Thirty-seven sounds like an engineer’s joke — why not forty? Why not a hundred? The answer reveals how prediction actually worked: each constituent cost a crank, a shaft, a pair of gears, and friction. Thirty-seven was where ambition met brass. Here are the waves worth paying for.
The big four
M2 — the principal lunar semidiurnal (12.42 h). The moon’s pull, twice daily, the backbone of most tides. Typically the largest single wave; everything else decorates it.
S2 — the principal solar semidiurnal (12.00 h). The sun’s twice-daily wave, about 46% of M2 in the open ocean. M2 plus S2 beating together creates the spring–neap cycle — watch it happen in my animated harmonic sketch.
K1 — luni-solar diurnal (23.93 h). Once-daily wave from the declination of moon and sun. Where K1 and O1 are strong (much of the Pacific, Southeast Asia), days have one big tide instead of two.
O1 — principal lunar diurnal (25.82 h). The moon’s once-daily wave. Together with K1 it produces the “daily inequality” — the morning high that dwarfs the evening one.
Relative sizes are drawn in the bar chart above; remember every port has its own proportions.
The supporting cast
Beyond the big four, analysts recognised: N2 (the moon’s elliptical-orbit companion to M2), K2 (the sun’s companion), P1 (solar diurnal), Q1, the long-period Mf (fortnightly) and Mm (monthly) that raise and lower the whole baseline, and the shallow-water overtides M4, MS4, M6 — children born when estuaries distort M2. By Doodson’s era the catalogue ran past sixty; my Doodson profile explains the numbering system that keeps them straight.
Why Machine No. 2 stopped at 37
Rollin Harris’s team for the US Machine No. 2 selected every constituent that moved the pen more than the machine’s own friction could hide — 37 of them. A 38th crank would have added more drag than signal. It was an honest engineering verdict, not numerology, and it held the world record for decades.
Questions with short answers
Do I need all 37 to understand a tide? No. The big four plus the story of springs and neaps explain 90% of what you see on a beach. Read the beginner’s guide first; come back here when you want names for the waves.
What is a Doodson number? A six-digit code identifying each constituent by its astronomical recipe — Doodson’s Dewey decimal system for tides. The glossary decodes the format.
Why do some places get one tide a day? Where diurnal constituents (K1, O1) outweigh semidiurnal ones (M2, S2), the twice-daily rhythm cancels into a single daily wave. The Gulf of Mexico is the textbook case.
Learn the waves by ear
Next time you are near water, try this: count the highs in 24 hours, and notice whether morning and evening match. Two equal highs — M2 country. One dwarfed — K1 and O1 at work. A fortnight of watching teaches what the bar chart above only promises, and when you come back, Inside Machine No. 2 will read like a parts list for the sea you just watched. The operators who dialled these waves in by hand are waiting in Setting Up a Prediction Run.