The different appearance of the head of the comet, after it has past its perihelion, from what it had before, confirms greatly this opinion of their tails: for smoke raised by a strong heat is blacker and grosser, than when raised by a less; and accordingly the heads of comets, at the same distance from the sun, are observed less bright and shining after the perihelion, than before, as if obscured by such a gross smoke. 15. THE observations of HEVELIUS upon the atmospheres of comets still farther illustrate the same; who relates, that the atmospheres, especially that part of them next the sun, are remarkably contracted when near the sun, and dilated again afterwards. 16. TO give a more full idea of these tails, a rule is laid down by our author, whereby to determine at any time, when the vapour in the extremity of the tail first rose from the head of the comet. By this rule it is found, that the tail does not consist of a fleeting vapour, dissipated soon after it is raised, but is of long continuance; that almost all the vapour, which rose about the time of the perihelion from the comet of 1680, continued to accompany it, ascending by degrees, being succeeded constantly by fresh matter, which rendered the tail contiguous to the comet. From this computation the tails are found to participate of another property of ascending vapours, that, when they ascend with the greatest velocity, they are least incurvated. 17. THE only objection that can be made against this opinion is the difficulty of explaining, how a sufficient quantity of vapour can be raised from the atmosphere of a comet to fill those vast spaces, through which their tails are sometimes extended. This our author removes by the following computation: our air being an elastic fluid, as has been said before[231], is more dense here near the surface of the earth, where it is pressed upon by the whole air above; than it is at a distance from the earth, where it has a less weight incumbent. I have observed, that the density of the air is reciprocally proportional to the compressing weight. From hence our author computes to what degree of rarity the air must be expanded, according to this rule, at an height equal to a semidiameter of the earth: and he finds, that a globe of such air, as we breath here on the surface of the earth, which shall be one inch only in diameter, if it were expanded to the degree of rarity, which the air must have at the height now mentioned, would fill all the planetary regions even to the very sphere of Saturn, and far beyond. Now since the air at a greater height will be still immensly more rarified, and the surface of the atmospheres of comets is usually about ten times the distance from the center of the comet, as the surface of the comet it self, and the tails are yet vastly farther removed from the center of the comet; the vapour, which composes those tails, may very well be allowed to be so expanded, as that a moderate