A clock is a mechanical or digital instrument for the measurement of time. The display can be analog, with hands, or digital, expressing the time in digits. The former has a circular scale of 12 hours, which also serves as a scale of 60 minutes, and often also as a scale of 60 seconds; the latter has an hour range of 1-12, with an indication am/pm, or 0-23. They are in homes and offices; smaller ones (watches) are carried along (alternatively, people can read the time from their mobile phone); big ones are in public places, e.g. a train station. A small clock is also often permanently shown in a corner of computer displays.
A clock, by measuring time (e.g. in seconds). supplies a numerical comparison between the durations of different time intervals. For example, a clock will provide the ratio of the duration of one day to the duration of a different day (for example, the earth is spinning slower today than it did a billion years ago. If the earth's spin is used as a clock, each rotation will take exactly one day, by definition.)
Modern clocks define constant units of time: an hour is always sixty minutes, of sixty seconds each. The medieval canonical hours[?], however, were the intervals between set times of prayer: they differed in length, and varied as the times of sunrise and sunset shifted.
Accurate navigation by ships beyond the sight of land depends on the ability to measure latitude and longitude. Latitude is fairly easy to determine through celestial navigation, but the measurement of longitude requires accurate measurement of time. This need was a major motivation for the development of accurate mechanical clocks.
An ideal clock appropriately measures the ratio of the duration of natural processes, and thus will give the appropriate time measure for use in physical theories. Therefore, to define an ideal clock in terms of any physical theory would be circular. An ideal clock is more appropriately defined in relationship to the set of all physical processes. This leads to the following definitions:
This definition can be further improved by the consideration of successive levels of smaller and smaller error tolerances.
While not all physical processes can be surveyed, the definition should be based on the set of physical processes which includes all individual physical processes which are proposed for consideration. Since atoms are so numerous and since, within current measurement tolerances, they all beat in a manner such that if one is chosen as periodic then the others are all deemed to be periodic also, it follows that atomic clocks represent ideal clocks to within present measurement tolerances and in relation to all presently known physical processes. However, they are not so designated by fiat. Rather, they are designated as the current ideal clock because they are currently the best instantiation of the definition.
Some noted clocks include: