PIERRE SIMON LAPLACE (1749-1827).PIERRE SIMON LAPLACE (1749-1827).
Planets and satellites would then all have similar motions, as noted at the beginning of this section, since in every case this motion is an inheritance from a commonsource, the rotation of the primitive nebula about its own axis. "All the bodies which circle around a planet having been thus formed from rings which its atmosphere successively abandoned as rotation became more and more rapid, this rotation should take place in less time than is required for the orbital revolution of any of the bodies which have been cast off, and this holds true for the sun as compared with the planets."
231.Objections to the nebular hypothesis.—In Laplace's time this slower rate of motion was also supposed to hold true for Saturn's rings as compared with the rotation of Saturn itself, but, as we have seen inChapter XI, this ring is made up of a great number of independent particles which move at different rates of speed, and comparing, through Kepler's Third Law, the motion of the inner edge of the ring with the known periodic time of the satellites, we may find that these particles must rotate about Saturn more rapidly than the planet turns upon its axis. Similarly the inner satellite of Mars completes its revolution in about one third of a Martian day, and we find in cases like this grounds for objection to the nebular theory. Compare also Laplace's argument with the peculiar rotations of Uranus, Neptune, and their satellites (Chapter XI). Do these fortify or weaken his case?
Despite these objections and others equally serious that have been raised, the nebular theory agrees with the facts of Nature at so many points that astronomers upon the whole are strongly inclined to accept its major outlines as being at least an approximation to the course of development actually followed by the solar system; but at some points—e. g., the formation of planets and satellites through the casting off of nebulous rings—the objections are so many and strong as to call for revision and possibly serious modification of the theory.
One proposed modification, much discussed in recent years, consists in substituting for the primitivegaseousnebula imagined by Laplace, a very diffuse cloud of meteoric matter which in the course of its development would become transformed into the gaseous state by rising temperature. From this point of view much of the meteoric dust still scattered throughout the solar system may be only the fragments left over in fashioning the sun and planets. Chamberlin and Moulton, who have recently given much attention to this subject, in dissenting from some of Laplace's views, consider that the primitive nebulous condition must have been one in which the matter of the system was "so brought together as to give low mass, high momentum, and irregular distribution to the outer part, and high mass, low momentum, and sphericity to the central part," and they suggest a possible oblique collision of a small nebula with the outer parts of a large one.
232.Bode's law.—We should not leave the theory of Laplace without noting the light it casts upon one point otherwise obscure—the meaning of Bode's law (§ 134). This law, stated in mathematical form, makes a geometrical series, and similar geometrical series apply to the distances of the satellites of Jupiter and Saturn from these planets. Now, Roche has shown by the application of physical laws to the shrinkage of a gaseous body that its radius at any time may be expressed by means of a certain mathematical formula very similar to Bode's law, save that it involves the amount of time that has elapsed since the beginning of the shrinking process. By comparing this formula with the one corresponding to Bode's law he reaches the conclusion that the peculiar spacing of the planets expressed by that law means that they were formed at successiveequalintervals of time—i. e., that Mars is as much older than the earth as the earth is older than Venus, etc. The failure of Bode's law in the case of Neptune would then imply that the interval of time between the formation of Neptune and Uranus was shorter than that which has prevailed for the other planets. Buttoo much stress should not be placed upon this conclusion. So long as the manner in which the planets came into being continues an open question, conclusions about their time of birth must remain of doubtful validity.
233.Tidal friction between earth and moon.—An important addition to theories of development within the solar system has been worked out by Prof. G. H. Darwin, who, starting with certain very simple assumptions as to the present condition of things in earth and moon, derives from these, by a strict process of mathematical reasoning, far-reaching conclusions of great interest and importance. The key to these conclusions lies in recognition of the fact that through the influence of the tides (§ 42) there is now in progress and has been in progress for a very long time, a gradual transfer of motion (moment of momentum) from the earth to the moon. The earth's motion of rotation is being slowly destroyed by the friction of the tides, as the motion of a bicycle is destroyed by the friction of a brake, and, in consequence of this slowing down, the moon is pushed farther and farther away from the earth, so that it now moves in a larger orbit than it had some millions of years ago.
