"Incensed with indignation, Satan stoodUnterrified, and like a comet burned,That fires the length of Ophiucus hugeIn the Arctic sky, and from his horrid trainShakes pestilence and war."—Milton.
"Incensed with indignation, Satan stoodUnterrified, and like a comet burned,That fires the length of Ophiucus hugeIn the Arctic sky, and from his horrid trainShakes pestilence and war."—Milton.
Amongother great results which have marked the history of Halley's comet, it has itself been a criterion of the existing state of the mathematical and astronomical sciences. We have just seen how far the knowledge of the great laws of physical astronomy, and of the higher mathematics, enabled the astronomers of 1682 and 1759, respectively, to deal with this wonderful body; and let us now see what higher advantages were possessed by the astronomers of 1835. During this last interval of seventy-six years, the science of mathematics, in its most profound and refined branches, has made prodigious advances, more especially in its application to the laws of the celestial motions, as exemplified in the 'Mecanique Celeste' of La Place. The methods of investigation have acquired greater simplicity, and have likewise become more general and comprehensive; and mechanical science, in the largest sense of that term, now embraces in its formularies the most complicated motions, and the most minute effects of the mutual influences of the various members of our system. You will probably find it difficult to comprehend, how such hidden facts can be disclosed by formularies, consisting ofa's andb's, andx's andy's, and other algebraic symbols; nor will it be easy to give you a clear idea of this subject, without a more extensive acquaintance than you have formed with algebraic investigations; but you can easily understand that evenan equation expressed in numbers may be so changed in its form, by adding, subtracting, multiplying and dividing, as to express some new truth at every transformation. Some idea of this may be formed by the simplest example. Take the following: 3+4=7. This equation expresses the fact, that three added to four is equal to seven. By multiplying all the terms by 2, we obtain a new equation, in which 6+8=14. This expresses a new truth; and by varying the form, by similar operations, an indefinite number of separate truths may be elicited from the simple fundamental expression. I will add another illustration, which involves a little more algebra, but not, I think, more than you can understand; or, if it does, you will please pass over it to the next paragraph. According to a rule of arithmetical progression,the sum of all the terms is equal to half the sum of the extremes multiplied into the number of terms. Calling the sum of the termss, the first terma, the lasth, and the number of termsn, and we have(½)n(a+h)=s; orn(a+h)=2s; ora+h=2s⁄n; ora=(2s⁄n)-h; orh=(2s⁄n)-a. These are only a few of the changes which may be made in the original expression, still preserving the equality between the quantities on the left hand and those on the right; yet each of these transformations expresses a new truth, indicating distinct and (as might be the case) before unknown relations between the several quantities of which the whole expression is composed. The last, for example, shows us that the last term in an arithmetical series is always equal to twice the sum of the whole series divided by the number of terms and diminished by the first term. In analytical formularies, as expressions of this kind are called, the value of a single unknown quantity is sometimes given in a very complicated expression, consisting of known quantities; but before we can ascertain their united value, we must reduce them, by actually performing all the additions, subtractions, multiplications, divisions, raising to powers, andextracting roots, which are denoted by the symbols. This makes the actual calculations derived from such formularies immensely laborious. We have already had an instance of this in the calculations made by Lalande and Madame Lepaute, from formularies furnished by Clairaut.
The analytical formularies, contained in such works as La Place's 'Mecanique Celeste,' exhibit to the eye of the mathematician a record of all the evolutions of the bodies of the solar system in ages past, and of all the changes they must undergo in ages to come. Such has been the result of the combination of transcendent mathematical genius and unexampled labor and perseverance, for the last century. The learned societies established in various centres of civilization have more especially directed their attention to the advancement of physical astronomy, and have stimulated the spirit of inquiry by a succession of prizes, offered for the solutions of problems arising out of the difficulties which were progressively developed by the advancement of astronomical knowledge. Among these questions, the determination of the return of comets, and the disturbances which they experience in their course, by the action of the planets near which they happen to pass, hold a prominent place. In 1826, the French Institute offered a prize for the determination of the exact time of the return of Halley's comet to its perihelion in 1835. M. Pontecoulant aspired to the honor. "After calculations," says he, "of which those alone who have engaged in such researches can estimate the extent and appreciate the fastidious monotony, I arrived at a result which satisfied all the conditions proposed by the Institute. I determined the perturbations of Halley's comet, by taking into account the simultaneous actions of Jupiter, Saturn, Uranus, and the Earth, and I then fixed its return to its perihelion for the seventh of November." Subsequently to this, however, M. Pontecoulant made some further researches, which led him to correct the former result; and he afterwardsaltered the time to November fourteenth. It actually came to its perihelion on the sixteenth, within two days of the time assigned.
Nothing can convince us more fully of the complete mastery which astronomers have at last acquired over these erratic bodies, than to read in the Edinburgh Review for April, 1835, the paragraph containing the final results of all the labors and anticipations of astronomers, matured as they were, in readiness for the approaching visitant, and then to compare the prediction with the event, as we saw it fulfilled a few months afterwards. The paragraph was as follows: "On the whole, it may be considered as tolerably certain, that the comet will become visible in every part of Europe about the latter end of August, or beginning of September, next. It will most probably be distinguishable by the naked eye, like a star of the first magnitude, but with a duller light than that of a planet, and surrounded with a pale nebulosity, which will slightly impair its splendor. On the night of the seventh of October, the comet will approach the well-known constellation of the Great Bear; and between that and the eleventh, it will pass directly through the seven conspicuous stars of that constellation, (the Dipper.) Towards the end of November, the comet will plunge among the rays of the sun, and disappear, and will not issue from them, on the other side, until the end of December."
