Σ

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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