Fig. 24has been used to illustrate the action of the moon in raising tides upon the earth, but in accordance with the third law of motion (§ 36) this action must be accompanied by an equal and contrary reaction whose nature may readily be seen from the same figure. The moon moves about its orbit from west to east and the earth rotates about its axis in the same direction, as shown by the curved arrow in the figure. The tidal wave,I, therefore points a littlein advanceof the moon's position in its orbit and by its attraction must tend to pull the moon ahead in its orbital motion a little faster than it would move if the whole substance of the earth were placed inside the sphere represented by the broken circle in the figure. It is true that the tidal wave atI''pullsback and tends to neutralize the effect of the wave atI, but on the whole the tidal wave nearer the moon has the stronger influence, and the moon on the whole moves a very little faster, and by virtue of this added impetus draws continually a little farther away from the earth than it would if there were no tides.
234.Consequences of tidal friction upon the earth.—This process of moving the moon away from the earth is a cumulative one, going on century after century, and with reference to it the moon's orbit must be described not as a circle or ellipse, or any other curve which returns into itself, but as a spiral, like the balance spring of a watch, each of whose coils is a little larger than the preceding one, although this excess is, to be sure, very small, because the tides themselves are small and the tidal influence feeble when compared with the whole attraction of the earth for the moon. But, given time enough, even this small force may accomplish great results, and something like 100,000,000 years of past opportunity would have sufficed for the tidal forces to move the moon from close proximity with the earth out to its present position.
For millions of years to come, if moon and earth endure so long, the distance between them must go on increasing, although at an ever slower rate, since the farther away the moon goes the smaller will be the tides and the slower the working out of their results. On the other hand, when the moon was nearer the earth than now, tidal influences must have been greater and their effects more rapidly produced than at the present time, particularly if, as seems probable, at some past epoch the earth was hot and plastic like Jupiter and Saturn. Then, instead of tides in the water of the sea, such as we now have, the whole substance of the earth would respond to the moon's attraction inbodily tidesof semi-fluid matter not only higher, but with greater internal friction of their molecules one upon another,and correspondingly greater effect in checking the earth's rotation.
But, whether the tide be a bodily one or confined to the waters of the sea, so long as the moon causes it to flow there will be a certain amount of friction which will affect the earth much as a brake affects a revolving wheel, slowing down its motion, and producing thus a longer day as well as a longer month on account of the moon's increased distance. Slowing down the earth's rotation is the direct action of the moon upon the earth. Pushing the moon away is the form in which the earth's equal and contrary reaction manifests itself.
235.Consequences of tidal friction upon the moon.—When the moon was plastic the earth must have raised in it a bodily tide manifold greater than the lunar tides upon the earth, and, as we have seen inChapter IX, this tide has long since worn out the greater part of the moon's rotation and brought our satellite to the condition in which it presents always the same face toward the earth.
These two processes, slowing down the rotation and pushing away the disturbing body, are inseparable—one requires the other; and it is worth noting in this connection that when for any reason the tide ceases to flow, and the tidal wave takes up a permanent position, as it has in the moon (§ 99), its work is ended, for when there is no motion of the wave there can be no friction to further reduce the rate of rotation of the one body, and no reaction to that friction to push away the other. But this permanent and stationary tidal wave in the moon, or elsewhere, means that the satellite presents always the same face toward its planet, moving once about its orbit in the time required for one revolution upon its axis, and the tide raised by the moon upon the earth tends to produce here the result long since achieved in our satellite, to make our day and month of equal length, and to make the earth turn always the same side toward the moon. But themoon's tidal force is small compared with that of the earth, and has a vastly greater momentum to overcome, so that its work upon the earth is not yet complete. According to Thomson and Tait, the moon must be pushed off another hundred thousand miles, and the day lengthened out by tidal influence to seven of our present weeks before the day and the lunar month are made of equal length, and the moon thereby permanently hidden from one hemisphere of the earth.
236.The earth-moon system.—Retracing into the past the course of development of the earth and moon, it is possible to reach back by means of the mathematical theory of tidal friction to a time at which these bodies were much nearer to each other than now, but it has not been found possible to trace out the mode of their separation from one body into two, as is supposed in the nebular theory. In the earliest part of their history accessible to mathematical analysis they are distinct bodies at some considerable distance from each other, with the earth rotating about an axis more nearly perpendicular to the moon's orbit and to the ecliptic than is now the case. Starting from such a condition, the lunar tides, according to Darwin, have been instrumental in tipping the earth's rotation axis into its present oblique position, and in determining the eccentricity of the moon's orbit and its position with respect to the ecliptic as well as the present length of day and month.
