viz. every solution of the problem. Observe that transposition of the diagrams furnishes a proof of the simplest of the laws of symmetry in the theory of symmetric functions.
For the next example we have a similar problem, but no restriction is placed upon the magnitude of the numbers which may appear in the compartments. The function is now hλ1hλ2... hλm, hλmbeing the homogeneous product sum of the quantities a, of order λ. The operator is as before
Dp1Dp2... Dpn,
and the solutions are enumerated by
Dp1Dp2... Dpnhλ1hλ2... hλm.
Putting as before λ1= 2, λ2= 2, λ3= 1, p1= 2, p2= 2, p3= 1, p4= 1, the reader will have no difficulty in constructing the diagrams of the eighteen solutions.
The next and last example of a multitude that might be given shows the extraordinary power of the method by solving the famous problem of the “Latin Square,” which for hundreds of years had proved beyond the powers of mathematicians. The problem consists in placing n letters a, b, c, ... n in the compartments of a square lattice of n² compartments, no compartment being empty, so that no letter occurs twice either in the same row or in the same column. The function is here
(Σ α12n-1α22n-2... α2n-1αn)n,
and the operator Dn2n-1, the enumeration being given by
Dn2n-1(Σ α12n-1α22n-2... α2n-1αn)n.
SeeTrans. Camb. Phil. Soc.vol. xvi. pt. iv. pp. 262-290.
Authorities.—P. A. MacMahon, “Combinatory Analysis: A Review of the Present State of Knowledge,”Proc. Lond. Math. Soc.vol. xxviii. (London, 1897). Here will be found a bibliography of the Theory of Partitions. Whitworth,Choice and Chance; Édouard Lucas,Théorie des nombres(Paris, 1891); Arthur Cayley,Collected Mathematical Papers(Cambridge, 1898), ii. 419; iii. 36, 37; iv. 166-170; v. 62-65, 617; vii. 575; ix. 480-483; x. 16, 38, 611; xi. 61, 62, 357-364, 589-591; xii. 217-219, 273-274; xiii. 47, 93-113, 269; Sylvester,Amer. Jour, of Math.v. 119 251; MacMahon,Proc. Lond. Math. Soc.xix. 228 et seq.;Phil. Trans.clxxxiv. 835-901; clxxxv. 111-160; clxxxvii. 619-673; cxcii. 351-401;Trans. Camb. Phil. Soc.xvi. 262-290.
Authorities.—P. A. MacMahon, “Combinatory Analysis: A Review of the Present State of Knowledge,”Proc. Lond. Math. Soc.vol. xxviii. (London, 1897). Here will be found a bibliography of the Theory of Partitions. Whitworth,Choice and Chance; Édouard Lucas,Théorie des nombres(Paris, 1891); Arthur Cayley,Collected Mathematical Papers(Cambridge, 1898), ii. 419; iii. 36, 37; iv. 166-170; v. 62-65, 617; vii. 575; ix. 480-483; x. 16, 38, 611; xi. 61, 62, 357-364, 589-591; xii. 217-219, 273-274; xiii. 47, 93-113, 269; Sylvester,Amer. Jour, of Math.v. 119 251; MacMahon,Proc. Lond. Math. Soc.xix. 228 et seq.;Phil. Trans.clxxxiv. 835-901; clxxxv. 111-160; clxxxvii. 619-673; cxcii. 351-401;Trans. Camb. Phil. Soc.xvi. 262-290.
(P. A. M.)
COMBUSTION(from the Lat.comburere, to burn up), in chemistry, the process of burning or, more scientifically, the oxidation of a substance, generally with the production of flame and the evolution of heat. The term is more customarily given to productions of flame such as we have in the burning of oils, gas, fuel, &c., but it is conveniently extended to other cases of oxidation, such as are met with when metals are heated for a long time in air or oxygen. The term “spontaneous combustion” is used when a substance smoulders or inflames apparently without the intervention of any external heat or light; in such cases, as, for example, in heaps of cotton-waste soaked in oil, the oxidation has proceeded slowly, but steadily, for some time, until the heat evolved has raised the mass to the temperature of ignition.
The explanation of the phenomena of combustion was attempted at very early times, and the early theories were generally bound up in the explanation of the nature of fire or flame. The idea that some extraneous substance is essential to the process is of ancient date; Clement of Alexandria (c. 3rd centuryA.D.) held that some “air” was necessary, and the same view was accepted during the middle ages, when it had been also found that the products of combustion weighed more than the original combustible, a fact which pointed to the conclusion that some substance had combined with the combustible during the process. This theory was supported by the French physician Jean Ray, who showed also that in the cases of tin and lead there was a limit to the increase in weight. Robert Boyle, who made many researches on the origin and nature of fire, regarded the increase as due to the fixation of the particles of fire. Ideas identical with the modern ones were expressed by John Mayow in hisTractatus quinque medico-physici(1674), but his death in 1679 undoubtedly accounts for the neglect of his suggestions by his contemporaries. Mayow perceived the similarity of the processes of respiration and combustion, and showed that one constituent of the atmosphere, which he termedspiritus nitro-aereus, was essential to combustion and life, and that the second constituent, which he termedspiritus nitri acidi, inhibited combustion and life. At the beginning of the 18th century a new theory of combustion was promulgated by Georg Ernst Stahl. This theory regarded combustibility as due to a principle named phlogiston (from the Gr.φλογιστός, burnt), which was present in all combustible bodies in an amount proportional to their degree of combustibility; for instance, coal was regarded as practicallypure phlogiston. On this theory, all substances which could be burnt were composed of phlogiston and some other substance, and the operation of burning was simply equivalent to the liberation of the phlogiston. The Stahlian theory, originally a theory of combustion, came to be a general theory of chemical reactions, since it provided simple explanations of the ordinary chemical processes (when regarded qualitatively) and permitted generalizations which largely stimulated its acceptance. Its inherent defect—that the products of combustion were invariably heavier than the original substance instead of less as the theory demanded—was ignored, and until late in the 18th century it dominated chemical thought. Its overthrow was effected by Lavoisier, who showed that combustion was simply an oxidation, the oxygen of the atmosphere (which was isolated at about this time by K. W. Scheele and J. Priestley) combining with the substance burnt.
COMEDY,the general term applied to a type of drama the chief object of which, according to modern notions, is to amuse. It is contrasted on the one hand with tragedy and on the other with farce, burlesque, &c. As compared with tragedy it is distinguished by having a happy ending (this being considered for a long time the essential difference), by quaint situations, and by lightness of dialogue and character-drawing. As compared with farce it abstains from crude and boisterous jesting, and is marked by some subtlety of dialogue and plot. It is, however, difficult to draw a hard and fast line of demarcation, there being a distinct tendency to combine the characteristics of farce with those of true comedy. This is perhaps more especially the case in the so-called “musical comedy,” which became popular in Great Britain and America in the later 19th century, where true comedy is frequently subservient to broad farce and spectacular effects.
The word “comedy” is derived from the Gr.κωμῳδία, which is a compound either ofκῶμος(revel) andἀοιδός(singer;ἀείδειν,ᾄδειν, to sing), or ofκώμη(village) andἀοιδός: it is possible thatκῶμοςitself is derived fromκώμη, and originally meant a village revel. The word comes into modern usage through the Lat.comoediaand Ital.commedia. It has passed through various shades of meaning. In the middle ages it meant simply a story with a happy ending. Thus some of Chaucer’s Tales are called comedies, and in this sense Dante used the term in the title of his poem,La Commedia(cf. hisEpistolaX., in which he speaks of the comic style as “loquutio vulgaris, in qua et mulierculae communicant”; again “comoedia vero remisse et humiliter”; “differt a tragoedia per hoc, quod t. in principio est admirabilis et quieta, in fine sive exitu est foetida et horribilis”). Subsequently the term is applied to mystery plays with a happy ending. The modern usage combines this sense with that in which Renaissance scholars applied it to the ancient comedies.
The adjective “comic” (Gr.κωμικός), which strictly means that which relates to comedy, is in modern usage generally confined to the sense of “laughter-provoking”: it is distinguished from “humorous” or “witty” inasmuch as it is applied to an incident or remark which provokes spontaneous laughter without a special mental effort. The phenomena connected with laughter and that which provokes it, the comic, have been carefully investigated by psychologists, in contrast with other phenomena connected with the emotions. It is very generally agreed that the predominating characteristics are incongruity or contrast in the object, and shock or emotional seizure on the part of the subject. It has also been held that the feeling of superiority is an essential, if not the essential, factor: thus Hobbes speaks of laughter as a “sudden glory.” Physiological explanations have been given by Kant, Spencer and Darwin. Modern investigators have paid much attention to the origin both of laughter and of smiling, babies being watched from infancy and the date of their first smile being carefully recorded. For an admirable analysis and account of the theories see James Sully,On Laughter(1902), who deals generally with the development of the “play instinct” and its emotional expression.
SeeDrama; alsoHumour;Caricature;Play, &c.
SeeDrama; alsoHumour;Caricature;Play, &c.
