Indexing the archive…
Your Universe of Digital Possibilities
Haldane, 1926: drop a mouse down a thousand-yard mine shaft and it walks away at the bottom; a rat is killed, a man is broken, a horse splashes. Weight grows as L³ but air resistance as L², so terminal speed grows only as √L. Drop your own body beside his four and run the log-time clock — the dashed rings fall in vacuum, every size together. Then turn the size dial below a millimetre and watch the rule bend again: under Re = 1, viscosity takes over and speed falls as L².
A falling body speeds up until drag equals weight. Weight grows as L³, Newton’s drag as L²v², so the speed at which they balance grows only as √L — the mouse lands slowly, the horse does not. (g′ is gravity less buoyancy.)
Below a Reynolds number of one, drag is viscous and linear in speed. Weight L³ against drag L·v gives v ∝ L²: halve a droplet and it falls four times slower — which is why fog hangs and bacteria never land.
One empirical curve joins Stokes (Cd = 24/Re) to Newton (Cd ≈ const). On the log–log plot of terminal speed it bends the slope from 2 down to ½ across a decade or two around Re = 1.
One dimensionless number decides everything: the ratio of inertia to viscosity. Low Re, the fluid moves in smooth sheets; past a critical value (~2000 in a pipe) it shatters into eddies on every scale. The readout above is this number, in the instrument’s own units.
The Lemuel grammar: a quantity as a power of body size. On log–log axes every allometric law is a straight line whose slope is the exponent b — fitted, on every instrument of the edition, from the sizes you visit.
The second size: the same race as The Bone — a surface against a volume — run through the air instead of a femur. It is Haldane’s other half of the argument, and the reason the rack’s small things live in a different physics: below Re = 1 inertia is irrelevant and a body stops the instant its push stops — the world The Swim makes you swim in. The mass of a body and the mass of the planet under it are the two numbers The Mountain will finally tie together.