Let us now see how far the actual appearances corresponded to these predictions. The comet was first discovered from the observatory at Rome, on the morning of the fifth of August; by Professor Struve, at Dorpat, on the twentieth; in England and France, on the twenty-third; and at Yale College, by Professor Loomis and myself, on the thirty-first. On the morning of that day, between two and three o'clock, in obedience to the directions which the great minds that had marked out its path among the stars had prescribed, we directed Clarke's telescope (a noble instrument, belongingto Yale College) towards the northeastern quarter of the heavens, and lo! there was the wanderer so long foretold,—a dim speck of fog on the confines of creation. It came on slowly, from night to night, increasing constantly in magnitude and brightness, but did not become distinctly visible to the naked eye until the twenty-second of September. For a month, therefore, astronomers enjoyed this interesting spectacle before it exhibited itself to the world at large. From this time it moved rapidly along the northern sky, until, about the tenth of October, it traversed the constellation of the Great Bear, passing a little above, instead of "through" the seven conspicuous stars constituting the Dipper. At this time it had a lengthened train, and became, as you doubtless remember, an object of universal interest. Early in November, the comet ran down to the sun, and was lost in his beams; but on the morning of December thirty-first, I again obtained, through Clarke's telescope, a distinct view of it on the other side of the sun, a moment before the morning dawn.
This return of Halley's comet was an astronomical event of transcendent importance. It was the chronicler of ages, and carried us, by a few steps, up to the origin of time. If a gallant ship, which has sailed round the globe, and commanded successively the admiration of many great cities, diverse in language and customs, is invested with a peculiar interest, what interest must attach to one that has made the circuit of the solar system, and fixed the gaze of successive worlds! So intimate, moreover, is the bond which binds together all truths in one indissoluble chain, that the establishment of one great truth often confirms a multitude of others, equally important. Thus the return of Halley's comet, in exact conformity with the predictions of astronomers, established the truth of all those principles by which those predictions were made. It afforded most triumphant proof of the doctrine of universal gravitation, and of course of the receivedlaws of physical astronomy; it inspired new confidence in the power and accuracy of that instrument (the calculus) by means of which its elements had been investigated; and it proved that the different planets, which exerted upon it severally a disturbing force proportioned to their quantity of matter, had been correctly weighed, as in a balance.
I must now leave this wonderful body to pursue its sublime march far beyond the confines of Uranus, (a distance it has long since reached,) and take a hasty notice of two other comets, whose periodic returns have also been ascertained; namely, those of Biela and Encke.
Biela's comet has a period of six years and three quarters. It has its perihelion near the orbit of the earth, and its aphelion a little beyond that of Jupiter. Its orbit, therefore, is far less eccentric than that of Halley's comet; (see Frontispiece;) it neither approaches so near the sun, nor departs so far from it, as most other known comets: some, indeed, never come nearer to the sun than the orbit of Jupiter, while they recede to an incomprehensible distance beyond the remotest planet. We might even imagine that they would get beyond the limits of the sun's attraction; nor is this impossible, although, according to La Place, the solar attraction is sensible throughout a sphere whose radius is a hundred millions of times greater than the distance of the earth from the sun, or nearly ten thousand billions of miles.
Some months before the expected return of Biela's comet, in 1832, it was announced by astronomers, who had calculated its path, that it would cross the plane of the earth's orbit very near to the earth's path, so that, should the earth happen at the time to be at that point of her revolution, a collision might take place. This announcement excited so much alarm among the ignorant classes in France, that it was deemed expedient by the French academy, that one of their number should prepare and publish an article on the subject,with the express view of allaying popular apprehension. This task was executed by M. Arago. He admitted that the earth would in fact pass so near the point where the comet crossed the plane of its orbit, that, should they chance to meet there, the earth would be enveloped in the nebulous atmosphere of the comet. He, however, showed that the earth would not be near that point at the same time with the comet, but fifty millions of miles from it.
The comet came at the appointed time, but was so exceedingly faint and small, that it was visible only to the largest telescopes. In one respect, its diminutive size and feeble light enhanced the interest with which it was contemplated; for it was a sublime spectacle to see a body, which, as projected on the celestial vault, even when magnified a thousand times, seemed but a dim speck of fog, still pursuing its way, in obedience to the laws of universal gravitation, with the same regularity as Jupiter and Saturn. We are apt to imagine that a body, consisting of such light materials that it can be compared only to the thinnest fog, would be dissipated and lost in the boundless regions of space; but so far is this from the truth, that, when subjected to the action of the same forces of projection and solar attraction, it will move through the void regions of space, and will describe its own orbit about the sun with the same unerring certainty, as the densest bodies of the system.
Encke's comet, by its frequent returns, (once in three and a third years,) affords peculiar facilities for ascertaining the laws of its revolution; and it has kept the appointments made for it with great exactness. On its return in 1839, it exhibited to the telescope a globular mass of nebulous matter, resembling fog, and moved towards its perihelion with great rapidity. It makes its entire excursions within the orbit of Jupiter.
But what has made Encke's comet particularly famous, is its having first revealed to us the existence of aresisting mediumin the planetary spaces. It haslong been a question, whether the earth and planets revolve in a perfect void, or whether a fluid of extreme rarity may not be diffused through space. A perfect vacuum was deemed most probable, because no such effects on the motions of the planets could be detected as indicated that they encountered a resisting medium. But a feather, or a lock of cotton, propelled with great velocity, might render obvious the resistance of a medium which would not be perceptible in the motions of a cannon ball. Accordingly, Encke's comet is thought to have plainly suffered a retardation from encountering a resisting medium in the planetary regions. The effect of this resistance, from the first discovery of the comet to the present time, has been to diminish the time of its revolution about two days. Such a resistance, by destroying a part of the projectile force, would cause the comet to approach nearer to the sun, and thus to have its periodic time shortened. The ultimate effect of this cause will be to bring the comet nearer to the sun, at every revolution, until it finally falls into that luminary, although many thousand years will be required to produce this catastrophe. It is conceivable, indeed, that the effects of such a resistance may be counteracted by the attraction of one or more of the planets, near which it may pass in its successive returns to the sun. Still, it is not probable that this cause will exactly counterbalance the other; so that, if there is such an elastic medium diffused through the planetary regions, it must follow that, in the lapse of ages, every comet will fall into the sun. Newton conjectured that this would be the case, although he did not found his opinion upon the existence of such a resisting medium as is now detected. To such an opinion he adhered to the end of life. At the age of eighty-three, in a conversation with his nephew, he expressed himself thus: "I cannot say when the comet of 1680 will fall into the sun; possibly after five or six revolutions; but whenever that time shall arrive, the heat of the sun will be raised by it to such a point, thatour globe will be burned, and all the animals upon it will perish."
Of thephysical natureof comets little is understood. The greater part of them are evidently mere masses of vapor, since they permit very small stars to be seen through them. In September, 1832, Sir John Herschel, when observing Biela's comet, saw that body pass directly between his eye and a small cluster of minute telescopic stars of the sixteenth or seventeenth magnitude. This little constellation occupied a space in the heavens, the breadth of which was not the twentieth part of that of the moon; yet the whole of the cluster was distinctly visible through the comet. "A more striking proof," says Sir John Herschel, "could not have been afforded, of the extreme transparency of the matter of which this comet consists. The most trifling fog would have entirely effaced this group of stars, yet they continued visible through a thickness of the comet which, calculating on its distance and apparent diameter, must have exceeded fifty thousand miles, at least towards its central parts." From this and similar observations, it is inferred, that the nebulous matter of comets is vastly more rare than that of the air we breathe, and hence, that, were more or less of it to be mingled with the earth's atmosphere, it would not be perceived, although it might possibly render the air unwholesome for respiration. M. Arago, however, is of the opinion, that some comets, at least, have a solid nucleus. It is difficult, on any other supposition, to account for the strong light which some of them have exhibited,—a light sufficiently intense to render them visible in the day-time, during the presence of the sun. The intense heat to which comets are subject, in approaching so near the sun as some of them do, is alleged as a sufficient reason for the great expansion of the thin vapory atmospheres which form their tails; and the inconceivable cold to which they are subject, in receding to such a distance from the sun, is supposed to account for the condensation of the same matter until it returnsto its original dimensions. Thus the great comet of 1680, at its perihelion, approached within one hundred and forty-six thousand miles of the surface of the sun, a distance of only one sixth part of the sun's diameter. The heat which it must have received was estimated to be equal to twenty-eight thousand times that which the earth receives in the same time, and two thousand times hotter than red-hot iron. This temperature would be sufficient to volatilize the most obdurate substances, and to expand the vapor to vast dimensions; and the opposite effects of the extreme cold to which it would be subject in the regions remote from the sun would be adequate to condense it into its former volume. This explanation, however, does not account for the direction of the tail, extending, as it usually does, only in a line opposite to the sun. Some writers, therefore, suppose that the nebulous matter of the comet, after being expanded to such a volume that the particles are no longer attracted to the nucleus, unless by the slightest conceivable force, are carried off in a direction from the sun, by the impulse of the solar rays themselves. But to assign such a power to the sun's rays, while they have never been proved to have any momentum, is unphilosophical; and we are compelled to place the phenomena of comets' tails among the points of astronomy yet to be explained.
Since comets which approach very near the sun, like the comet of 1680, cross the orbits of all the planets, the possibility that one of them may strike the earth has frequently been suggested. Still it may quiet our apprehensions on this subject, to reflect on the vast amplitude of the planetary spaces, in which these bodies are not crowded together, as we see them erroneously represented in orreries and diagrams, but are sparsely scattered at immense distances from each other. They are like insects flying, singly, in the expanse of heaven. If a comet's tail lay with its axis in the plane of the ecliptic when it was near the sun, we can imagine that the tail might sweep over the earth; but thetail may be situated at any angle with the ecliptic, as well as in the same plane with it, and the chances that it will not be in the same plane are almost infinite. It is also extremely improbable that a comet will cross the plane of the ecliptic precisely at the earth's path in that plane, since it may as probably cross it at any other point nearer or more remote from the sun. A French writer of some eminence (Du Sejour) has discussed this subject with ability, and arrived at the following conclusions: That of all the comets whose paths had been ascertained, nonecould passnearer to the earth than about twice the moon's distance; and that none everdid passnearer to the earth than nine times the moon's distance. The comet of 1770, already mentioned, which became entangled among the satellites of Jupiter, came within this limit. Some have taken alarm at the idea that a comet, by approaching very near to the earth, might raise so high atide, as to endanger the safety of maritime countries especially: but this writer shows, that the comet could not possibly remain more than two hours so near the earth as a fourth part of the moon's distance; and it could not remain even so long, unless it passed the earth under very peculiar circumstances. For example, if its orbit were nearly perpendicular to that of the earth, it could not remain more than half an hour in such a position. Under such circumstances, the production of a tide would be impossible. Eleven hours, at least, would be necessary to enable a comet to produce an effect on the waters of the earth, from which the injurious effects so much dreaded would follow. The final conclusion at which he arrives is, that although, in strict geometrical rigor, it is not physically impossible that a comet should encounter the earth, yet the probability of such an event is absolutely nothing.
M. Arago, also, has investigated the probability of such a collision on the mathematical doctrine of chances, and remarks as follows: "Suppose, now, a comet, of which we know nothing but that, at its perihelion, itwill be nearer the sun than we are, and that its diameter is equal to one fourth that of the earth; the doctrine of chances shows that, out of two hundred and eighty-one millions of cases, there is but one against us; but one, in which the two bodies could meet."
La Place has assigned the consequences that would result from a direct collision between the earth and a comet. "It is easy," says he, "to represent the effects of the shock produced by the earth's encountering a comet. The axis and the motion of rotation changed; the waters abandoning their former position to precipitate themselves towards the new equator; a great part of men and animals whelmed in a universal deluge, or destroyed by the violent shock imparted to the terrestrial globe; entire species annihilated; all the monuments of human industry overthrown;—such are the disasters which the shock of a comet would necessarily produce." La Place, nevertheless, expresses a decided opinion that the orbits of the planets have never yet been disturbed by the influence of comets. Comets, moreover, have been, and are still to some degree, supposed to exercise much influence in the affairs of this world, affecting the weather, the crops, the public health, and a great variety of atmospheric commotions. Even Halley, finding that his comet must have been near the earth at the time of the Deluge, suggested the possibility that the comet caused that event,—an idea which was taken up by Whiston, and formed into a regular theory. In Gregory's Astronomy, an able work, published at Oxford in 1702, the author remarks, that among all nations and in all ages, it has been observed, that the appearance of a comet has always been followed by great calamities; and he adds, "it does not become philosophers lightly to set down these things as fables." Among the various things ascribed to comets by a late English writer, are hot and cold seasons, tempests, hurricanes, violent hail-storms, great falls of snow, heavy rains, inundations, droughts, famines, thick fogs, flies, grasshoppers, plague, dysentery, contagious diseases among animals, sickness among cats, volcanic eruptions, and meteors, or shooting stars. These notions are too ridiculous to require a distinct refutation; and I will only add, that we have no evidence that comets have hitherto ever exercised the least influence upon the affairs of this world; and we still remain in darkness, with respect to their physical nature, and the purposes for which they were created.
"Oft shalt thou see, ere brooding storms arise,Star after star glide headlong down the skies,And, where they shot, long trails of lingering lightSweep far behind, and gild the shades of night."—Virgil.
"Oft shalt thou see, ere brooding storms arise,Star after star glide headlong down the skies,And, where they shot, long trails of lingering lightSweep far behind, and gild the shades of night."—Virgil.
Fewsubjects of astronomy have excited a more general interest, for several years past, than those extraordinary exhibitions of shooting stars, which have acquired the name of meteoric showers. My reason for introducing the subject to your notice, in this place, is, that these small bodies are, as I believe, derived from nebulous or cometary bodies, which belong to the solar system, and which, therefore, ought to be considered, before we take our leave of this department of creation, and naturally come next in order to comets.
The attention of astronomers was particularly directed to this subject by the extraordinary shower of meteors which occurred on the morning of the thirteenth of November, 1833. I had the good fortune to witness these grand celestial fire-works, and felt a strong desire that a phenomenon, which, as it afterwards appeared, was confined chiefly to North America, should here command that diligent inquiry into its causes, which so sublime a spectacle might justly claim.
As I think you were not so happy as to witness this magnificent display, I will endeavor to give you some faint idea of it, as it appeared to me a little before daybreak. Imagine a constant succession of fire-balls, resembling sky-rockets, radiating in all directions from a point in the heavens a few degrees southeast of the zenith, and following the arch of the sky towards the horizon. They commenced their progress at different distances from the radiating point; but their directions were uniformly such, that the lines they described, if produced upwards, would all have met in the same part of the heavens. Around this point, or imaginary radiant, was a circular space of several degrees, within which no meteors were observed. The balls, as they travelled down the vault, usually left after them a vivid streak of light; and, just before they disappeared, exploded, or suddenly resolved themselves into smoke. No report of any kind was observed, although we listened attentively.
Beside the foregoing distinct concretions, or individual bodies, the atmosphere exhibitedphosphoric lines, following in the train of minute points, that shot off in the greatest abundance in a northwesterly direction. These did not so fully copy the figure of the sky, but moved in paths more nearly rectilinear, and appeared to be much nearer the spectator than the fire-balls. The light of their trains was also of a paler hue, not unlike that produced by writing with a stick of phosphorus on the walls of a dark room. The number of these luminous trains increased and diminished alternately, now and then crossing the field of view, like snow drifted before the wind, although, in fact, their course was towards the wind.
