Part 20

+--------------------------------------------------------------------+ | Designations | Periodic | Inclination | Motion | Planetary | | of the Comets. | times. | of | in Orbit. | Intervals. | | | | Major Axes | | | |--------------------------------------------------------------------| |Encke | 1818 | 3 years. | 1d | Direct |Mars & Ceres.| |--------------------------------------------------------------------| |De Vico | 1814 | | 2 | Direct | | |Fayo | 1843 | | 4 | Direct | Ceres | |De Avrest| 1851 | From | 1 | Direct | | |Brorsen | 1846 | five | 7 | Direct | and | |Messier | 1766 | to | 0 | Direct | | |Clausen | 1743 | six | 0 | Direct | Jupiter. | |Pigott | 1783 | or | 4 | Direct | | |Pous | 1819 | seven | 3 | Direct | | |Biela | 1826 | years. | 9 | Direct | | |Blaupain | 1819 | | 2 | Direct | | |Lexell | 1770 | | 1 | Direct | | |--------------------------------------------------------------------| |Pous | 1812 | | 17 | Direct | | |Olbers | 1816 | about | 40 | Direct | Saturn | |De Vico | 1846 | 75 | 13 | Direct | and | |Brorsen | 1847 | years. | 12 | Direct | Uranus. | |Westphal | 1852 | | 21 | Direct | | |Halley | 1682 | | 16 | Retrograde| | +--------------------------------------------------------------------+

From which it appears, that the objection arising from the great inclination of the planes of these orbits is much less important than at first it appears to be.

Regarding then, that a comet's mean distance depends on its mean atomic density, as in the case of the planets, the undue enlargement of their orbits by planetary perturbations is inadmissible. In 1770 Messier discovered a comet which approached nearer the earth than any comet known, and it was found to move in a small ellipse with a period of five and a half years; but although repeatedly sought for, it was the opinion of many, that it has never been since seen. The cause of this seeming anomaly is found by astronomers in the disturbing power of Jupiter,--near which planet the comet must have passed in 1779, but the comet was not seen in 1776 before it passed near Jupiter, although a very close search was kept up about this time. Now there are two suppositions in reference to this body: the comet either moved in a larger orbit previous to 1767, and was then caused by Jupiter to diminish its velocity sufficiently to give it a period of five and a half years, and that after perihelion it recovered a portion of its velocity in endeavoring to get back into its natural orbit; or if moving in the natural orbit in 1770, and by passing near Jupiter in 1779 this orbit was deranged, the comet will ultimately return to that mean distance although not necessarily having elements even approximating those of 1770. In 1844, September 15th, the author discovered a comet in the constellation Cetus, (the same previously discovered by De Vico at Home,) and from positions estimated with the naked eye approximately determined the form of its orbit and its periodic time to be very similar to the lost comet of 1770. These conclusions were published in a western paper in October 1844, on which occasion he expressed the conviction, that this was no other than the comet of 1770. As the question bore strongly on his theory he paid the greater attention to it, and had, previously to this time, often searched in hopes of finding that very comet. Since then, M. Le Verrier has examined the question of identity and given his decision against it; but the author is still sanguine that the comet of 1844 is the same as that of 1770, once more settled at its natural distance from the sun. This comet returns to its perihelion on the 6th of August, 1855, according to Dr. Brunnow, when, it is hoped, the question of identity will be reconsidered with reference to the author's principles; and, that when astronomers become satisfied of this, they will do him the justice of acknowledging that he was the first who gave publicity to the fact, that the "Lost Comet" was found.

