“But, papa, why surely the duration of its vibration must depend upon the force which you may happen to give to the chandelier?” “Not in the least; and this brings us at once to the consideration of the most curious and important fact in the history of the pendulum, and for a knowledge of which we are also indebted to Galileo.[34] It is termed _isochronous_[35] property, or that by which all its vibrations, whether great or small, are performed in exactly the same period of time; but that you may be better able to comprehend this subject, attend to the diagram which I have prepared for your instruction. Suppose that the swing or pendulum A B be raised to C, it will, in effect, be raised the perpendicular height E C, and in falling will describe the arc C B; and, in the point B, it will have that velocity which is acquired by descending through C B, or by a body falling freely through the perpendicular C E. This velocity will be sufficient to cause it to ascend through an equal arc B D, to the same height from whence it fell at C; and since the times of ascent and descent are equal, it will describe both these arcs in exactly the same space of time. Having lost all its motion at D, it will again begin to descend by its own gravity; and in the lowest point B it will acquire the same velocity as before, which will cause it to reascend to C; and thus, by ascending and descending, it will perform continual vibrations in the circumference C B D; and, were it not for the resistance of the air, and the friction at the centre of motion A, the vibrations would never cease: but from these obstructions, though small, it happens, that the velocity of the mass of matter at B is a little diminished in every vibration; and consequently it does not return precisely to the same points C or D, but the arcs described continually become shorter and shorter, till at length they grow insensible; and yet the very same time is required for the performance of the shorter as the longer arcs; for, although in the one case the body passes over less space, still its velocity is proportionally decreased. You perceive, then, that in an attempt to ascertain the height of a ceiling by the vibrations of a chandelier, the extent of its swing cannot alter the time which may be required for its completion. And, if you will place your little brother in the swing, you will perceive that he will return to your hand in nearly the same space of time, whether he describes a large or small arc; although this experiment must be considered as extremely rude, since there are many disturbing causes for which the theory cannot possibly make any allowance. I must, moreover, warn you that where the arc described is very considerable, the difference in the time will be greater; for, in order to ensure this property of vibrating through unequal arcs in equal times, it is necessary that the path of the body should describe a peculiar curve, called a cycloid(24), and not the