$$h(t) = H_0 + \sum_{n=1}^{N} A_n \cos(\omega_n t + \phi_n)$$

Equation 1 · History of Computing

The Machine Before Electronics

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Tides are the response of a rotating, irregularly shaped ocean to the gravitational forcing of the Moon and Sun. The forcing is not one periodic term but many, because the relevant astronomical cycles — lunar day, solar day, lunar month, the inclination of the orbits, the precession of the lunar nodes — beat against one another. The insight that made mechanical prediction possible was that the local water level can be written as a constant plus a sum of sinusoids whose frequencies are fixed by astronomy and whose amplitudes and phases are fixed by the harbour: $h(t) = H_0 + \sum_{n=1}^{N} A_n \cos(\omega_n t + \phi_n)$. Here $\omega_n$ is a known astronomical angular frequency, while $A_n$ and $\phi_n$ are constituents determined by…

Meanings in this article

• $A_n$: the while.
• $\omega_n$: a known astronomical angular frequency.
• $\phi_n$: constituents determined by fitting the expression to a record of observed water levels at that specific place.

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