our table which perform their revolutions, the one in 18,400 centuries, the other in 28,000 centuries, reach at their aphelia to regions of space so remote that their light would require 171 days and 230 days respectively to reach our earth. The comet of 1864 (the last on the list) attains a distance from the sun equal to one-fifth of the distance of the star Alpha Centauri from our system, the distance of this star being assumed to be equal to 200,000 times the mean distance of the sun from the earth. The voyage outward, it is true, takes 1,400,000 years, and the return also 1,400,000 years. It has been said of the comet of 1844 (that of 102,000 years period) that it has left us for depths of space more remote than Vega, Capella, or Sirius. This is not true; it would not be true even for comets with periods measured by millions of years; but there is nothing to prevent it being so for comets which have hyperbolic or parabolic orbits. [Reference is made to certain points in this chapter and in the next, in the editor's "note upon the designation of comets and the catalogue of comets," which will be found at the end of the volume.-ED.] SECTION I. THE NUMBER OF COMETS. Kepler's remark upon the number of comets-Comets observed-Comets calculated and catalogued-Conjecture as to the number of comets which traverse the solar system or belong to it; calculations and estimates of Lambert and Arago-Calculation of the probable number of comets from the actual data; Kepler's remark verified. 'COMETS are as numerous in the heavens,' said Kepler, 'as fishes in the ocean, ut pisces in oceano.' In quoting this comparison of the great astronomer we only follow the invariable custom of all the authors who have hitherto treated the question of the number of comets; but we remark that the expression employed by Kepler is only the result of an opinion which is little more than a conjecture, and that the words ought to be taken in their poetical rather than in their literal sense; but, making allowance for some exaggeration in the expression, we shall see that Kepler was justified in considering the number of comets as very great. Our inquiry, it is evident, must be confined to comets which are liable temporarily to traverse our system, or to revolve for ever about the sun as an integral part of the solar system. Any attempted estimate of comets situated outside this sphere, beyond our range of vision, and exterior to the planets which belong to our group, could not rest upon any certain data. Our calculations and conjectures must be limited to the domain of that which admits of proof, and is strictly within the power |