Twice a month the tides swell; twice they shrink. Fishermen, smugglers, and harbour masters have timed their lives to this breathing for millennia. The cause is beautifully simple: two waves — M2 and S2 — sliding in and out of step. Watch it happen in the animated sketch above.
The beating of two waves
M2 (moon, 12.42 h) and S2 (sun, 12.00 h) run at nearly the same speed. Like two almost-identical tuning forks, they drift in and out of phase: aligned at new and full moon, opposed at the quarters. Aligned → their amplitudes add → spring tides (big range). Opposed → they cancel → neap tides (small range). The full mathematics is in my harmonic analysis explainer.
Why “spring”?
Nothing to do with the season — “spring” as in springing up, leaping. The term predates Kelvin’s machines by centuries; the machines simply reproduced what sailors already knew, with numbers attached.
The age of tide
Springs lag a day or two behind new/full moon — the ocean’s inertia, called the age of tide (see glossary). Local friction and basin resonance set the exact lag, which is why every port needed its own analysed constants and its own machine setup.
A fortnight in numbers
Abstraction ends where tables begin. Here is a fortnight at a typical semidiurnal port (fictitious but realistic — modelled on M2 1.8 m, S2 0.6 m), morning high-water heights day by day:
| Day | Moon | Morning high | Character |
|---|---|---|---|
| 1 | new | 4.6 m | springs building |
| 3 | crescent | 4.4 m | springs |
| 5 | first quarter | 3.1 m | easing |
| 7 | gibbous | 2.4 m | neaps |
| 9 | full | 4.7 m | springs |
| 11 | waning | 4.2 m | easing |
| 13 | last quarter | 2.5 m | neaps |
Read the right column down: 4.6 → 2.4 → 4.7 → 2.5. That breathing is M2 and S2 sliding past each other, exactly as the animation above shows. Machine operators read this same envelope off every prediction roll as a first correctness check — a roll that doesn’t breathe is a roll with a wrong setup (see the 1910 ritual).
When springs kill
Springs alone flood nothing — but springs plus a storm surge drown coasts. The North Sea flood of January 1953 rode in on spring tides: the surge stacked atop the fortnight’s highest natural waters and overtopped defences in Britain and the Netherlands, killing over 2,000 people. Hamburg’s 1962 flood struck the same way, near springs. This is why modern surge warnings still quote the underlying astronomical tide first: the machines’ old numbers — M2, S2, and their beating — remain the baseline every warning is built on. The wartime offices that learned this urgency are covered in Tides at War.
Settling doubts
Are spring tides dangerous? They give the highest high waters of the fortnight — the ones that overtop quays combined with surge. Historical flood stories cluster on springs; modern warnings still do.
Do neaps ever disappear? Where diurnal constituents dominate (see M2/S2/K1/O1), the spring–neap rhythm weakens into a daily-inequality rhythm instead. The Gulf of Mexico barely breathes fortnightly at all.
How did machines show this? Automatically — it falls out of the sum. Operators read the swelling and shrinking envelope straight off the prediction roll as a correctness check.
Watch it this month
Check tonight’s moon phase, then predict: near new or full, expect big-range springs within a day or two; near quarters, expect sleepy neaps. Watch the water prove you right — or catch your port’s personal lag, the age of tide, and wonder why. When curiosity sharpens, meet the individual waves in Why 37? and see them embodied in brass in Inside Machine No. 2.