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 of the Distances. | Reduced 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,[44] (taking no account of the decrease of gravitation by increase of distance;) so that the diameter of the aërial 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.[45] 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 | 99°.7 | December 7 | 154°.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.