237.Tidal friction upon the planets.—The satellites of the outer planets are equally subject to influences of this kind, and there appears to be independent evidence that some of them, at least, turn always the same face toward their respective planets, indicating that the work of tidal friction has here been accomplished. We saw inChapter XIthat it is at present an open question whether the inner planets, Venus and Mercury, do not always turn the same face toward the sun, their day and year being of equal length. In addition to the direct observational evidence upon thispoint, Schiaparelli has sought to show by an appeal to tidal theory that such is probably the case, at least for Mercury, since the tidal forces which tend to bring about this result in that planet are about as great as the forces which have certainly produced it in the case of the moon and Saturn's satellite, Japetus. The same line of reasoning would show that every satellite in the solar system, save possibly the newly discovered ninth satellite of Saturn, must, as a consequence of tidal friction, turn always the same face toward its planet.
238.The solar tide.—The sun also raises tides in the earth, and their influence must be similar in character to that of the lunar tides, checking the rotation of the earth and thrusting earth and sun apart, although quantitatively these effects are small compared with those of the moon. They must, however, continue so long as the solar tide lasts, possibly until the day and year are made of equal length—i. e., they may continue long after the lunar tidal influence has ceased to push earth and moon apart. Should this be the case, a curious inverse effect will be produced. The day being then longer than the month, the moon will again raise a tide in the earth which will run around itfrom west to east, opposite to the course of the present tide, thus tending to accelerate the earth's rotation, and by its reaction to bring the moon back toward the earth again, and ultimately to fall upon it.
We may note that an effect of this kind must be in progress now between Mars and its inner satellite, Phobos, whose time of orbital revolution is only one third of a Martian day. It seems probable that this satellite is in the last stages of its existence as an independent body, and must ultimately fall into Mars.
239.Roche's limit.—In looking forward to such a catastrophe, however, due regard must be paid to a dynamical principle of a different character. The moon can never be precipitated upon the earth entire, since before it reachesus it will have been torn asunder by the excess of the earth's attraction for the near side of its satellite over that which it exerts upon the far side. As the result of Roche's mathematical analysis we are able to assign a limiting distance between any planet and its satellite within which the satellite, if it turns always the same face toward the planet, can not come without being broken into fragments. If we represent the radius of the planet byr, and the quotient obtained by dividing the density of the planet by the density of the satellite byq, then
Roche's limit = 2.44r∛q.
Thus in the case of earth and moon we find from the densities given in§ 95,q= 1.65, and withr= 3,963 miles we obtain 11,400 miles as the nearest approach which the moon could make to the earth without being broken up by the difference of the earth's attractions for its opposite sides.
We must observe, however, that Roche's limit takes no account of molecular forces, the adhesion of one molecule to another, by virtue of which a stick or stone resists fracture, but is concerned only with the gravitative forces by which the molecules are attracted toward the moon's center and toward the earth. Within a stone or rock of moderate size these gravitative forces are insignificant, and cohesion is the chief factor in preserving its integrity, but in a large body like the moon, the case is just reversed, cohesion plays a small part and gravitation a large one in holding the body together. We may conclude, therefore, that at a proper distance these forces are capable of breaking up the moon, or any other large body, into fragments of a size such that molecular cohesion instead of gravitation is the chief agent in preserving them from further disintegration.
240.Saturn's rings.—Saturn's rings are of peculiar interest in this connection. The outer edge of the ring system lies just inside of Roche's limit for this planet, and we have already seen that the rings are composed of small fragmentsindependent of each other. Whatever may have been the process by which the nine satellites of Saturn came into existence, we have in Roche's limit the explanation why the material of the ring was not worked up into satellites; the forces exerted by Saturn would tear into pieces any considerable satellite thus formed and equally would prevent the formation of one from raw material.
