Equation 7 · Part 1 · The Machine Before Electronics

Symbol omega_n

\omega_n

\omega_n

What this part means

a known astronomical angular frequency.

Its job in the formula

omeg $a_n$ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Full expressionSymbol omega_nArticle meaning

Where the article explains it

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 fitting the expression to a record of observed water levels at that specific place.

The passage around this formula

Thomson’s machine implements exactly that division. Each of the ten shafts in the 1872 instrument carries an overhead crank with a pulley pivoted on a parallel axis that is adjustable for the range applying to that place — the amplitude $A_n$ — and each crank can be positioned and clamped to correspond to the required tidal epoch — the phase $\phi_n$ . The shafts are geared so that their periods are proportional to the periods of the tidal constituents — the frequencies $\omega_n$ [ 3 ] . The summing cord performs the $\sum$ . The pen writes h(t) against a moving paper roll while a single crank drives everything at once.

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A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the surrounding passage

[3] William Thomson's Tide Predicting Machine, 1872 ↗

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