On a horizontal sundial, the gnomon's edge points at the celestial pole, tilted up from the dial by an angle equal to the site's latitude φ. The shadow of that edge sweeps across the face, and the angle of each hour line measured from the noon (12:00) line is
θ = atan( sin(φ) · tan(H) )
where H = 15°·(t − 12) is the hour angle of apparent solar time t. Because sin(φ) scales the tangent, the lines are bunched tightly near noon and splay out toward 6 AM/6 PM — evenly spaced only at the poles (φ = ±90°) and collapsed onto the noon line at the equator (φ = 0°).
A sundial shows apparent solar time, which drifts from clock (mean solar) time through the year by the equation of time, EoT ≈ 9.87·sin(2B) − 7.53·cos(B) − 1.5·sin(B) minutes, with B = 360°/365·(day − 81). Plotting EoT against the sun's declination δ ≈ 23.44°·sin(360°/365·(day + 284)) for every day of the year traces the analemma — the figure-eight the sun makes at the same clock hour across a year, shown in the strip below.
Shadow length (unlike its angle) depends on the sun's altitude sin(alt) = sin(φ)sin(δ) + cos(φ)cos(δ)cos(H): a low sun casts a long shadow, and below the horizon (alt ≤ 0) there is no shadow at all.