Physiologia Kircheriana Experimentalis

SECTION II.

On the motion of pendulums, or on the motion of acceleration.

PRAGMATIA I.

To measure the heights of things by means of pendulums.

Let there be, for example, a rope with a lamp attached, which is let down through a dome into the lower part of a temple, and let someone wish to know the height of the dome from the ground. You must first have a thread of one foot in length prepared with a lead weight; having obtained this, proceed as follows. Note how many vibrations the one-foot thread makes while the rope being tested makes one vibration; and I find, for example, that the smaller one-foot thread makes eight vibrations, that is, it runs and returns eight times, while the larger rope runs and returns once. You shall then multiply the eight vibrations by themselves, that is, square them, and you will have 64, the desired height of the dome to the end of the lamp; if you add to this the height from the end of the larger rope to the surface of the floor, you will have the total height; since we showed above that the motion of pendulums is in the duplicate ratio of the times, it necessarily follows that the eight times, which the smaller thread measures eight times over in its course and return, when multiplied by themselves, assign the height.

Hence it follows that from the table placed here, the height of any things whatsoever can be measured without any trouble, with the aid of only a one-foot thread; for if you find your thread to run and return six times for one vibration of the rope, the number in the second column opposite the 6 in the first column will give you the desired height, namely 36 feet; if it returns ten times, you will have a height of 100 feet; if twenty times, 400; if thirty times, 900; if finally it runs and returns forty times, you will have a height of 1600 feet, even though you would scarcely find a rope of such length.

But if you desire to know how many vibrations a one-foot thread makes for any given height, take any square number, and its root will give the desired result. For example, let someone desire to know how many vibrations the smaller thread makes while the larger rope, 3600 long, makes one vibration. Extract the root from 3600 and you will have 60, the vibrations in the smaller thread sought. Let the rope be of such length as is the distance from the center to the surface of the earth, namely 16,975,000 feet, which represents the semi-diameter of the earth, and you wish to know how many vibrations the 1-foot thread makes while the rope equal to the semi-diameter of the earth completes one: extract the square root from 16,975,000 and you will have the desired result, namely 4120 + 600 vibrations.

PRAGMATIA II.

To construct another table, so that with the lengths of the ropes shown, it may be known how much time, that is, how many seconds, the vibrations of each of the given ropes last.

This table is constructed thus; let the seconds be placed in the first column in order, as far as you wish, e.g., 60, to which in the second column the squares of the corresponding times will be added; which are indeed had without any trouble, since the second in order multiplied by itself exhibits them; and thus for the first column