COMENIUS(orKomensky),JOHANN AMOS(1592-1671), a famous writer on education, and the last bishop of the old church of the Moravian and Bohemian Brethren, was born at Comna, or, according to another account, at Niwnitz, in Moravia, of poor parents belonging to the sect of the Moravian Brethren. Having studied at Herborn and Heidelberg, and travelled in Holland and England, he became rector of a school at Prerau, and after that pastor and rector of a school at Fulnek. In 1621 the Spanish invasion and persecution of the Protestants robbed him of all he possessed, and drove him into Poland. Soon after he was made bishop of the church of the Brethren. He supported himself by teaching Latin at Lissa, and it was here that he published hisPansophiae prodromus(1630), a work on education, and hisJanua linguarum reserata(1631), the latter of which gained for him a widespread reputation, being produced in twelve European languages, and also in Arabic, Persian and Turkish. He subsequently published several other works of a similar kind, as theEruditionis scholasticae januaand theJanua linguarum trilinguis. His method of teaching languages, which he seems to have been the first to adopt, consisted in giving, in parallel columns, sentences conveying useful information, in the vernacular and the languages intended to be taught (i.e.in Comenius’s works, Latin and sometimes Greek). In some of his books, as theOrbis sensualium pictus(1658), pictures are added; this work is, indeed, the first children’s picture-book. In 1638 Comenius was requested by the government of Sweden to draw up a scheme for the management of the schools of that country; and a few years after he was invited to join the commission that the English parliament then intended to appoint, in order to reform the system of education. He visited England in 1641, but the disturbed state of politics prevented the appointment of the commission, and Comenius passed over to Sweden in August 1642. The great Swedish minister, Oxenstjerna, obtained for him a pension, and a commission to furnish a plan for regulating the Swedish schools according to his own method. Devoting himself to the elaboration of his scheme, Comenius settled first at Elbing, and then at Lissa; but, at the burning of the latter city by the Poles, he lost nearly all his manuscripts, and he finally removed to Amsterdam, where he died in 1671.
As an educationist, Comenius holds a prominent place in history. He was disgusted at the pedantic teaching of his own day, and he insisted that the teaching of words and things must go together. Languages should be taught, like the mother tongue, by conversation on ordinary topics; pictures, object lessons, should be used; teaching should go hand in hand with a happy life. In his course he included singing, economy, politics, world-history, geography, and the arts and handicrafts. He was one of the first to advocate teaching science in schools.
As a theologian, Comenius was greatly influenced by Boehme. In hisSynopsis physicae ad lumen divinum reformataehe gives a physical theory of his own, said to be taken from the book of Genesis. He was also famous for his prophecies and the support he gave to visionaries. In hisLux in tenebrishe published the visions of Kotterus, Dabricius and Christina Poniatovia. Attempting to interpret the book of Revelation, he promised the millennium in 1672, and guaranteed miraculous assistance to those who would undertake the destruction of the Pope and the house of Austria, even venturing to prophesy that Cromwell, Gustavus Adolphus, and Rakoczy, prince of Transylvania, would perform the task. He also wrote to Louis XIV., informing him that the empire of the world should be his reward if he would overthrow the enemies of God.
Comenius also wrote against the Socinians, and published three historical works—Ratio disciplinae ordinisque in unitate fratrum Bohemorum, which was republished with remarks by Buddaeus,Historia persecutionum ecclesiae Bohemicae(1648), andMartyrologium Bohemicum. See Raumer’sGeschichte der Pädogogik, and Carpzov’sReligionsuntersuchung der böhmischen und mährischen Brüder.
Comenius also wrote against the Socinians, and published three historical works—Ratio disciplinae ordinisque in unitate fratrum Bohemorum, which was republished with remarks by Buddaeus,Historia persecutionum ecclesiae Bohemicae(1648), andMartyrologium Bohemicum. See Raumer’sGeschichte der Pädogogik, and Carpzov’sReligionsuntersuchung der böhmischen und mährischen Brüder.
COMET(Gr.κομήτης, long-haired), in astronomy, one of a class of seemingly nebulous bodies, moving under the influence of the sun’s attraction in very eccentric orbits. A comet is visible only in a small arc of its orbit near perihelion, differing but slightlyfrom the arc of a parabola. An obvious but not sharp classification of comets is into bright comets visible to the naked eye, and telescopic comets which can be seen only with a telescope. The telescopic class is much the more numerous of the two, only from 20 to 30 bright comets usually appearing in any one century, while several telescopic comets, frequently 6 or 8, are generally observed in the course of a year.