Saturn's rings present the only case within the solar system where matter is known to be revolving about a planet at a distance less than Roche's limit, and it is an interesting question whether these rings can remain as a permanent part of the planet's system or are only a temporary feature. The drawings of Saturn made two centuries ago agree among themselves in representing the rings as larger than they now appear, and there is some reason to suppose that as a consequence of mutual disturbances—collisions—their momentum is being slowly wasted so that ultimately they must be precipitated into the planet. But the direct evidence of such a progress that can be drawn from present data is too scanty to justify positive conclusions in the matter. On the other hand, Nolan suggests that in the outer parts of the ring small satellites might be formed whose tidal influence upon Saturn would suffice to push them away from the ring beyond Roche's limit, and that the very small inner satellites of Saturn may have been thus formed at the expense of the ring.
The inner satellite of Mars is very close to Roche's limit for that planet, and, as we have seen above, must be approaching still nearer to the danger line.
241.The moon's development.—The fine series of photographs of the moon obtained within the last few years at Paris, have been used by the astronomers of that observatory for a minute study of the lunar formations, much as geologists study the surface of the earth to determine something about the manner in which it was formed. Their conclusions are, in general, that at some past time the moonwas a hot and fluid body which, as it cooled and condensed, formed a solid crust whose further shrinkage compressed the liquid nucleus and led to a long series of fractures in the crust and outbursts of liquid matter, whose latest and feeblest stages produced the lunar craters, while traces of the earlier ones, connected with a general settling of the crust, although nearly obliterated, are still preserved in certain large but vague features of the lunar topography, such as the distribution of the seas, etc. They find also in certain markings of the surface what they consider convincing evidence of the existence in past times of a lunar atmosphere. But this seems doubtful, since the force of gravity at the moon's surface is so small that an atmosphere similar to that of the earth, even though placed upon the moon, could not permanently endure, but would be lost by the gradual escape of its molecules into the surrounding space.
The molecules of a gas are quite independent one of another, and are in a state of ceaseless agitation, each one darting to and fro, colliding with its neighbors or with whatever else opposes its forward motion, and traveling with velocities which, on the average, amount to a good many hundreds of feet per second, although in the case of any individual molecule they may be much less or much greater than the average value, an occasional molecule having possibly a velocity several times as great as the average. In the upper regions of our own atmosphere, if one of these swiftly moving particles of oxygen or nitrogen were headed away from the earth with a velocity of seven miles per second, the whole attractive power of the earth would be insufficient to check its motion, and it would therefore, unless stopped by some collision, escape from the earth and return no more. But, since this velocity of seven miles per second is more than thirty times as great as the average velocity of the molecules of air, it must be very seldom indeed that one is found to move so swiftly, and the loss of the earth's atmosphere by leakage of this sort is insignificant.But upon the moon, or any other body where the force of gravity is small, conditions are quite different, and in our satellite a velocity of little more than one mile per second would suffice to carry a molecule away from the outer limits of its atmosphere. This velocity, only five times the average, would be frequently attained, particularly in former times when the moon's temperature was high, for then the average velocity of all the molecules would be considerably increased, and the amount of leakage might become, and probably would become, a serious matter, steadily depleting the moon's atmosphere and leading finally to its present state of exhaustion. It is possible that the moon may at one time have had an atmosphere, but if so it could have been only a temporary possession, and the same line of reasoning may be applied to the asteroids and to most of the satellites of the solar system, and also, though in less degree, to the smaller planets, Mercury and Mars.
242.Stellar development.—We have already considered in this chapter the line of development followed by one star, the sun, and treating this as a typical case, it is commonly believed that the life history of a star, in so far as it lies within our reach, begins with a condition in which its matter is widely diffused, and presumably at a low temperature. Contracting in bulk under the influence of its own gravitative forces, the star's temperature rises to a maximum, and then falls off in later stages until the body ceases to shine and passes over to the list of dark stars whose existence can only be detected in exceptional cases, such as are noted inChapter XIII. The most systematic development of this idea is due to Lockyer, who looks upon all the celestial bodies—sun, moon and planets, stars, nebulæ, and comets—as being only collections of meteoric matter in different stages of development, and who has sought by means of their spectra to classify these bodies and to determine their stage of advancement. While the fundamental ideas involved in this "meteoritic hypothesis" are not seriouslycontroverted, the detailed application of its principles is open to more question, and for the most part those astronomers who hold that in the present state of knowledge stellar spectra furnish a key to a star's age or degree of advancement do not venture beyond broad general statements.
