Dial
Sundials were fixtures of the same 18th-century English gardens the ha-ha next door came from — Castle Howard's own walled garden still holds a mid-18th-century bronze one, “a delicately-wrought gnomon” on a later stone pedestal. A ha-ha's whole job was hiding something. A sundial's is the opposite: it computes something, continuously, in public, using nothing but a straight edge and the sun's own position — and unlike almost everything else this site grows, it needed no date to be right.
A horizontal sundial has two numbers cut into it once and never again: the angle its gnomon (the blade that casts the shadow) tilts up off the plate, and the angle of every hour line radiating out from noon. Both come from one fact: the gnomon has to point at the celestial pole, which means tilting it up from the plate by exactly the site's own latitude. Once that's true, the shadow's angle A from the noon line, at hour angle H (15° per hour of solar time, either side of noon), works out to
A = tan−1(sin(latitude) × tan(H))
which is why the hour lines on a real horizontal dial are not evenly spaced 15° apart the way a clock face's numbers are — they bunch up tight around noon and splay out wide toward 6am and 6pm, more so the further the dial sits from the pole. Nowhere in that formula is a day, a month, or a season. The sun's height changes all year, which is why a shadow's length drifts with the date — but its direction at a given clock time and latitude doesn't, which is the unglamorous reason one set of cut lines keeps correct time in January and July both.
The same two real places the home page already
asks Open-Meteo about for its own live wind (see
wind.js) — picked again here for the same reason:
they sit in opposite hemispheres. Kew is 51.48°N; Melbourne is
37.83°S. Flip between them and watch every hour line swing to
the far side of noon, and the live shadow start sweeping the other
way round the plate through the day. Nothing about the code changes
between the two — only the sign of one latitude, which the formula
above already carries.
That reversal isn't just a curiosity of this page: it's the reason clocks run the way they do. European clockmakers built the first mechanical clocks copying a shape already familiar from centuries of sundials — in the Northern Hemisphere, where the sun arcs across the southern sky, a horizontal dial's shadow sweeps the same direction we now call clockwise. A sundial built south of the equator sweeps the other way; if clockmaking had first flourished there instead, “clockwise” might point the direction Melbourne's dial points above. It's a repeated historical account, not a single traceable original decision, so this page states it as exactly that.
Honest gap: this reads the real UTC clock and converts it to each garden's own apparent solar time using longitude alone (time = UTC + longitude÷15), with no equation-of-time correction — the real difference between sundial time and clock time that drifts through the year and reaches as much as 16 minutes either way (US Naval Observatory). It also draws a fixed 06:00–18:00 window rather than that garden's actual sunrise and sunset, which shift with the season and would take a second calculation (solar declination) this page doesn't do. The side-view gnomon triangle is schematic, not to scale of any real instrument's dimensions; the top-view's short thick line at center marks the gnomon's own footprint, not a measurement of one. What isn't approximated: the hour-line formula itself, and the fact that it never needs to know the date.
Sources: schoolphysics.co.uk's Sundials
page, for the hour-line formula and the gnomon-equals-latitude rule
quoted above; the Wikipedia entry for the Walled
Garden, Castle Howard, for its own sundial's date and
description; the US Naval Observatory's equation of time page,
for the honest gap above; and History Facts' Why
Do Clocks Move Clockwise? for the clock-hands account. The
latitude and longitude for both gardens are wind.js's
own, not looked up again here.