A bright comet consists of (1) a star-like nucleus; (2) a nebulous haze, called thecoma, surrounding this nucleus, the latter fading into the haze by insensible gradations; (3) a tail or luminous stream flowing from the coma in a direction opposite to that of the sun. The nuclei and comae of different comets exhibit few peculiarities to the unaided vision except in respect to brightness; but the tails of comets differ widely, both in brightness and in extent. They range from a barely visible brush or feather of light to a phenomenon extending over a considerable arc of the heavens, which, comparatively bright near the head of the comet, becomes gradually fainter and more diffuse towards its end, fading out by gradations so insensible that a precise length cannot be assigned to it. When a telescopic comet is first discovered the nucleus is frequently invisible, the object presenting the appearance of a faint nebulous haze, scarcely distinguishable in aspect from a nebula. When the nucleus appears it may at first be only a comparatively faint condensation, and may or may not develop into a point of light as the comet approaches the sun. A tail also is generally not seen at great distances from the sun, but gradually develops as the comet approaches perihelion, to fade away again as the comet recedes from the sun.
A few comets are known to revolve in orbits with a regular period, while, in the case of others, no evidence is afforded by observation that the orbit deviates from a parabola. Were the orbit a parabola or hyperbola the comet would never return (seeOrbit). Periodicity may be recognized in two ways: observations during the apparition may show that the motion is in an elliptic and not in a parabolic orbit; or a comet may have been observed at more than one return. In the latter case the comet is recognized as distinctly periodic, and therefore a member of the solar system. The shortest periods range between 3 and 10 years. The majority of comets which have been observed are shown by observation to be periodic; the period is usually very long, being sometimes measured by centuries, but generally by thousands of years. It is conceivable that a comet might revolve in a hyperbolic orbit. Although there are several of these bodies observations on which indicate such an orbit, the deviation from the parabolic form has not in any case been so well marked as to be fully established. Circumstances lead to the classification of newly appearing comets asexpectedandunexpected. An expected comet is a periodic one of which the return is looked for at a determinate time and in a certain region of the heavens. When this is not the case the comet is an unexpected one.
Physical Constitution of Comets.—The subject of the physical constitution of these bodies is one as to the details of which much uncertainty still exists. The considerations on which conclusions in this field rest are very various, and can best be set forth by beginning with what we may consider to be the best established facts.
We must regard it as well established that comets are not, like planets and satellites, permanent in mass, but are continuously losing minute portions of the matter which belongs to them, through a progressive dissipation—at least when they are in the neighbourhood of the sun. When near perihelion the matter of a comet is seen to be undergoing a process in the nature of evaporation, successive envelopes of vapour rising from the nucleus to form the coma, and then gradually repelled from the sun to form the tail. If this process went on indefinitely every comet would, in the course of ages, be entirely dissipated. This result has actually happened in the case of some known comets, the best established example of which is that of Biela, in which the process of disintegration was clearly followed. As the amount of matter lost by a comet at any one return cannot be estimated, and may be very small, it is impossible to set any limit to the period during which its life may continue. It is still an unsettled question whether, in every case, the evaporation will ultimately cease, leaving a residuum as permanent as any other mass of matter.
The next question in logical order is one of great difficulty. It is whether the nucleus of a comet is an opaque solid body, a cluster of such bodies, or a mass of particles of extreme tenuity. Some light is thrown on this and other questions by the spectroscope. This instrument shows in the spectrum of nearly every comet three bright bands, recognized as those of hydrocarbons. The obvious conclusion is that the light forming these bands is not reflected sunlight, but light radiated by the gaseous hydrocarbons. Since a gas at so great a distance from the sun cannot be heated to incandescence, the question arises how incandescence is excited. The generalizations of recent years growing out of the phenomena of radioactivity make it highly probable that the source is to be found in some form of electrical excitation, produced by electrons or other corpuscles thrown out by the sun. The resemblance of the cometary spectrum to the spectrum of hydrocarbons in the Geissler tube lends great plausibility to this view. It is remarkable that the great comet of 1882 also showed the bright lines of sodium with such intensity that they were observed in daylight by R. Copeland and W. O. Lohse. In addition to these gaseous spectra, all but the fainter comets show a continuous spectrum, crossed by the Fraunhofer lines, which is doubtless due to reflected sunlight. It happens that, since the spectroscope has been perfected, no comet of great brilliancy has been favourably situated for observation. Until the opportunity is offered, the conclusions to be derived from spectroscopic observation cannot be further extended.
Plate I.
By permission of Lick Observatory (E. E. Barnard)
By permission of Yerkes Observatory (E. E. Barnard).
Plate II.
By permission of Helwân Observatory, Egypt.
By permission of Yerkes Observatory (E. E. Barnard).
In the telescope the nucleus of a bright comet appears as an opaque mass, one or more seconds in diameter, the absolute dimensions comparing with those of the satellites of the planets, sometimes, indeed, equal to our moon. But the actual results of micrometric measures are found to differ very widely. In the case of Donati’s comet of 1858 the nucleus seemed to grow smaller as perihelion was approached. This is evidently due to the fact that the coma immediately around the nucleus was so bright as apparently to form a part of it at considerable distances from the sun. G. P. Bond estimated the diameter of the actual nucleus at 500 m. That the nucleus is a body of appreciable mass seems to be made probable by the fact that, except for the central attraction of such a body, a comet would speedily be dissipated by the different attractions of the sun on different parts of the mass, which would result in each particle pursuing an orbit of its own. It follows that there must be a mass sufficient to hold the parts of the comet, if not absolutely together, at least in each other’s immediate neighbourhood. How great a central mass may be required for this is a subject not yet investigated. It might be supposed that the amount of matter must be sufficient to make the nucleus quite opaque. But two considerations based on observations militate against this view. One is that an opaque body, reflecting much sunlight, would show a brighter continuous spectrum than has yet been found in any comet. Another and yet more remarkable observation is on record which goes far to prove not only the tenuity, but the transparency of a cometary nucleus. The great comet of 1882 made a transit over the sun on the 17th of September, an occurrence unique in the history of astronomy. But the fact of the transit escaped attention except at the observatory of the Cape of Good Hope. Here the comet was watched by W. H. Finlay and by W. L. Elkin as it approached the sun, and was kept in sight until it came almost or quite in contact with the sun’s disk, when it disappeared. It should, if opaque, have appeared a few minutes later, projected on the sun’s disk; but not a trace of it could be seen. The sun was approaching Table Mountain at the critical moment, and its limb was undulating badly, making the detection of a minute point difficult. The possibility of a very small opaque nucleus is therefore still left open; yet the remarkable conclusion still holds, that, immediately around a possible central nucleus, the matter of the head of the comet was so rare as not to interceptany appreciable fraction of the sun’s light. This result seems also to show that, with the possible exception of a very small central mass, what seems to telescopic vision as a nucleus is really only the central portion of the coma, which, as the distance from the centre increases, becomes less and less dense by imperceptible gradations.
Another fact tending towards this same conclusion is that after this comet passed perihelion it showed several nuclei following each other. Evidently the powerful attraction of the sun had separated the parts of the apparent nucleus, which were following each other in nearly the same orbit. As they could not have been completely brought together again, we may suppose that in such cases the smaller nuclei were permanently separated from the main body. In addition to this, the remarkable similarity of the orbit of this comet to that of several others indicates a group of bodies moving in nearly the same orbit. The other members of the group were the great comets of 1843, 1880 and 1887. The latter, though so bright as to be conspicuous to the naked eye, showed no nucleus whatever. The closely related orbits of the four bodies are also remarkable for approaching nearer the sun at perihelion than does the orbit of any other known body. All of these comets pass through the matter of the sun’s corona with a velocity of more than 100 m. per second without suffering any retardation. As it is beyond all reasonable probability that several independent bodies should have moved in orbits so nearly the same, the conclusion is that the comets were originally portions of one mass, which gradually separated in the course of ages by the powerful attraction of the sun as the collection successively passed the perihelion. It may be remarked that observations on the comet of 1843 seemed to show a slight ellipticity of the orbit, corresponding to a period of several centuries; but the deviation of all the orbits from a parabola is too slight to be established by observations. The periods of the comets are therefore unknown except that they must be counted by centuries and possibly by thousands of years.
Another fact which increases the complexity of the question is the well-established connexion of comets with meteoric showers. The shower of November 13-15, now known as the Leonids, which recurred for several centuries at intervals of about one-third of a century, are undoubtedly due to a stream of particles left behind by a comet observed in 1866. The same is true of Biela’s comet, the disintegrated particles of which give rise to the Andromedids, and probably true also of the Perseids, or August meteors, the orbits of which have a great similarity to a comet seen in 1862. The general and well-established conclusion seems to be that, in addition to the visible features of a comet, every such body is followed in its orbit by a swarm of meteoric particles which must have been gradually detached and separated from it. (SeeMeteor.)
