So he was led by a similar phenomenon to precisely the same opinion about Vesta that has lately been put forth concerning Eros.

The importance of this coincidence is that it tends to revive a remarkable theory of the origin of the asteroids which has long been in abeyance, and, in the minds of many, perhaps discredited.
This theory, which is due to Olbers, begins with the startling assumption that a planet, perhaps as large as Mars, formerly revolving in an orbit situated between the orbits of Mars and Jupiter, was destroyed by an explosion! Although, at first glance, such a catastrophe may appear too wildly improbable for belief, yet it was not the improbability of a world's blowing up that led to a temporary abandonment of Olbers's bold theory.

The great French mathematician Lagrange investigated the explosive force "which would be necessary to detach a fragment of matter from a planet revolving at a given distance from the sun," and published the results in the Connaissance des Temps for 1814.
"Applying his results to the earth, Lagrange found that if the velocity of the detached fragment exceeded that of a cannon ball in the proportion of 121 to 1 the fragment would become a comet with a direct motion; but if the velocity rose in the proportion of 156 to 1 the motion of the comet would be retrograde.

If the velocity was less than in either of these cases the fragment would revolve as a planet in an elliptic orbit.

For any other planet besides the earth the velocity of explosion corresponding to the different cases would vary in the inverse ratio of the square root of the mean distance.