The theory of an exploded planet now seemed to have everything in its favour. It required that the mean or average distances of the newly-discovered bodies should be nearly the same, but admitted a wide range of variety in the shapes and positions of their orbits, provided always that they preserved common points of intersection. These conditions were fulfilled with a striking approach to exactness. Three of the four "asteroids" (a designation introduced by Sir. W. Herschel[207]) conformed with very approximate precision to "Bode's law" of distances; they all traversed, in their circuits round the sun, nearly the same parts of Cetus and Virgo; while the eccentricities and inclinations of their paths departed widely from the planetary type--that of Pallas, to take an extreme instance, making with the ecliptic an angle of nearly 35°. The minuteness of these bodies appeared further to strengthen the imputation of a fragmentary character. Herschel estimated the diameter of Ceres at 162, that of Pallas at 147 miles.[208] But these values are now known to be considerably too small. A suspected variability of brightness in some of the asteroids, somewhat hazardously explained as due to the irregularities of figure to be expected in cosmical _potsherds_ (so to speak), was added to the confirmatory evidence.[209] The strong point of the theory, however, lay not in what it explained, but in what it had predicted. It had been twice confirmed by actual exploration of the skies, and had produced, in the recognition of Vesta, the first recorded instance of the _premeditated_ discovery of a heavenly body. The view not only commended itself to the facile imagination of the unlearned, but received the sanction of the highest scientific authority. The great Lagrange bestowed upon it his analytical _imprimatur_, showing that the explosive forces required to produce the supposed catastrophe came well within the bounds of possibility; since a velocity of less than twenty times that of a cannon-ball leaving the gun's mouth would have sufficed, according to his calculation, to launch the asteroidal fragments on their respective paths. Indeed, he was disposed to regard the hypothesis of disruption as more generally available than its author had designed it to be, and proposed to supplement with it, as explanatory of the eccentric orbits of comets, the nebular theory of Laplace, thereby obtaining, as he said, "a complete view of the origin of the planetary system more conformable to Nature and mechanical laws than any yet proposed."[210]