The source of the repulsive force by which the matter forming the tail of a comet is driven away from the sun is another question that has not yet been decisively answered. Two causes have been suggested, of which one has only recently been brought to light. This is the repulsion of the sun’s rays, a form of action the probability of which was shown by J. Clerk Maxwell in 1870, and which was experimentally established about thirty years later. The intensity of this action on a particle is proportional to the surface presented by the particle to the rays, and therefore to the square of its diameter, while its mass, and therefore its gravitation to the sun, are proportional to the cube of the diameter. It follows that if the size and mass of a particle in space are below a certain limit, the repulsion of the rays will exceed the attraction of the sun, and the particle will be driven off into space. But, in order that this repulsive force may act, the particles, however minute they may be, must be opaque. Moreover, theory shows that there is a lower as well as an upper limit to their magnitude, and that it is only between certain definable limits of magnitude that the force acts. Conceiving the particle to be of the density of water, and considering its diameter as a diminishing variable, theory shows that the repulsion will balance gravity when the diameter has reached 0.0015 of a millimetre. As the diameter is reduced below this limit the ratio of the repulsive to the attractive force increases, but soon reaches a maximum, after which it diminishes down to a diameter of 0.00007 mm., when the two actions are again balanced. Below this limit the light speedily ceases to act. It follows that a purely gaseous body, such as would emit a characteristic bright line spectrum, would not be subject to the repulsion. We must therefore conclude that both the solid and gaseous forms of matter are here at play, and this view is consonant with the fact that the comet leaves behind it particles of meteoric matter.
Another possible cause is electrical repulsion. The probability of this cause is suggested by recent discoveries in radioactivity and by the fact that the sun undoubtedly sends forth electrical emanations which may ionize the gaseous molecules rising from the nucleus, and lead to their repulsion from the sun, thus resulting in the phenomena of the tail. But well-established laws are not yet sufficiently developed to lead to definite conclusions on this point, and the question whether both causes are combined, and, if not, to which one the phenomena in question are mainly due, must be left to the future.
A curious circumstance, which may be explained by a duplex character of the matter forming a cometary tail, is the great difference between the visual and photographic aspect of these bodies. The soft, delicate, feathery-like form which the comet with its tail presents to the eye is wanting in a photograph, which shows principally a round head with an irregularly formed tail much like the knotted stalk of a plant. It follows that the light emitted by the central axis of the tail greatly exceeds in actinic power the diffuse light around it. A careful comparison of the form and intensity of the photographic and visual tails may throw much light on the question of the constitution of these bodies, but no good opportunity of making the comparison has been afforded since the art of celestial photography has been brought to its present state of perfection.
The main conclusion to which the preceding facts and considerations point is that the matter of a comet is partly solid and partly gaseous. The gaseous form is shown conclusively by the spectroscope, but in view of the extreme delicacy of the indications with this instrument no quantitative estimate of the gas can be made. As there is no central mass sufficient to hold together a continuous atmosphere of elastic gas of any sort, it seems probable that the gaseous molecules are only those rising from the coma, possibly by ordinary evaporation, but more probably by the action of the ultra-violet and other rays of the sun giving rise to an ionization of disconnected gaseous molecules. The matter cannot be wholly gaseous because in this case there could be no central force sufficient to keep the parts of the comet together.
The facts also point to the conclusion that the solid matter of a comet is formed of a swarm or cloud of small disconnected masses, probably having much resemblance to the meteoric masses which are known to be flying through the solar system and possibly of the same general kind as these. The question whether there is any central solid of considerable mass is still undecided; it can only be said that if so, it is probably small relative to cosmic masses in general—more likely less than greater than 100 m. in diameter. The light of the comet therefore proceeds from two sources: one the incandescence of gases, the other the sunlight reflected from the solid parts. No estimate can be formed of the ratio between these two kinds of light until a bright comet shall be spectroscopically observed during an entire apparition.
Origin and Orbits of Comets.—The great difference which we have pointed out between comets and the permanent bodies of the solar system naturally suggested the idea that these bodies do not belong to that system at all, but are nebulous masses, scattered through the stellar spaces, and brought one by one into the sphere of the sun’s attraction. The results of this view are easily shown to be incompatible with the observed facts. The sun, carrying the whole solar system with it, is moving through space with a speed of about 10 m. per second. If it approached a comet nearly at rest the result would be a relative motion of this amount which, as the comet came nearer,would be constantly increased, and would result in the comet describing relative to the sun a markedly hyperbolic orbit, deviating too widely from a parabola to leave any doubt, even in the most extreme cases. Moreover, a large majority of comets would then have their aphelia in the direction of the sun’s motion, and therefore their perihelia in the opposite direction. Neither of these results corresponds to the fact. The conclusion is that if we regard a comet as a body not belonging to the solar system, it is at least a body which before its approach to the sun had the same motion through the stellar spaces that the sun has. As this unity of motion must have been maintained from the beginning, we may regard comets as belonging to the solar system in the sense of not being visitors from distant regions of space.
