As eye-catching as the finely detailed moon-phase display on the back of the A. Lange & Söhne Richard Lange Perpetual Calendar Terraluna (www.alange-soehne.com) may be, the real beauty of this $229,400 watch is its precision. The regulator-dial layout—a time-honored symbol of accuracy—hints at such internal features as the constant-force mechanism that feeds steady power to the balance wheel and house-made hairspring. The display on the watch’s reverse side, which plots the position and phase of the moon relative to the sun (represented by the balance wheel), marks the company’s entry into the field of astronomic complications.