analogies up to those laws of motion, or to those mechanical principles, which the Author conceived must be their efficient, though latent, causes. The Author was encouraged to this arduous undertaking from the conviction that the analogies would be guides that he could depend upon in the desired discovery.

The only method of proceeding which the proposed discovery would admit of, was to form, à priori, a theory or hypothesis from which all these analogies might be demonstrated, or with which, at least, they would be consistent. This was a matter of imagi

nation or of conjecture.

The Author's first conjecture (and he was so happy as not to have occasion to make a second) was that the vis or affection of gravitation proceeds from the Sun's whole hemisphere to the planets as a cone diminishing towards the planets, and terminat

ing in points or vertices a little beyond them. According to this hypothesis the distances of the planets would be the altitudes of the cones; and these altitudes, the resultants of the forces; the ratio of which being inverse, it was to be inferred that the forces would be inversely as the distances or altitudes; but this did not agree with our analogies, according to which the forces are inversely as the square-roots of the distances.

This discrepancy, however, did not induce the Author to abandon his conjecture as illfounded. He considered that to a certain extent, though not altogether, the deductions from his hypothesis were conformable to the analogy; and he considered that the want of their entire agreement was owing to some disturbing cause. This consideration set the Author upon the discovery of the disturbing cause.

He soon perceived that the action of gravi

tation on the more distant of two planets was less oblique, and therefore greater than the action upon the nearer one, and that the ratio of this action was directly as the distances; this he considered the disturbing cause, and on investigating it he found it to be the case, and therefore that his hypothesis was conformable to the analogy.

In the following work the Author has demonstrated the analogies from general principles, with which his hypothesis is consistent; yet as his theories are pregnant with abundant matter for further speculations, he is aware that they ought not to be admitted without due investigation, lest they should prove to be a check, instead of a furtherance, to science.

London, May, 1842.

AN EXPOSITION,

&c.

THE analogy discovered by Kepler in the beginning of the seventeenth century, viz., that the cubes of the mean distances of the planets from the Sun are as the squares of their periodic times, is found to be invariably consistent with observation, and is therefore so firmly established, as not to admit of any theory or hypothesis being advanced that purports to be at variance with it.

The author of these pages, taking this analogy as his basis, was induced to investigate the subject somewhat further, and in a short tract entitled, "A new Analogy for

determining the distances of the Planets from the Sun, and of the Satellites from their Primaries;" he has shown that the mean velocities of the planets are inversely as the square-roots of their distances from the Sun, and also inversely as the cube-roots of their periodic times; which two analogies, as they confirm that of Kepler, are confirmed by his, and also confirm each other.

The Author was further led to enquire what could be the nature of the force and action of gravitation, so as to produce the analogies which are shown to subsist between the times, distances, and velocities of the planets.

From these investigations (which have been made with the greatest diligence as well as caution) it appears that the Sun's gravitation acts upon the planets as if it emanated from his whole hemisphere, in the figure of a cone, of which his hemisphere is