The acceptance of this seemingly inevitable conclusion leads to another: that no comet yet known moves in a really hyperbolic orbit, but that the limit of eccentricity must be regarded as 1, or that of the parabola. It is true that seeming evidence of hyperbolic eccentricity is sometimes afforded by observations and regarded by some astronomers as sufficient. The objections to the reality of the hyperbolic orbit are two: (1) A comet moving in a decidedly hyperbolic orbit must have come from so great a distance within a finite time, say a few millions of years, as to have no relation to the sun, and must after its approach to the sun return into space, never again to visit our system. In this case the motion of the sun through space renders it almost infinitely improbable that the orbit would have been so nearly a parabola as all such orbits are actually found to be. (2) The apparent deviation from a very elongated ellipse has never been in any case greater than might have been the result of errors of observation on bodies of this class.
This being granted, a luminous view of the causes which lead to the observed orbits of comets is readily gained by imagining these bodies to be formed of nebulous masses, which originally accompanied the sun in its journey through space, but at distances, in most cases, vastly greater than that of the farthest planet. Such a mass, when drawn towards the sun, would move round it in a nearly parabolic orbit, similar to the actual orbits of the great majority of comets. The period might be measured by thousands, tens of thousands, or hundreds of thousands of years, according to the distances of the comet in the beginning; but instead of bodies extraneous to the system, we should have bodies properly belonging to the system and making revolutions around the sun.
Were it not for the effect of planetary attraction long periods like these would be the general rule, though not necessarily universal. But at every return to perihelion the motion of a comet will be to some extent either accelerated or retarded by the action of Jupiter or any other planet in the neighbourhood of which it may pass. Commonly the action will be so slight as to have little influence on the orbit and the time of revolution. But should the comet chance to pass the orbit of Jupiter just in front of the planet, its motion would be retarded and the orbit would be changed into one of shorter period. Should it pass behind the planet, its motion would be accelerated and its period lengthened. In such cases the orbit might be changed to a hyperbola, and then the comet would never return. It follows that there is a tendency towards a gradual but constant diminution in the total number of comets. If we call Δe the amount by which the eccentricity of a cometary orbit is less than unity, Δe will be an extremely minute fraction in the case of the original orbits. If we call ± δ the change which the eccentricity 1 - Δe undergoes by the action of the planets during the passage of the comet through our system, it will leave the system with the eccentricity 1 - Δe ± δ. The possibilities are even whether δ shall be positive or negative. If negative, the eccentricity will be diminished and the period shortened. If positive, and greater than Δe, the eccentricity 1 - Δe + δ will be greater than 1, and then the comet will be thrown into a hyperbolic orbit and become for ever a wanderer through the stellar spaces.
The nearer a comet passes to a planet, especially to Jupiter, the greatest planet, the greater δ may be. If δ is a considerable negative fraction, the eccentricity will be so reduced that the comet will after the approach be one of short period. It follows that, however long the period of a comet may be, there is a possibility of its becoming one of short period if it approaches Jupiter. There have been several cases of this during the past two centuries, the most recent being that of Brooks’s comet, 1889, V. Soon after its discovery this body was found to have a period of only about seven years. The question why it had not been observed at previous returns was settled after the orbit had been determined by computing its motion in the past. It was thus found that in October 1886 the comet had passed in the immediate neighbourhood of Jupiter, the action of which had been such as to change its orbit from one of long period to the short observed period. A similar case was that of Lexel’s comet, seen in 1770. Originally moving in an unknown orbit, it encountered the planet Jupiter, made two revolutions round the sun, in the second of which it was observed, then again encountered the planet, to be thrown out of its orbit into one which did not admit of determination. The comet was never again found.
A general conclusion which seems to follow from these conditions, and is justified by observations, so far as the latter go, is that comets are not to be regarded as permanent bodies like the planets, but that the conglomerations of matter which compose them are undergoing a process of gradual dissipation in space. This process is especially rapid in the case of the fainter periodic comets. It was first strikingly brought out in the case of Biela’s comet. This object was discovered in 1772, was observed to be periodic after several revolutions had been made, and was observed with a fair degree of regularity at different returns until 1852. At the previous apparition it was found to have separated into two masses, and in 1852 these masses were so widely separated that they might be considered as forming two comets. Notwithstanding careful search at times and places when the comet was due, no trace of it has since been seen. An examination of the table of periodic comets given at the end of this article will show that the same thing is probably true of several other comets, especially Brorsen’s and Tempel’s, which have each made several revolutions since last observed, and have been sought for in vain.
