A simple calculator or reckoner, involving a rotating disc or discs, usually fitted as an accessory to a portable sundial or astronomical compendium. Each disc usually carries a projecting index, reading on a circular scale; alternatively, the disc may have perforated slots through which indications on a fixed surface below may be read. In a common form, the fixed circular scales read 1-12, 1-12 in succession, and 1-29 1/2, and the rotating disc also has a scale of 1-12, 1-12 at its outer edge. By setting the index to the age of the moon, the solar time corresponding to a given lunar time can be read off. The rotating disc also has an eccentric circular hole through which the phase of the moon can be seen pictorially. Volvelles are also made to relate equal and unequal hours, equal and Italian or Babylonian hours, or the lengths of the day and night and times of sunrise and sunset according to season.