Indexing the archive…
Your Universe of Digital Possibilities
Below 2.7 mm surface tension wins; above it, gravity. Grow a water drop from a nanolitre to a litre and it slumps from a perfect cap into a puddle whose height stops at 2ℓc sin(θ/2) — and its whole shape is one ordinary differential equation away from exact. The engine solves it, the plot fits the exponent from your own samples, and a dashed ghost shows the drop surface tension alone would have made.
A curved liquid surface holds a pressure jump proportional to its surface tension and its total curvature. Add gravity’s hydrostatic pressure and integrate from the apex, and it is the whole shape of a drop, a meniscus or a soap film.
The three surface tensions meeting at the contact line balance along the plate, fixing the angle the liquid meets it at — near 160° on a lotus leaf, near 10° on clean glass.
The size at which surface tension and gravity are equal. Below it a drop is a spherical cap; above it, a puddle whose height stops at 2ℓc sin(θ/2).
Gravity on a volume against tension on a surface — the square–cube race for liquids. The crossover the drop’s fit may not cross is Bo = 1.
A wetting liquid climbs a tube until the column’s weight matches the pull of its meniscus: halve the bore, double the rise (slope −1). Non-wetting mercury is pushed down instead.
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 fifth size is the race of a surface against a volume once more — The Bone’s square–cube law, with surface tension in place of bone strength. Below the capillary length the surface wins and the shape is pure geometry; above it the drop becomes a sheet whose thickness no longer cares how much you pour. Young and Laplace wrote the law in two years, 1805 and 1806; Bashforth and Adams tabulated its solutions by hand in 1883. The same pressure jump shapes the films of The Soap; the swimmers that live below a millimetre are The Swim’s.