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 numberof 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.