Other stars situated near the one in question will also send beams of light along slightly different directions to the lens, and these will be concentrated, each in its appropriate place, in thefocal plane,F H, passed through the focus,F, perpendicular to the line,F G, andwe shall find in this plane a picture of all the stars or other objects within the range of the lens.
Fig. 39.—Essential parts of a reflecting telescope.Fig. 39.—Essential parts of a reflecting telescope.
78.Telescopes.—The simplest kind of telescope consists of a concave mirror to produce images, and a magnifying glass, called aneyepiece, through which to examine them; but for convenience' sake, so that the observer may not stand in his own light, a small mirror is frequently added to this combination, as atHinFig. 39, where the lines represent the directions along which the energy is propagated. By reflection from this mirror the focal plane and the images are shifted toF, where they may be examined from one side through the magnifying glassE.
Such a combination of parts is called areflectingtelescope, while one in which the images are produced by a lens or combination of lenses is called arefractingtelescope, the adjective having reference to the bending, refraction, produced by the glass upon the direction in which the energy is propagated. The customary arrangement of parts in such a telescope is shown inFig. 40, where the part markedOis called the objective andV E(the magnifying glass) is the eyepiece, or ocular, as it is sometimes called.
Fig. 40.—A simple form of refracting telescope.Fig. 40.—A simple form of refracting telescope.
Most objects with which we have to deal in using a telescope send to it not light of one color only, but a mixtureof light of many colors, many different wave lengths, some of which are refracted more than others by the glass of which the lens is composed, and in consequence of these different amounts of refraction a single lens does not furnish a single image of a star, but gives a confused jumble of red and yellow and blue images much inferior in sharpness of outline (definition) to the images made by a good concave mirror. To remedy this defect it is customary to make the objective of two or more pieces of glass of different densities and ground to different shapes as is shown atOinFig. 40. The two pieces of glass thus mounted in one frame constitute a compound lens having its own focal plane, shown atFin the figure, and similarly the lenses composing the eyepiece have a focal plane between the eyepiece and the objective which must also fall atF, and in the use of a telescope the eyepiece must be pushed out or in until its focal plane coincides with that of the objective. This process, which is called focusing, is what is accomplished in the ordinary opera glass by turning a screw placed between the two tubes, and it must be carefully done with every telescope in order to obtain distinct vision.
79.Magnifying power.—The amount by which a given telescope magnifies depends upon the focal length of the objective (or mirror) and the focal length of the eyepiece, and is equal to the ratio of these two quantities. Thus inFig. 40the distance of the objective from the focal planeFis about 16 times as great as the distance of the eyepiece from the same plane, and the magnifying power of this telescope is therefore 16 diameters. A magnifying power of 16 diameters means that the diameter of any object seen in the telescope looks 16 times as large as it appears without the telescope, and is nearly equivalent to saying that the object appears only one sixteenth as far off. Sometimes the magnifying power is assumed to be the number of times that theareaof an object seems increased; and since areas are proportional to the squares of lines, themagnifying power of 16 diameters might be called a power of 256. Every large telescope is provided with several eyepieces of different focal lengths, ranging from a quarter of an inch to two and a half inches, which are used to furnish different magnifying powers as may be required for the different kinds of work undertaken with the instrument. Higher powers can be used with large telescopes than with small ones, but it is seldom advantageous to use with any telescope an eyepiece giving a higher power than 60 diameters for each inch of diameter of the objective.
The part played by the eyepiece in determining magnifying power will be readily understood from the following experiment:
Make a pin hole in a piece of cardboard. Bring a printed page so close to one eye that you can no longer see the letters distinctly, and then place the pin hole between the eye and the page. The letters which were before blurred may now be seen plainly through the pin hole, even when the page is brought nearer to the eye than before. As it is brought nearer, notice how the letters seem to become larger, solely because they are nearer. A pin hole is the simplest kind of a magnifier, and the eyepiece in a telescope plays the same part as does the pin hole in the experiment; it enables the eye to be brought nearer to the image, and the shorter the focal length of the eyepiece the nearer is the eye brought to the image and the higher is the magnifying power.