From these two varieties, we were presented with meteors of various sizes and degrees of splendor: some were mere points, while others were larger and brighter than Jupiter or Venus; and one, seen by a credible witness, at an earlier hour, was judged to be nearly as large as the moon. The flashes of light, although less intense than lightning, were so bright, as to awaken people in their beds. One ball that shot off in the northwest direction, and exploded a little northward ofthe star Capella, left, just behind the place of explosion, a phosphorescent train of peculiar beauty. This train was at first nearly straight, but it shortly began to contract in length, to dilate in breadth, and to assume the figure of a serpent drawing itself up, until it appeared like a small luminous cloud of vapor. This cloud was borne eastward, (by the wind, as was supposed, which was blowing gently in that direction,) opposite to the direction in which the meteor itself had moved, remaining in sight several minutes. The point from which the meteors seemed to radiate kept a fixed position among the stars, being constantly near a star in Leo, called Gamma Leonis.
Such is a brief description of this grand and beautiful display, as I saw it at New Haven. The newspapers shortly brought us intelligence of similar appearances in all parts of the United States, and many minute descriptions were published by various observers; from which it appeared, that the exhibition had been marked by very nearly the same characteristics wherever it had been seen. Probably no celestial phenomenon has ever occurred in this country, since its first settlement, which was viewed with so much admiration and delight by one class of spectators, or with so much astonishment and fear by another class. It strikingly evinced the progress of knowledge and civilization, that the latter class was comparatively so small, although it afforded some few examples of the dismay with which, in barbarous ages of the world, such spectacles as this were wont to be regarded. One or two instances were reported, of persons who died with terror; many others thought the last great day had come; and the untutored black population of the South gave expression to their fears in cries and shrieks.
After collecting and collating the accounts given in all the periodicals of the country, and also in numerous letters addressed either to my scientific friends or to myself, the following appeared to be theleading factsattending the phenomenon. The shower pervaded nearly the whole of North America, having appeared in nearly equal splendor from the British possessions on the north to the West-India Islands and Mexico on the south, and from sixty-one degrees of longitude east of the American coast, quite to the Pacific Ocean on the west. Throughout this immense region, the duration was nearly the same. The meteors began to attract attention by their unusual frequency and brilliancy, fromnine to twelveo'clock in the evening; were most striking in their appearance fromtwo to five;arrived at their maximum, in many places, aboutfouro'clock; and continued until rendered invisible by the light of day. The meteors moved either in right lines, or in such apparent curves, as, upon optical principles, can be resolved into right lines. Their general tendency was towards the northwest, although, by the effect of perspective, they appeared to move in various directions.
Such were the leading phenomena of the great meteoric shower of November 13, 1833. For a fuller detail of the facts, as well as of the reasonings that were built on them, I must beg leave to refer you to some papers of mine in the twenty-fifth and twenty-sixth volumes of the American Journal of Science.
Soon after this wonderful occurrence, it was ascertained that a similar meteoric shower had appeared in 1799, and, what was remarkable, almost at exactly the same time of year, namely, on the morning of the twelfth of November; and we were again surprised as well as delighted, at receiving successive accounts from different parts of the world of the phenomenon, as having occurred on the morning of the same thirteenth of November, in 1830, 1831, and 1832. Hence this was evidently an event independent of the casual changes of the atmosphere; for, having a periodical return, it was undoubtedly to be referred to astronomical causes, and its recurrence, at a certain definite period of the year, plainly indicatedsomerelation to the revolution of the earth around the sun. It remained, however, todevelope the nature of this relation, by investigating, if possible, the origin of the meteors. The views to which I was led on this subject suggested the probability that the same phenomenon would recur on the corresponding seasons of the year, for at least several years afterwards; and such proved to be the fact, although the appearances, at every succeeding return, were less and less striking, until 1839, when, so far as I have heard, they ceased altogether.
Mean-while, two other distinct periods of meteoric showers have, as already intimated, been determined; namely, about the ninth of August, and seventh of December. The facts relative to the history of these periods have been collected with great industry by Mr. Edward C. Herrick; and several of the most ingenious and most useful conclusions, respecting the laws that regulate these singular exhibitions, have been deduced by Professor Twining. Several of the most distinguished astronomers of the Old World, also, have engaged in these investigations with great zeal, as Messrs. Arago and Biot, of Paris; Doctor Olbers, of Bremen; M. Wartmann, of Geneva; and M. Quetelet, of Brussels.
But you will be desirous to learn what are theconclusionswhich have been drawn respecting these new and extraordinary phenomena of the heavens. As the inferences to which I was led, as explained in the twenty-sixth volume of the 'American Journal of Science,' have, at least in their most important points, been sanctioned by astronomers of the highest respectability, I will venture to give you a brief abstract of them, with such modifications as the progress of investigation since that period has rendered necessary.
The principal questions involved in the inquiry were the following:—Was theoriginof the meteors within the atmosphere, or beyond it? What was theheightof the place above the surface of the earth? By whatforcewere the meteors drawn or impelled towards the earth? In whatdirectionsdid they move? With whatvelocity? What was the cause of theirlightandheat? Of whatsizewere the larger varieties? At what height above the earth did theydisappear? What was the nature of theluminous trainswhich sometimes remained behind? Whatsort of bodieswere the meteors themselves; of whatkind of matterconstituted; and in what manner did they existbefore they fell to the earth? Finally, whatrelationsdid the source from which they emanated sustain to our earth?
