Читать книгу The Modern Clock. A Study of Time Keeping Mechanism; Its Construction, Regulation and Repair онлайн

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Now we will apply these figures to our pendulum. A body falling in vacuo, in London, moves 32.2 feet in one second. This distance has by common consent among mathematicians been designated as g. The circumference of a circle equals 3.1416 times its diameter. This is represented as π. Now, if we call the time t, we shall have the formula:

t=π√(1/g)

Substituting the time, one second, for t, and doing the same with the others, we shall have:

(32.2 ft.) 1=—————=3.2616feet. (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: