Substituting the time, one second, for t, and doing the same with the others, we shall have:
(32.2 ft.)
1 = ————— = 3.2616 feet.
(3.1416)²
Turning this into its equivalent in inches by multiplying by 12, we shall have 39.1393 inches as the length of a one-second pendulum at London.
Now, as the force of gravity varies somewhat with its distance from the center of the earth, we shall find the value of g in the above formula varying slightly, and this will give us slightly different lengths of pendulum at different places. These values have been found to be as follows:
| Inches. | |
| The Equator is | 39 |
| Rio de Janeiro | 39.01 |
| Madras | 39.02 |
| New York | 39.1012 |
| Paris | 39.13 |
| London | 39.14 |
| Edinburgh | 39.15 |
| Greenland | 39.20 |
| North and South Pole | 39.206 |
Now, taking another look at our formula, we shall see that we may get the length of any pendulum by multiplying π (which is 3.1416) by the square of the time required: To find the length of a pendulum to beat three seconds:
3² = 9.
39.1393 × 9 = 352.2537 inches = 29.3544 feet.
A pendulum beating two-thirds of a second, or 90 beats:
(⅔)² = ⁴⁄₉