In the first place,the meteors had their origin beyond the limits of our atmosphere. We know whether a given appearance in the sky is within the atmosphere or beyond it, by this circumstance: all bodies near the earth, including the atmosphere itself, have a common motion with the earth around its axis from west to east. When we see a celestial object moving regularly from west to east, at the same rate as the earth moves, leaving the stars behind, we know it is near the earth, and partakes, in common with the atmosphere, of its diurnal rotation: but when the earth leaves the object behind; or, in other words, when the object moves westward along with the stars, then we know that it is so distant as not to participate in the diurnal revolution of the earth, and of course to be beyond the atmosphere. The source from which the meteors emanated thus kept pace with the stars, and hence was beyond the atmosphere.
In the second place,the height of the place whence the meteors proceeded was very great, but it has not yet been accurately determined. Regarding the body whence the meteors emanated after the similitude of a cloud, it seemed possible to obtain its height in the same manner as we measure the height of a cloud, or indeed the height of the moon. Although we could not see the body itself, yet the part of the heavens whence the meteors came would indicate its position. This point we called theradiant; and the question was, whether the radiant was projected by distant observers on different parts of the sky; that is, whether it had anyparallax. I took much pains to ascertain the truth of this matter, by corresponding with variousobservers in different parts of the United States, who had accurately noted the position of the radiant among the fixed stars, and supposed I had obtained such materials as would enable us to determine the parallax, at least approximately; although such discordances existed in the evidence as reasonably to create some distrust of its validity. Putting together, however, the best materials I could obtain, I made the height of the radiant above the surface of the earthtwenty-two hundred and thirty-eight miles. When, however, I afterwards obtained, as I supposed, some insight into the celestial origin of the meteors, I at once saw that the meteoric body must be much further off than this distance; and my present impression is, that we have not the means of determining what its height really is. We may safely place it at many thousand miles.
In the third place, with respect to theforceby which the meteors weredrawnor impelled towards the earth, my first impression was, that they fell merely by the force ofgravity; but the velocity which, on careful investigation by Professor Twining and others, has been ascribed to them, is greater than can possibly result from gravity, since a body can never acquire, by gravity alone, a velocity greater than about seven miles per second. Some other cause, beside gravity, must therefore act, in order to give the meteors so great an apparent velocity.
In the fourth place,the meteors fell towards the earth in straight lines, and in directions which, within considerable distances, were nearly parallel with each other. The courses are inferred to have been instraight lines, because no others could have appeared to spectators in different situations to have described arcs of great circles. In order to be projected into the arc of a great circle, the line of descent must be in a plane passing through the eye of the spectator; and the intersection of such planes, passing through the eyes of different spectators, must be straight lines. The lines of direction are inferred to have beenparallel, on account of their apparent radiation from one point, thatbeing the vanishing point of parallel lines. This may appear to you a little paradoxical, to infer that lines are parallel, because theydivergefrom one and the same point; but it is a well-known principle of perspective, that parallel lines, when continued to a great distance from the eye, appear to converge towards the remoter end. You may observe this in two long rows of trees, or of street lamps.
Fig. 69.Fig. 69.
Some idea of the manner in which the meteors fell, and of the reason of their apparent radiation from a common point, may be gathered from the annexed diagram. Let A B C, Fig. 69, represent the vault of thesky, the centre of which, D, being the place of the spectator. Let 1, 2, 3, &c., represent parallel lines directed towards the earth. A luminous body descending through 1´ 1, coinciding with the line D E, coincident with the axis of vision, (or the line drawn from the meteoric body to the eye,) would appear stationary all the while at 1´, because distant bodies always appear stationary when they are moving either directly towards us or directly from us. A body descending through 2 2, would seem to describe the short arc 2´ 2´, appearing to move on the concave of the sky between the lines drawn from the eye to the two extremities of its line of motion; and, for a similar reason, a body descending through 3 3, would appear to describe the larger arc 3´ 3´. Hence, those meteors which fell nearer to the axis of vision, would describe shorter arcs, and move slower, while those which were further from the axis and nearer the horizon would appear to describe longer arcs, and to move with greater velocity; the meteors would all seem to radiate from a common centre, namely, the point where the axis of vision met the celestial vault; and if any meteor chanced to move directly in the line of vision, it would be seen as a luminous body, stationary, for a few seconds, at the centre of radiation. To see how exactly the facts, as observed, corresponded to these inferences, derived from the supposition that the meteors moved inparallel lines, take the following description, as given immediately after the occurrence, by Professor Twining. "In the vicinity of the radiant point, a few star-like bodies were observed, possessing very little motion, and leaving very little length of trace. Further off, the motions were more rapid and the traces longer; and most rapid of all, and longest in their traces, were those which originated but a few degrees above the horizon, and descended down to it."
In the fifth place, had the meteors come from a point twenty-two hundred and thirty-eight miles from the earth, and derived their apparent velocity from gravityalone, then it would be found, by a very easy calculation, that their actual velocity was about four miles per second; but, as already intimated, the velocity observed was estimated much greater than could be accounted for on these principles; not less, indeed, than fourteen miles per second, and, in some instances, much greater even than this. The motion of the earth in its orbit is about nineteen miles per second; and the most reasonable supposition we can make, at present, to account for the great velocity of the meteors, is, that they derived a relative motion from the earth's passing rapidly by them,—a supposition which is countenanced by the fact that they generally tendedwestwardcontrary to the earth's motion in its orbit.
In the sixth place,the meteors consisted of combustible matter, and took fire, and were consumed, in traversing the atmosphere. That these bodies underwent combustion, we had the direct evidence of the senses, inasmuch as we saw them burn. That they took fire in theatmosphere, was inferred from the fact that they were not luminous in their original situations in space, otherwise, we should have seen the body from which they emanated; and had they been luminous before reaching the atmosphere, we should have seen them for a much longer period than they were in sight, as they must have occupied a considerable time in descending towards the earth from so great a distance, even at the rapid rate at which they travelled. The immediate consequence of the prodigious velocity with which the meteors fell into the atmosphere must be a powerful condensation of the air before them, retarding their progress, and producing, by a sudden compression of the air, a great evolution of heat. There is a little instrument called theair-match, consisting of a piston and cylinder, like a syringe, in which we strike a light by suddenly forcing down the piston upon the air below. As the air cannot escape, it is suddenly compressed, and gives a spark sufficient to light a piece of tinder at the bottom of the cylinder. Indeed, it is a well-known fact, that, whenever air is suddenly and forcibly compressed, heat is elicited; and, if by such a compression as may be given by the hand in the air-match, heat is evolved sufficient to fire tinder, what must be the heat evolved by the motion of a large body in the atmosphere, with a velocity so immense. It is common to resort to electricity as the agent which produces the heat and light of shooting stars; but even were electricity competent to produce this effect, its presence, in the case before us, is not proved; and its agency is unnecessary, since so swift a motion of the meteors themselves, suddenly condensing the air before them, is both a known and adequate cause of an intense light and heat. A combustible body falling into the atmosphere, under such circumstances, would become speedily ignited, but could not burn freely, until it became enveloped in air of greater density; but, on reaching the lower portions of the atmosphere, it would burn with great rapidity.
In the seventh place,some of the larger meteors must have been bodies of great size. According to the testimony of various individuals, in different parts of the United States, a few fire-balls appeared as large as the full moon. Dr. Smith, (then of North Carolina, but since surgeon-general of the Texian army,) who was travelling all night on professional business, describes one which he saw in the following terms: "In size it appeared somewhat larger than the full moon rising. I was startled by the splendid light in which the surrounding scene was exhibited, rendering even small objects quite visible; but I heard no noise, although every sense seemed to be suddenly aroused, in sympathy with the violent impression on the sight." This description implies not only that the body was very large, but that it was at a considerable distance from the spectator. Its actual size will depend upon the distance; for, as it appeared under the same angle as the moon, its diameter will bear the same ratio to the moon's, as its distance bears to the moon's distance.We could, therefore, easily ascertain how large it was, provided we could find how far it was from the observer. If it was one hundred and ten miles distant, its diameter was one mile, and in the same proportion for a greater or less distance; and, if only at the distance of one mile, its diameter was forty-eight feet. For a moderate estimate, we will suppose it to have been twenty-two miles off; then its diameter was eleven hundred and fifty-six feet. Upon every view of the case, therefore, it must be admitted, that these were bodies of great size, compared with other objects which traverse the atmosphere. We may further infer the great magnitude of some of the meteors, from the dimensions of the trains, or clouds, which resulted from their destruction. These often extended over several degrees, and at length were borne along in the direction of the wind, exactly in the manner of a small cloud.
It was an interesting problem to ascertain, if possible, the height above the earth at which these fire-balls exploded, or resolved themselves into a cloud of smoke. This would be an easy task, provided we could be certain that two or more distant observers could be sure that both saw the same meteor; for as each would refer the place of explosion, or the position of the cloud that resulted from it, to a different point of the sky, a parallax would thus be obtained, from which the height might be determined. The large meteor which is mentioned in my account of the shower, (see page 348,) as having exploded near the star Capella, was so peculiar in its appearance, and in the form and motions of the small cloud which resulted from its combustion, that it was noticed and distinguished by a number of observers in distant parts of the country. All described the meteor as exhibiting, substantially, the same peculiarities of appearance; all agreed very nearly in the time of its occurrence; and, on drawing lines, to represent the course and direction of the place where it exploded to the view of each of the observers respectively, these lines met in nearly one and the same point, and that was over the place where it was seen in the zenith. Little doubt, therefore, could remain, that all saw the same body; and on ascertaining, from a comparison of their observations, the amount of parallax, and thence deducing its height,—a task which was ably executed by Professor Twining,—the following results were obtained: that this meteor, and probably all the meteors, entered the atmosphere with a velocity not less, but perhaps greater, thanfourteen miles in a second; that they became luminous many miles from the earth,—in this case, overeighty miles; and became extinct high above the surface,—in this case, nearlythirty miles.