That comets do experience a resistance, is undeniable; but not in the way astronomers suppose, if these views be correct. The investigations of Professor Encke, of Berlin, on the comet which bears his name, has determined the necessity of a correction, which has been applied for several returns with apparent success. But there is this peculiarity about it, which adds strength to our theory: "The Constant of Resistance" requires a change after perihelion. The necessity for this change shows the action of the radial stream. From the law of this force, (reckoning on the central plane of the vortex,) there is an outstanding portion, acting as a disturbing power, in the sub-duplicate ratio of the distances inversely. If we only consider the mean or average effect in orbits nearly circular, this force may be considered as an ablatitious force at all distances below the mean, counterbalanced by an opposite effect at all distances above the mean. But when the orbits become very eccentrical, we must consider this force as momentarily affecting a comet's velocity, diminishing it as it approaches the perihelion, and increasing it when leaving the perihelion. A resolution of this force is also requisite for the comet's distance above the central plane of the vortex, and a correction, likewise, for the intensity of the force estimated in that plane. There is also a correction necessary for the perihelion distance, and another for the tangential current; but we are only considering here the general effect. By diminishing the comet's proper velocity in its orbit, if we consider the attraction of the sun to remain the same, the general effect may be (for this depends on the tangential portion of the resolved force preponderating) that the absolute velocity will be increased, and the periodic time shortened; but after passing the perihelion, with the velocity of a smaller orbit, there is also superadded to this already undue velocity, the expulsive power of the radial stream, adding additional velocity to the comet; the orbit is therefore enlarged, and the periodic time increased. Hence the necessity of changing the "Constant of Resistance" after perihelion, and this will generally be found necessary in all cometary orbits, if this theory be true. But this question is one which may be emphatically called the most difficult of dynamical problems, and it may be long before it is fully understood.

According to the calculations of Professor Encke, the comet's period is accelerated about 2 hours, 30 minutes, at each return, which he considers due to a resisting medium. May it not rather be owing to the change of inclination of the major axis of the orbit, to the central plane of the vortex? Suppose the inclination of the plane of the orbit to remain unchanged, and the eccentricity of the orbit also, if the longitude of the perihelion coincides with that of either node, the major axis of the orbit lies in the ecliptic, and the comet then experiences the greatest mean effect from the radial stream; its mean distance is then, ceteris paribus, the greatest. When the angle between the perihelion and the nearest node increases, the mean force of the radial stream is diminished, and the mean distance is diminished also. When the angle is 90d, the effect is least, and the mean distance least. This is supposing the ecliptic the central plane of the vortex. When Encke's formula was applied to Biela's comet, it was inadequate to account for a tenth part of the acceleration; and although Biela moves in a much denser medium, and is of less dense materials, even this taken into account will not satisfy the observations,--making no other change in Encke's formula. We must therefore attribute it to changes in the elements of the orbits of these comets. Now, the effect of resistance should also have been noticed, as an acceleration of Halley's comet in 1835, yet the period was prolonged. To show, that our theory of the cause of these anomalies corresponds with facts, we subjoin the elements in the following tables, taken from Mr. Hind's catalogue:

THE ELEMENTS OF ENCKE'S COMET.

Date of Longitude of Longitude of Difference of Perihelion. Perihelion. nearest Node Longitude. 1822 157d 11' 44" 154d 25' 9" 2d 46' 35" 1825 157 14 31 154 27 30 2 47 1 1829 157 17 53 154 29 32 2 48 21 1832 157 21 1 154 32 9 2 41 52 1835 157 23 29 154 34 59 2 48 30 1838 157 27 4 154 36 41 2 50 23 1842 157 29 27 154 39 10 2 50 17 1845 157 44 21 154 19 33 3 24 48 1848 157 47 8 154 22 12 3 24 56 1852 157 51 2 154 23 21 3 27 41

In this we see a regular increase of the angle, which ought to be attended with a small acceleration of the comet; but the change of inclination of the orbit ought also to be taken into consideration, to get the mean distance of the comet above the plane of the vortex, and, by this, the mean force of the radial stream.

In the following table, the same comparison is made for Biela's comet:--

ELEMENTS OF BIELA'S COMET.

Date of Longitude of Longitude of Difference of Perihelion. Perihelion. nearest Node. Longitude. 1772 110d 14' 54" 74d 0' 1" 36d 14' 53" 1806 109 32 23 71 15 15 38 17 8 1826 109 45 50 71 28 12 38 17 38 1832 110 55 55 68 15 36 41 45 19 1846 109 2 20 65 54 39 43 7 41

Between 1832 and 1846, the increase of the angle is twice as great for Biela as for Encke, and the angle itself throws the major axis of Biela 10d above the ecliptic, whereas the angle made by Encke's major axis, is only about 1d; the cosine of the first angle, diminishes much faster therefore, and consequently the same difference of longitude between the perihelion and node, will cause a greater acceleration of Biela; and according to Prof. Encke's theory, Biela would require a resisting medium twenty-five times greater than the comet of Encke to reconcile observation with the theory. Halley's comet can scarcely be considered to have had an orbit with perfect elements before 1835. If they were known accurately for 1759, we should no doubt find, that the angle between the node and perihelion diminished in the interval between 1750 and 1835, as according to the calculations of M. Rosenberg, the comet was six days behind its time--a fact fatal to the common ideas of a resisting medium; but this amount of error must be received as only approximate.

No comet that has revisited the sun, has given astronomers more trouble than the great comet of 1843. Various orbits have been tried, elliptical, parabolic and hyperbolic; yet none will accord with all the observations. The day before this comet was seen in Europe and the United States, it was seen close to the body of the sun at Conception, in South America; yet this observation, combined with those following, would give an orbital velocity due to a very moderate mean distance. Subsequent observations best accorded with a hyperbolic orbit; and it was in view of this anomaly, that the late Sears C. Walker considered that the comet came into collision with the sun in an elliptical orbit, and its debris passed off again in a hyperbola. That a concussion would not add to its velocity is certain, and the departure in a hyperbolic orbit would be contrary to the law of gravitation. This principle is thus stated by Newton:--"In parabola velocitas ubiquo equalis est velocitati corporis revolventis in circulo ad dimidiam distantiam; in ellipsi minor est in hyperbola major." (Vid. Prin. Lib. 1. Prop. 6 Cor. 7.)

But as regards the fact, it is probable that Mr. Walker's views are correct, so far as the change from an ellipse to an hyperbola is considered. The Conception observation cannot be summarily set aside, and Professor Peirce acknowledges, that "If it was made with anything of the accuracy which might be expected from Captain Ray, it exhibits a decided anomaly in the nature of the forces to which the comet was subjected during its perihelion passage." The comet came up to the sun almost in a straight line against the full force of the radial stream; its velocity must therefore necessarily have been diminished. After its perihelion, its path was directly from the sun, and an undue velocity would be kept up by the auxiliary force impressed upon it by the same radial stream; and hence, the later observations give orbits much larger than the early ones, and there can be no chance of identifying this comet with any of its former appearances, even should its orbit be elliptical. This unexpected confirmation of the theory by the observation of Capt. Ray, cannot easily be surmounted.