Fig. 151.—Types of stellar spectra substantially according to Secchi.Fig. 151.—Types of stellar spectra substantially according toSecchi.
243.Stellar spectra.—Thus the types of stellar spectra shown inFig. 151are supposed to illustrate successive stages in the development of an average star. Type I corresponds to the period in which its temperature is near the maximum; Type II belongs to a later stage in which the temperature has commenced to fall; and Type III to the period immediately preceding extinction.
While human life, or even the duration of the human race, is too short to permit a single star to be followed through all the stages of its career, an adequate picture of that development might be obtained by examining many stars, each at a different stage of progress, and, followingthis idea, numerous subdivisions of the types of stellar spectra shown inFig. 151have been proposed in order to represent with more detail the process of stellar growth and decay; but for the most part these subdivisions and their interpretation are accepted by astronomers with much reserve.
It is significant that there are comparatively few stars with spectra of Type III, for this is what we should expect to find if the development of a star through the last stages of its visible career occupied but a small fraction of its total life. From the same point of view the great number of stars with spectra of the first type would point to a long duration of this stage of life. The period in which the sun belongs, represented by Type II, probably has a duration intermediate between the others. Since most of the variable stars, save those of the Algol class, have spectra of the third type, we conclude that variability, with its associated ruddy color and great atmospheric absorption of light, is a sign of old age and approaching extinction. The Algol or eclipse variables, on the other hand, having spectra of the first type, are comparatively young stars, and, as we shall see a little later, the shortness of their light periods in some measure confirms this conclusion drawn from their spectra.
We have noted in§ 196that the sun's near neighbors are prevailingly stars with spectra of the second type, while the Milky Way is mainly composed of first-type stars, and from this we may now conclude that in our particular part of the entire celestial space the stars are, as a rule, somewhat further developed than is the case elsewhere.
244.Double stars.—The double stars present special problems of development growing out of the effects of tidal friction, which must operate in them much as it does between earth and moon, tending steadily to increase the distance between the components of such a star. So, too, in such a system as is shown inFig. 132, gravity must tend to make each component of the double star shrink tosmaller dimensions, and this shrinkage must result in faster rotation and increased tidal friction, which in turn must push the components apart, so that in view of the small density and close proximity of those particular stars we may fairly regard a star like β Lyræ as in the early stages of its career and destined with increasing age to lose its variability of light, since the eclipses which now take place must cease with increasing distance between the components unless the orbit is turned exactly edgewise toward the earth. Close proximity and the resulting shortness of periodic time in a double star seem, therefore, to be evidence of its youth, and since this shortness of periodic time is characteristic of both Algol variables and spectroscopic binaries as a class, we may set them down as being, upon the whole, stars in the early stages of their career. On the other hand, it is generally true that the larger the orbit, and the greater the periodic time in the orbit, the farther is the star advanced in its development.
In his theory of tidal friction, Darwin has pointed out that whenever the periodic time in the orbit is more than twice as long as the time required for rotation about the axis, the effect of the tides is to increase the eccentricity of the orbit, and, following this indication, See has urged that with increasing distance between the components of a double star their orbits about the common center of gravity must grow more and more eccentric, so that we have in the shape of such orbits a new index of stellar development; the more eccentric the orbit, the farther advanced are the stars. It is important to note in this connection that among the double stars whose orbits have been computed there seems to run a general rule—the larger the orbit the greater is its eccentricity—a relation which must hold true if tidal friction operates as above supposed, and which, being found to hold true, confirms in some degree the criteria of stellar age which are furnished by the theory of tidal friction.
245.Nebulæ.—The nebular hypothesis of Laplace has inclined astronomers to look upon nebulæ in general as material destined to be worked up into stars, but which is now in a very crude and undeveloped stage. Their great bulk and small density seem also to indicate that gravitation has not yet produced in them results at all comparable with what we see in sun and stars. But even among nebulæ there are to be found very different stages of development. The irregular nebula, shapeless and void like that of Orion; the spiral, ring, and planetary nebulæ and the star cluster, clearly differ in amount of progress toward their final goal. But it is by no means sure that these several types are different stages in one line of development; for example, the primitive nebula which grows into a spiral may never become a ring or planetary nebula, andvice versa. So too there is no reason to suppose that a star cluster will ever break up into isolated stars such as those whose relation to each other is shown inFig. 122.