In the eighth place,the meteors were combustible bodies, and were constituted of light and transparent materials. The fact that they burned is sufficient proof that they belonged to the class ofcombustiblebodies; and they must have been composed of verylight materials, otherwise their momentum would have been sufficient to enable them to make their way through the atmosphere to the surface of the earth. To compare great things with small, we may liken them to a wad discharged from a piece of artillery, its velocity being supposed to be increased (as it may be) to such a degree, that it shall take fire as it moves through the air. Although it would force its way to a great distance from the gun, yet, if not consumed too soon, it would at length be stopped by the resistance of the air. Although it is supposed that the meteors did in fact slightly disturb the atmospheric equilibrium, yet, had they been constituted of dense matter, like meteoric stones, they would doubtless have disturbed it vastly more. Their own momentum would be lost only as it was imparted to the air; and had such a number of bodies,—some of them quite large, perhaps a mile in diameter, and entering the atmosphere with a velocity more than forty times the greatest velocity of a cannon ball,—had they been composed of dense, ponderousmatter, we should have had appalling evidence of this fact, not only in the violent winds which they would have produced in the atmosphere, but in the calamities they would have occasioned on the surface of the earth. The meteors weretransparentbodies; otherwise, we cannot conceive why the body from which they emanated was not distinctly visible, at least by reflecting the light of the sun. If only the meteors which were known to fall towards the earth had been collected and restored to their original connexion in space, they would have composed a body of great extent; and we cannot imagine a body of such dimensions, under such circumstances, which would not be visible, unless formed of highly transparent materials. By these unavoidable inferences respecting the kind of matter of which the meteors were composed, we are unexpectedly led to recognise a body bearing, in its constitution, a strong analogy to comets, which are also composed of exceedingly light and transparent, and, as there is much reason to believe, of combustible matter.
We now arrive at the final inquiry,what relations did the body which afforded the meteoric shower sustain to the earth? Was it of the nature of a satellite, or terrestrial comet, that revolves around the earth as its centre of motion? Was it a collection of nebulous, or cometary matter, which the earth encountered in its annual progress? or was it a comet, which chanced at this time to be pursuing its path along with the earth, around their common centre of motion? It could not have been of the nature of a satellite to the earth, (or one of those bodies which are held by some to afford the meteoric stones, which sometimes fall to the earth from huge meteors that traverse the atmosphere,) because it remained so long stationary with respect to the earth. A body so near the earth as meteors of this class are known to be, could not remain apparently stationary among the stars for a moment; whereas the body in question occupied the same position, withhardly any perceptible variation, for at least two hours. Nor can we suppose that the earth, in its annual progress, came into the vicinity of anebula, which was either stationary, or wandering lawless through space. Such a collection of matter could not remain stationary within the solar system, in an insulated state, for, if not prevented by a motion of its own, or by the attraction of some nearer body, it would have proceeded directly towards the sun; and had it been in motion in any other direction than that in which the earth was moving, it would soon have been separated from the earth; since, during the eight hours, while the meteoric shower was visible, the earth moved in its orbit through the space of nearly five hundred and fifty thousand miles.
The foregoing considerations conduct us to the following train of reasoning. First, if all the meteors which fell on the morning of November 13, 1833, had been collected and restored to their original connexion in space, they would of themselves have constituted a nebulous body of great extent; but we have reason to suppose that they, in fact, composed but a small part of the mass from which they emanated, since, after the loss of so much matter as proceeded from it in the great meteoric shower of 1799, and in the several repetitions of it that preceded the year 1833, it was still capable of affording so copious a shower on that year; and similar showers, more limited in extent, were repeated for at least five years afterwards. We are therefore to regard the part that descended only asthe extreme portions of a body or collection of meteors, of unknown extent, existing in the planetary spaces.
Secondly, since the earth fell in with this body in the same part of its orbit, for several years in succession, it must either have remained there while the earth was performing its whole revolution around the sun, or it must itself have had a revolution, as well as the earth. But I have already shown that it could not have remained stationary in that part of space; therefore,it must have had a revolution around the sun.
Thirdly, its period of revolution must have either been greater than the earth's, equal to it, or less. It could not have been greater, for then the two bodies could not have been together again at the end of the year, since the meteoric body would not have completed its revolution in a year. Its period might obviously be the same as the earth's, for then they might easily come together again after one revolution of each; although their orbits might differ so much in shape as to prevent their being together at any intermediate point. But the period of the body might also be less than that of the earth, provided it were somealiquot part of a year, so as to revolve just twice, or three times, for example, while the earth revolves once. Let us suppose that the period is one third of a year. Then, since we have given the periodic times of the two bodies, and the major axis of the orbit of one of them, namely, of the earth, we can, by Kepler's law, find the major axis of the other orbit; for the square of the earth's periodic time 12is to the square of the body's time (1⁄3)2as the cube of the major axis of the earth's orbit is to the cube of the major axis of the orbit in question. Now, the three first terms of this proportion are known, and consequently, it is only to solve a case in the simple rule of three, to find the term required. On making the calculation, it is found, that the supposition of a periodic time of only one third of a year gives an orbit of insufficient length; the whole major axis would not reach from the sun to the earth; and consequently, a body revolving in it could never come near to the earth. On making trial of six months, we obtain an orbit which satisfies the conditions, being such as is represented by the diagram on page 362, Fig. 69´, where the outer circle denotes the earth's orbit, the sun being in the centre, and the inner ellipse denotes the path of the meteoric body. The two bodies are together at the top of the figure, being the place of the meteoric body's aphelion on the thirteenth of November, and the figures 10, 20, &c., denote the relative positionsof the earth and the body for every ten days, for a period of six months, in which time the body would have returned to its aphelion.