In view of the seemingly inevitable dissipation of comets in the course of ages, and of the actually observed changes of their orbits by the attraction of Jupiter, the question arises whether the orbits of all comets of short period may not have been determined by the attraction of the planets, especially of Jupiter. In this case the orbit would, for a period of several centuries, have continued to nearly intersect that of the planet. We find, as a matter of fact, that several periodic comets either pass near Jupiter or have their aphelia in the neighbourhood of the orbit of Jupiter. The approach, however, is not sufficiently close to have led to the change unless in former times the proximity of the orbits was much greater than it is now. As the orbits of all the bodies of the solar system are subject to a slow secular change of their form and position, this may only show that it must have been thousands of years since the comet became one of short period. The two cases of most difficulty are those of Halley’s and Encke’s comets. The orbit of the former is so elongated and so inclined to the general plane of the planetary orbits that its secular variation must be very slow indeed. But it does not pass near the orbit of any planet except Venus; and even here the proximity is far from being sufficient to have produced an appreciable change in the period. The orbit of Encke’s comet is entirely within the orbit of Jupiter, and it also cannot have passed near enough to a planet for thousands of years to have had its orbit changed by the action in question. It therefore seems difficult to regard these two comets as other than permanent members of the solar system.
Special Periodic Comets.—One of the most remarkable periodic comets with which we are acquainted is that known to astronomers as Halley’s. Having perceived that the elements of the comet of 1682 were nearly the same as those of two comets which had respectively appeared in 1531 and 1607, EdmundHalley concluded that all the three orbits belonged to the same comet, of which the periodic time was about 76 years. After a rough estimate of the perturbations it must sustain from the attraction of the planets, he predicted its return for 1757,—a bold prediction at that time, but justified by the event, for the comet again made its appearance as was expected, though it did not pass through its perihelion till the month of March 1759, the attraction of Jupiter and Saturn having caused, as was computed by Clairault previously to its return, a retardation of 618 days. This comet had been observed in 1066, and the accounts which have been preserved represent it as having then appeared to be four times the size of Venus, and to have shone with a light equal to a fourth of that of the moon. History is silent respecting it from that time till the year 1456, when it passed very near to the earth: its tail then extended over 60° of the heavens, and had the form of a sabre. It returned to its perihelion in 1835, and was well observed in almost every observatory. But its brightness was far from comparing with the glorious accounts of its former apparitions. That this should have been due to the process of dissipation does not seem possible in so short a period; we must therefore consider either that the earlier accounts are greatly exaggerated, or that the brightness of the comet is subject to changes from some unknown cause. Previous appearances of Halley’s comet have been calculated by J. R. Hind, and more recently by P. H. Cowell and A. C. D. Crommelin of Greenwich, the latter having carried the comet back to 87B.C.with certainty, and to 240B.C.with fair probability. It was detected by Max Wolf at Heidelberg on plates exposed on Sept. 11, 1909, and subsequently on a Greenwich plate of Sept. 9.
The known comet of shortest period bears the name of J. F. Encke, the astronomer who first investigated its orbit and showed its periodicity. It was originally discovered in 1789, but its periodicity was not recognized until 1818, after it had been observed at several returns. This comet has given rise to a longer series of investigations than any other, owing to Encke’s result that the orbit was becoming smaller, and the revolutions therefore accelerated, by some unknown cause, of which the most plausible was a resisting medium surrounding the sun. As this comet is almost the only one that passes within the orbit of Mercury, it is quite possible that it alone would show the effect of such a medium. Recent investigations of this subject have been made at the Pulkova Observatory, first by F. E. von Asten and later by J. O. Backlund who, in 1909, was awarded the Gold Medal of the Royal Astronomical Society for his researches in this field. During some revolutions there was evidence of a slight acceleration of the return, and during others there was not.
The following is a list (compiled in 1909) of comets which are well established as periodic, through having been observed at one or more returns. In addition to what has already been said of several comets in this list the following remarks may be made. Tuttle’s comet was first seen by P. F. A. Méchain in 1790, but was not recognized as periodic until found by Tuttle in 1858, when the resemblance of the two orbits led to the conclusion of the identity of the bodies, the period of which was soon made evident by continued observations. The comets of Pons and Olbers are remarkable for having an almost equal period. But their orbits are otherwise totally different, so that there does not seem to be any connexion between them. Brorsen’s comet seems also to be completely dissipated, not having been seen since 1879.
List of Periodic Comets observed at more than one Return.
There are also a number of cases in which a comet has been observed through one apparition, and found to be apparently periodic, but which was not seen to return at the end of its supposed period. In some of these cases it seems likely that the comet passed near the planet Jupiter and thus had its orbit entirely changed. It is possible that in other cases the apparent periodicity is due to the unavoidable errors of observation to which, owing to their diffused outline, the nuclei of comets are liable.