246.Classification.—Considering the heavenly bodies with respect to their stage of development, and arranging them in due order, we should probably find lowest down in the scale of progress the irregular nebulæ of chaotic appearance such as that represented inFig. 146. Above these in point of development stand the spiral, ring, and planetary nebulæ, although the exact sequence in which they should be arranged remains a matter of doubt. Still higher up in the scale are star clusters whose individual members, as well as isolated stars, are to be classified by means of their spectra, as shown inFig. 151, where the order of development of each star is probably from Type I, through II, into III and beyond, to extinction of its light and the cutting off of most of its radiant energy. Jupiter and Saturn are to be regarded as stars which have recently entered this dark stage. The earth is further developed than these, but it is not so far along as are Mars and Mercury; while the moon is to be looked upon as the mostadvanced heavenly body accessible to our research, having reached a state of decrepitude which may almost be called death—a stage typical of that toward which all the others are moving.
Meteors and comets are to be regarded as fragments of celestial matter, chips, too small to achieve by themselves much progress along the normal lines of development, but destined sooner or later, by collision with some larger body, to share thenceforth in its fortunes.
247.Stability of the universe.—It was considered a great achievement in the mathematical astronomy of a century ago when Laplace showed that the mutual attractions of sun and planets might indeed produce endless perturbations in the motions and positions of these bodies, but could never bring about collisions among them or greatly alter their existing orbits. But in the proof of this great theorem two influences were neglected, either of which is fatal to its validity. One of these—tidal friction—as we have already seen, tends to wreck the systems of satellites, and the same effect must be produced upon the planets by any other influence which tends to impede their orbital motion. It is the inertia of the planet in its forward movement that balances the sun's attraction, and any diminution of the planet's velocity will give this attraction the upper hand and must ultimately precipitate the planet into the sun. The meteoric matter with which the earth comes ceaselessly into collision must have just this influence, although its effects are very small, and something of the same kind may come from the medium which transmits radiant energy through the interstellar spaces.
It seems incredible that the luminiferous ether, which is supposed to pervade all space, should present absolutely no resistance to the motion of stars and planets rushing through it with velocities which in many cases exceed 50,000 miles per hour. If there is a resistance to this motion,however small, we may extend to the whole visible universe the words of Thomson and Tait, who say in their great Treatise on Natural Philosophy, "We have no data in the present state of science for estimating the relative importance of tidal friction and of the resistance of the resisting medium through which the earth and moon move; but, whatever it may be, there can be but one ultimate result for such a system as that of the sun and planets, if continuing long enough under existing laws and not disturbed by meeting with other moving masses in space. That result is the falling together of all into one mass, which, although rotating for a time, must in the end come to rest relatively to the surrounding medium."
Compare with this the words of a great poet who in The Tempest puts into the mouth of Prospero the lines:
"The cloud-capp'd towers, the gorgeous palaces,The solemn temples, the great globe itself,Yea, all which it inherit, shall dissolve;And, like this insubstantial pageant faded,Leave not a rack behind."
"The cloud-capp'd towers, the gorgeous palaces,The solemn temples, the great globe itself,Yea, all which it inherit, shall dissolve;And, like this insubstantial pageant faded,Leave not a rack behind."
248.The future.—In spite of statements like these, it lies beyond the scope of scientific research to affirm that the visible order of things will ever come to naught, and the outcome of present tendencies, as sketched above, may be profoundly modified in ages to come, by influences of which we are now ignorant. We have already noted that the farther our speculation extends into either past or future, the more insecure are its conclusions, and the remoter consequences of present laws are to be accepted with a corresponding reserve. But the one great fact which stands out clear in this connection is that ofchange. The old concept of a universe created in finished form and destined so to abide until its final dissolution, has passed away from scientific thought and is replaced by the idea of slowdevelopment. A universe which is ever becoming something else and is never finished, as shadowed forth by Goethe in the lines:
"Thus work I at the roaring loom of Time,And weave for Deity a living robe sublime."
"Thus work I at the roaring loom of Time,And weave for Deity a living robe sublime."
