Let us now see under what circumstances the pendulum offers itself as an element of measure. The motion of the earth on its axis from noon to noon of a mean solar day, has been divided from time immemorial, and by very general consent, into 86,400 portions of time called seconds. The length of a pendulum vibrating in one of these portions, is determined by the laws of nature, is invariable under the same parallel, and accessible independently to all men. Like a degree of the meridian, indeed, it varies in its length from the equator to the pole, and like it, too, requires to be reduced to a mean. In seeking a mean in the first case, the 45th degree occurs with unrivalled preferences. It is the mid-way of the celestial ark from the equator to the pole. It is a mean between the two extreme degrees of the terrestrial ark, or between any two equi-distant from it, and it is also a mean value of all its degrees. In like manner, when seeking a mean for the pendulum, the same 45th degree offers itself on the same grounds, its increments being governed by the same laws which determine those of the different degrees of the meridian. In a pendulum loaded with a Bob, some difficulty occurs in finding the centre of oscillation; and consequently the distance between that and the point of suspension. To lessen this, it has been proposed to substitute for the pendulum, a cylindrical rod of small diameter, in which the displacement of the centre of oscillation would be lessened. It has also been proposed to prolong the suspending wire of the pendulum below the Bob, until their centres of oscillation shall coincide. But these propositions not appearing to have received general approbation, we recur to the pendulum, suspended and charged as has been usual. And the rather as the laws which determine the centre of oscillation leave no room for error in finding it, other than that minimum in practice to which all operations are subject in their execution. The other sources of inaccuracy in the length of the pendulum need not be mentioned, because easily guarded against. But the great and decisive superiority of the pendulum, as a standard of measure, is in its accessibility to all men, at all times and in all places. To obtain the second pendulum for 45° it is not necessary to go actually to that latitude. Having ascertained its length in our own parallel, both theory and observation give us a law for ascertaining the difference between that and the pendulum of any other. To make a new measure therefore, or verify an old one, nothing is necessary in any place but a well-regulated time-piece, or a good meridian, and such a knowledge of the subject as is common in all civilized nations.