The comets which passed their perihelia in August, 1862, and January, 1866, will ever be memorable in the annals of science, as having led to the discovery of the intimate relationship between comets and meteors. These various bodies found revolving about the sun in very eccentric orbits may all be regarded as similar in their nature and origin, differing mainly in the accidents of magnitude and density. The recent researches, moreover, of Hoek, Leverrier and Schiaparelli, have led to the conclusion that such objects exist in great numbers in the interstellar spaces; that in consequence of the sun's progressive motion they are sometimes drawn towards the centre of our system; and that if undisturbed by any of the large planets they again pass off in parabolas or hyperbolas. When, however, as must sometimes be the case, they approach near Jupiter, Saturn, Uranus or Neptune, their orbits may be transformed into ellipses. Such, doubtless, has been the origin of the periodicity of the August and November meteors, as well as of numerous comets. In the present paper it is proposed to consider the probable consequences of the sun's motion through regions of space in which cosmical matter is widely diffused; to compare these theoretical deductions with the observed phenomena of comets, aerolites and falling stars; and thus, if possible, explain a variety of facts in regard to those bodies, which have hitherto received no satisfactory explanation.