FOOTNOTES[A]The circle and straight line are considered to be special cases of these curves, which, taken collectively, are called the conic sections.[B]Aristophanes, The Clouds, Whewell's translation.[C]Schiaparelli, Osservazioni sulle Stelle Doppie.
[A]The circle and straight line are considered to be special cases of these curves, which, taken collectively, are called the conic sections.
[A]The circle and straight line are considered to be special cases of these curves, which, taken collectively, are called the conic sections.
[B]Aristophanes, The Clouds, Whewell's translation.
[B]Aristophanes, The Clouds, Whewell's translation.
[C]Schiaparelli, Osservazioni sulle Stelle Doppie.
[C]Schiaparelli, Osservazioni sulle Stelle Doppie.
The Greek letters are so much used by astronomers in connection with the names of the stars, and for other purposes, that the Greek alphabet is printed below—not necessarily to be learned, but for convenient reference:
Greek.Name.English.ΑαAlphaaΒβBetabΓγGammagΔδDeltadΕε or ϵEpsilonĕΖζZetazΗηEtaēΘϑ or θThetathΙιIotaiΚκKappakΛλLambdalΜμMumΝνNunΞξXixΟοOmicronŏΠπPipΡρRhorΣσ or ςSigmasΤτTautΥυUpsilonuΦφPhiphΧχChichΨψPsipsΩωOmegaō
The following brief bibliography, while making no pretense at completeness, may serve as a useful guide to supplementary reading:
Young.General Astronomy.An admirable general survey of the entire field.
Newcomb.Popular Astronomy.The second edition of a German translation of this work by Engelmann and Vogel is especially valuable.
Ball.Story of the Heavens.Somewhat easier reading than either of the preceding.
Chambers.Descriptive Astronomy.An elaborate but elementary work in three volumes.
Langley.The New Astronomy.Treats mainly of the physical condition of the celestial bodies.
ProctorandRanyard.Old and New Astronomy.
Proctor.The Moon.A general treatment of the subject.
NasmythandCarpenter.The Moon.An admirably illustrated but expensive work dealing mainly with the topography and physical conditions of the moon. There is a cheaper and very good edition in German.
Young.The Sun.International Scientific Series. The most recent and authoritative treatise on this subject.
Proctor.Other Worlds than Ours.An account of planets, comets, etc.
Newton.Meteor.Encyclopædia Britannica.
Airy.Gravitation.A non-mathematical exposition of the laws of planetary motion.
Stokes.On Light as a Means of Investigation.Burnett Lectures. II. The basis of spectrum analysis.
Schellen.Spectrum Analysis.
Thomson(Sir W., LordKelvin),Popular Lectures, etc.Lectures on the Tides, The Sun's Heat, etc.
Ball.Time and Tide.An exposition of the researches of G. H. Darwin upon tidal friction.
Gore.The Visible Universe.Deals with a class of problems inadequately treated in most popular astronomies.
Darwin.The Tides.An admirable elementary exposition.
Clerke.The System of the Stars.Stellar astronomy.
Newcomb.Chapters on the Stars, inPopular Science Monthlyfor 1900.
Clerke.History of Astronomy during the Nineteenth Century.An admirable work.
Wolf.Geschichte der Astronomie.München, 1877. An excellent German work.
See§ 20.
Name.Magnitude.Right Ascension.Declination.h.m.°β Ceti2038.6-18.5η Ceti313.6-10.7α Ceti3257.1+3.7γ Eridani3353.4-13.8Aldebaran1430.2+16.3Rigel059.7-8.3κ Orionis2543.0-9.7β Canis Majoris2618.3-17.9Sirius-1640.7-16.6Procyon0734.1+5.5α Hydræ2922.7-8.2Regulus1103.0+12.5ν Hydræ31044.7-15.7ϵ Corvi3125.0-22.1γ Corvi31210.7-17.0Spica11319.9-10.6ζ Virginis31329.6-0.1α Libræ31445.3-15.6β Libræ31511.6-9.0Antares11623.3-26.2α Ophiuchi21730.3+12.6ϵ Sagittarii21817.5-34.4δ Aquilæ31920.5+2.9Altair11945.9+8.6β Aquarii32126.3-6.0α Aquarii3220.6-0.8Fomalhaut12252.1-30.2
The references are to section numbers.