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,[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.