We must now endeavor to explain the physical peculiarities of comets, in accordance with the principles laid down. The most prominent phenomenon of this class is the change of diameter of the visible nebulosity. It is a most singular circumstance, but well established as a fact, that a comet contracts in its dimensions on approaching the sun, and expands on leaving it. In 1829, accurate measures were taken on different days, of the diameter of Encke's comet, and again in 1838. The comet of 1618 was also observed by Kepler with this very object, and also the comet of 1807; but without multiplying instances, it may be asserted that it is one of those facts in cometary phenomena, to which there are no exceptions. According to all analogy, the very reverse of this ought to obtain. If a comet is chiefly vaporous, (as this change of volume would seem to indicate,) its approach to the sun ought to be attended by a corresponding expansion by increase of temperature. When the contrary is observed, and invariably so, it ought to be regarded as an index of the existence of other forces besides gravitation, increasing rapidly in the neighborhood of the sun; for the disturbing power of the sun's attraction would be to enlarge the diameter of a comet in proportion to its proximity. Now, the force of the radial stream, as we have shown, is as the 2.5th power of the distances inversely. If this alternate contraction and expansion be due to the action of this force, there ought to be an approximate correspondence of the law of the effect with the law of the cause. Arago, in speaking of the comet of 1829, states, "that between the 28th of October and the 24th of December, the volume of the comet was reduced as 16000 to 1, the change of distance in the meantime only varying about 3 to 1." To account for this, a memoir was published on the subject by M. Valz, in which he supposes an atmosphere around the sun, whose condensation increases rapidly from superincumbent pressure; so that the deeper the comet penetrates into this atmosphere the greater will be the pressure, and the less the volume. In this it is evident, that the ponderous nature of a resisting medium is not yet banished from the schools. In commenting on this memoir, Arago justly observes, that "there would be no difficulty in this if it could be admitted that the exterior envelope of the nebulosity were not permeable to the ether; but this difficulty seems insurmountable, and merits our sincere regret; for M. Valz's ingenious hypothesis has laid down the law of variation of the bulk of the nebulosity, as well for the short-period comet as for that of 1618, with a truly wonderful exactness." Now, if we make the calculation, we shall find that the diameter of the nebulosity of a comet is inversely as the force of the radial stream. This force is inversely as the 2.5 power of the distances from the axis, and not from the sun: it will, therefore, be in the inverse ratio of the cosine of the comet's heliocentric latitude to radius, and to this ratio the comet's distance ought to be reduced. But, this will only be correct for the same plane or for equal distances above the ecliptic plane, considering this last as approximately the central plane of the vortex. From the principles already advanced, the radial stream is far more powerful on the central plane than in more remote planes; therefore, if a comet, by increase of latitude, approaches near the axis, thus receiving a larger amount of force from the radial stream in that plane than pertains to its actual distance from the sun, it will also receive a less amount of force in that plane than it would in the central plane at the same distance from the axis. Now, we do not know the difference of force at different elevations above the central plane of the vortex; but as the two differences due to elevation are contrary in their effects and tend to neutralize each other, we shall make the calculation as if the distances were truly reckoned from the centre of the sun.

The following table is extracted from Arago's tract on Comets, and represents the variations of the diameter of Encke's comet at different distances from the sun,--the radius of the orbis magnus being taken as unity.

Times of observation, Distances of the Real diameters 1828. comet from the sun. in radii of the earth. Oct. 28 1.4617 79.4 Nov. 7 1.3217 64.8 Nov. 30 0.9668 29.8 Dec. 7 0.8473 19.9 Dec. 14 0.7285 11.3 Dec. 24 0.6419 3.1

In order the better to compare the diameters with the force, we will reduce them by making the first numbers equal.

Distances. Diameters. The 2.5th power Reduced of the Distances. Diameters. 1.4617 79.4 2.58 2.58 1.3217 64.8 2.10 2.10 0.9668 29.8 0.92 0.97 0.8473 19.9 0.66 0.65 0.7285 11.3 0.45 0.37 0.5419 3.1 0.21 0.10

This is a very close approximation, when we consider the difficulty of micrometric measurement, and the fact, that as the comet gets nearer to the sun, as at the last date of the table, the diameter is more than proportionally diminished by the fainter nebulosity becoming invisible. But, there may be a reality in the discrepancy apparent at the last date, as the comet was then very near the plane of the ecliptic, and was, consequently, exposed to the more violent action of the radial stream.

To attempt to explain the modus agendi is, perhaps, premature. Our principal aim is to pioneer the way into the labyrinth, and it is sufficient to connect this seeming anomaly with the same general law we have deduced from other phenomena. Still, an explanation may be given in strict accordance with the general principles of the theory.

Admitting the nucleus of a comet to be gaseous, there is no difficulty about the solution. According to Sir John Herschel, "stars of the smallest magnitude remain distinctly visible, though covered by what appears the densest portion of their substances; and since it is an observed fact, that the large comets which have presented the appearance of a nucleus, have yet exhibited no phases, though we cannot doubt that they shine by the reflected solar light, it follows that even these can only be regarded as great masses of thin vapor." That comets shine solely by reflected solar light, is a position that we shall presently question; but that they are masses of vapor is too evident to dispute. According to the same authority quoted above, "If the earth were reduced to the one thousandth part of its actual mass, its coercive power over the atmosphere would be diminished in the same proportion, and in consequence the latter would expand to a thousand times its actual bulk." If this were so, and comets composed of the elementary gases, some of them would have very respectable masses, as the nuclei are frequently not more than 5,000 miles in diameter, and consequently it becomes important to examine the principle. From all experiments the density of an elastic fluid is directly as the compressing force; and if a cylinder reached to the top of our atmosphere, compressed by the gravitation of the earth, considered equal at each end of the cylinder, it would represent the actual compressing force to which it owes its density. If the gravitation of the earth were diminished one thousand times this atmospheric column would expand one thousand times, (taking no account of the decrease of gravitation by increase of distance;) so that the diameter of the aerial globe would be increased to 108,000 miles, taking the atmosphere at 50 miles. But the mere increasing the bulk of the atmosphere 1000 times would increase the diameter to little more than double. Even giving the correct expansion, a comet's mass must be much greater than is generally supposed, or the diameters of the nuclei would be greater if composed of any gas lighter than atmospheric air.

It is very improbable that a comet is composed of only one elementary gas, and if of many, their specific gravities will vary; the lighter, of course, occupying the exterior layers. With such a small mass, therefore, the upper portion of its atmosphere must be very attenuated. Now let us remember that the density of the ether at a comet's aphelion, is greater than at the perihelion, in the direct ratio of the square roots of the distances from the sun nearly. At the aphelion the comet lingers through half his period, giving ample time for the nucleus to be permeated by ether proportionally dense with the surrounding ether of the vortex at that distance. Thus situated, the comet descends to its perihelion, getting faster and faster into a medium far less dense, and there must consequently be an escape from the nucleus, or in common parlance, the comet is positively electric. This escaping ether, in passing through the attenuated layers composing the surface of the nucleus, impels the lighter atoms of cometic dust further from the centre, and as for as this doubly attenuated atmosphere of isolated particles extends, so far will the escaping ether be rendered luminous. It may be objected here, that a contrary effect ought to be produced when the comet is forsaking, its perihelion; but the objection is premature, as the heat received from the sun will have the same effect in increasing the elasticity, as change of density, and the comet will probably part with its internal ether as long as it is visible to the earth; and not fully regain it perhaps, until after it arrives at its aphelion. Suppose that we admit that a comet continues to expand in the same ratio for all distances, as is laid down for the comet of Encke when near its perihelion; it would follow, that the comet of 1811, would have a diameter at its aphelion of fifty millions of millions of miles, that is, its outside would extend one thousand times further from the sun, at the opposite side to that occupied by the centre of the comet, than the distance of the comet's centre from the sun, at its enormous aphelion distance. Such an absurdity shows us that there is a limit of expansion due to natural causes, and that if there were no radial stream the volume of a comet would be greatest when nearest the sun.

But while the comet is shortening its distance and hastening to the sun in the form of a huge globular mass of diffuse light, it is continually encountering another force, increasing in a far more rapid ratio than the law of gravitation. At great distances from the sun, the force of the radial stream was insufficient to detach any portion of the comet's atmosphere; presently, however, the globular form is changed to an ellipsoid, the radial stream begins to strip the comet of that doubly attenuated atmosphere of which we have spoken, and the diameter of the comet is diminished, merely because the luminosity of the escaping ether is terminated at the limit of that atmosphere. Meanwhile the mass of the comet has suffered only an infinitely small diminution; but if the perihelion distance be small, the force may become powerful enough to detach the heavier particles of the nucleus, and thus a comet may suffer in mass by this denudating process. We regard, therefore, the nucleus of a comet to represent the mass of the comet and the coma, as auroral rays passing through a very attenuated envelope of detached particles. The individual gravitating force of these particles to the comet's centre, may be therefore considered as inversely as the squares of the distances, and directly as the density of the particles; and this density will, according to analogical reasoning, be as the distances or square roots of the distances;--grant the last ratio, and the gravitating force of the particles composing the exterior envelope of a comet, becomes inversely as the 2.5th power of the distances from the comet's centre. This being the law of the radial stream, it follows, of course, that a comet's diameter is inversely as the force of the radial stream. It must, however, be borne in mind, that we are speaking of the atomic density, and not of density by compression; for this cometary dust, which renders luminous the escaping ether of the nucleus, must be far too much diffused to merit the name of an elastic fluid. May not the concentric rings, which were so conspicuous in the comet of 1811, be owing to differences in the gravitating forces of such particles, sifted, as it were, and thus arranged, according to some ratio of the distances, by the centripulsive force of the electric coma, leaving vacant intervals, through which the ether passed without becoming luminous? This at least is the explanation given by our theory. We may, indeed, consider it possible that the escaping ether, when very intense, might be rendered luminous by passing into the surrounding ether, and, as it became more diffused by radiation, at last become invisible. In this case, as the law of radiation is as the squares of the distances from the centre inversely, the rays would be more and more bent at right angles, or apparently shortened, as the power of the radial stream increased, and the apparent diameters of the coma would be diminished faster than the ratio of the 2.5th power of the distances. But whichever view we adopt, the diameter would again increase in the same ratio on leaving the sun, if we make allowance for increase of temperature, as well as for diminution of density, for the ordinary distance of a comet's visibility. We, however, regard the change of diameter, as due to both these nodes of action, as best agreeing with the indications afforded by their tails.

From the preceding remarks, it results that the density of the particles producing the nebulous envelope of a comet, renders the variations of diameter only approximate to the law of the radial stream; a comet's own electric energy, or the intensity of the escaping ether, may also modify this expression, and many other causes may be suggested. That the radial stream is the cause, in the way we have pointed out, is proved by the positions of the major axis of the short-period comet, making frequently nearly a right angle with the radius vector of the orbit in 1828. A soap bubble gently blown aside, without detaching it from the pipe, will afford a good illustration of the mode, and a confirmation of the cause. The angles measured by Struve, reckoned from the radius vector, prolonged towards the sun, are subjoined:

November 7 99d.7 | December 7 154d.0 November 30 145 .3 | December 14 149 .4

At this last date, the comet was getting pretty close to the sun. When the angle was greater, as on November 7th, the comet appeared to make almost a right angle with the radius vector; and in this position of the earth and comet, the longer axis of the elliptical comet was directed to the axis of the vortex, as may be verified by experiment. At the later dates, the comet was more rapidly descending, and, at the same time, the axis of the comet was getting more directed towards the earth; so that the angle increased between this axis and the radius vector, and consequently became more coincident with it. We have now to consider the luminous appendage of a comet, commonly called a tail.

The various theories hitherto proposed to account for this appendage are liable to grave objections. That it is not refracted light needs not a word of comment. Newton supposes the tail to partake of the nature of vapor, rising from the sun by its extreme levity, as smoke in a chimney, and rendered visible by the reflected light of the sun. But, how vapor should rise towards opposition in a vacuum, is utterly inexplicable. In speaking of the greater number of comets near the sun than on the opposite side, he observes: "Hinc etiam manifestum est quod coeli resistentia destituuntur." And again, in another place, speaking of the tail moving with the same velocity of the comet, he says: "Et hinc rursus colligitur spatia coelestia vi resistendi destitui; utpote in quibus non solum solida planetarum et cometarum corpora, sed etiam rarissimi candarum vapores motus suos velocissimos liberrime peragunt ac diutissime conservant." On what principle, therefore, Newton relied to cause the vapors to ascend, does not appear. Hydrogen rises in our atmosphere because specifically lighter. If there were no atmosphere, hydrogen would not rise, but merely expand on all sides. But, a comet's tail shoots off into space in a straight line of one hundred millions of miles, and frequently as much as ten millions of miles in a single day, as in the case of the comet of 1843. Sir John Herschel observes, that "no rational or even plausible account has yet been rendered of those immensely luminous appendages which they bear about with them, and which are known as their tails." Yet, he believes, and astronomers generally believe, that a comet shines by reflected light. This theory of reflexion is the incubus which clogs the question with such formidable difficulties; for, it follows, that the reflecting matter must come from the comet. But, what wonderful elements must a comet be made of, to project themselves into space with such immense velocity, and in such enormous quantities as to exceed in volume the body from which they emanate many millions of times. This theory may be, therefore, safely rejected.