You can feel what Kelvin’s operators felt — with cardboard, string, and pocket change. This two-constituent adder reproduces the exact principle of the brass pulley cascade: two “cranks” waving, one string summing, a pencil drawing the tide.
Parts list
Corrugated cardboard, three metres of smooth string, two cardboard discs (15 cm and 14 cm — nearly the same size, like M2 and S2), four drawing pins, two washers, a pencil, tape, a ruler, and a patient friend (one cranks, one reads).
Build steps
1. The cranks. Pin each disc to a cardboard backboard through its centre so it spins. Punch a hole near each rim, tie a short string loop through it — these are your crank pins. Set both pins at the same radius first (equal amplitudes, like springs).
2. The floating pulley. Thread the long string: tie one end to crank A’s loop, run it down around a washer hanging free, up over a drawing-pin “guide” at the top, down around a second free washer, and tie the end to crank B’s loop. The washers are your floating pulleys.
3. The pen. Tape the pencil to the meeting point between the washers so its tip touches a paper strip pinned beside the board.
4. Run springs. Turn both discs together in the same direction at the same speed — the pencil draws a big wave (M2 + S2 aligned: spring tide).
5. Run neaps. Turn them in opposite phase — one pin up while the other is down — and watch the pencil barely move. You have just computed a neap tide with string.
What it teaches
Friction is the whole lesson: sticky washers swallow the small motions first — exactly why 37 cranks was the economic limit and why German engineers shortened wire runs. Oil the pins (a pencil scribble of graphite) and feel accuracy return.
After the demonstration
How accurate is cardboard? Good enough to show springs, neaps, and daily inequality qualitatively — the same demonstration value as the museum models in my museums guide. Nobody will navigate by it.
What next after two constituents? Add a third slower disc (a K1 impersonator, one turn per two of M2’s) and watch daily inequality appear — the phenomenon behind Why 37?.
Is this safe for kids? Yes with supervision — pins are the only sharp parts. It is the best tide lesson I know for a curious twelve-year-old.
Show a twelve-year-old
The real test of this build is not accuracy — it is explanation. If you can crank your cardboard adder while a curious kid watches the pencil breathe in and out, and she gets why the moon makes two tides a day, you have taught what took Kelvin’s generation a decade to prove. Photograph the rig, note what stuck and what slipped, and compare notes with the professionals’ version in The Pulley Adder. Then graduate to decoding real machine output in Reading a Prediction Roll.