The time unit **second** is one of the SI base units. Until 1956 the second was derived from the Earth’s rotation around its axis, later from the Earth’s motion around the Sun. In 1967, the change from the astronomical to the atomic definition of the second was done, because the atom’s resonance frequency is much more constant in time than the angular frequency of the Earth, the oscillation frequency of a pendulum or of a quartz oscillator. The new definition of the SI second is based on the (non-radioactive) caesium, ^{133}Cs, whose atomic frequency had been fixed at 9,192,631,770 Hz in 1967. See Cesium Atomic Clock page at USNO.

**International Atomic Time — Temps Atomique International (TAI)** is calculated by the BIPM from the readings of more than 260 atomic clocks located in metrology institutes and observatories in more than 40 countries around the world. BIPM estimates that TAI does not lose or gain with respect to an imaginary perfect clock by more than about 100 nanoseconds per year.

**Coordinated Universal Time (UTC)** is the basis for legal time worldwide and follows TAI (see above) exactly except for an integral number of seconds, presently 33 (since 2006-01-01). These leap seconds are inserted on the advice of the International Earth Rotation Service (IERS) to ensure that, on average over the years, the Sun is overhead within 0.9 seconds of 12:00:00 UTC on the meridian of Greenwich. UTC is thus the modern successor of Greenwich Mean Time, GMT, which was used when the unit of time was the mean solar day.

**Leap second**: An intentional time step of one second used to adjust UTC to ensure approximate agreement with UT1. An inserted second is called a positive leap second (see page at NPL and at USNO), and an omitted second is called a negative leap second. A positive leap second used to be inserted about once every year and a half, but hasn’t been inserted since 1999-01-01 until 2006-01-01. Here is the historical list of leap seconds at USNO.

**Clock**: (a) A device for maintaining and displaying time. (b) A device that counts the number of seconds occurring from an arbitrary starting time. A clock needs three basic parts. First, a source of events to be counted. This source can be labeled a frequency standard, frequency source, or time interval standard. Second, a means of accumulating (counting, adding, integrating) these events or oscillations. Third, a means of displaying the accumulation of time.

**Disciplined oscillator**: An oscillator with a servo loop that has its phase and frequency locked to an external reference signal.

**Accuracy**: (a) The degree of conformity of a measured or calculated value to its definition or with respect to a standard reference. (b) The closeness of a measurement to the true value as fixed by a universally accepted standard.

**Precision**: (a) The degree of mutual agreement among a series of individual measurements. Precision is often, but not necessarily, expressed by the standard deviation of the measurements. (b) Random uncertainty of a measured value, expressed by the standard deviation or by a multiple of a standard deviation.

**Resolution**: The degree to which a measurement can be determined is called the resolution of the measurement. The smallest significant difference that can be measured with a given instrument. For example, a measurement made with a time interval counter might have a resolution of 10 ns.

**Frequency stability**: Statistical estimate of the frequency fluctuations of a signal over a given time interval. Long term stability usually involves measurement averages beyond 100 s, short term stability usually involves measurement averages from a few tenths of a second to 100 s.

NOTE: Generally, there is a distinction between systematic effects such as frequency drift, and stochastic frequency fluctuations. Systematic instabilities may be caused by temperature, humidity, pressure, radiation, orientation, magnetic and gravitational field, etc. Random or stochastic instabilities are typically characterized in the time domain or frequency domain. They are typically dependent on the measurement system bandwidth or on the sample time or integration time.

**Frequency drift**: The linear (first-order) component of a systematic change in frequency of an oscillator over time. Drift is due to ageing plus changes in the environment and other factors external to the oscillator.

**Ageing** (or **Aging**, both forms are correct): The systematic change in frequency over time because of internal changes in the oscillator. For example, a 100 kHz quartz oscillator may age until its frequency becomes 100.01 kHz. NOTE: Ageing is the frequency change with time when factors external to the oscillator such as environment and power supply are kept constant.

**Jitter**: clock phase variation, or time interval error (TIE) occurring at rates above 10 Hz.

The jitter in the context of NTP is calculated as the exponential average of the first-order time differences.

**Wander**: clock phase variation, or time interval error (TIE) occurring at rates below 10 Hz.

The wander in the context of NTP is calculated as the exponential average of the first-order frequency differences.

**Synchronization**: The process of measuring the difference in time of two time scales such as the output signals generated by two clocks. In the context of timing, synchronization means to bring two clocks or data streams into phase so that their difference is 0.

**Syntonization**: Relative adjustment of two frequency sources with the purpose of canceling their frequency difference but not necessarily their phase difference. (Telecom almost always uses the word *synchronization* when they mean *syntonization*)

**Epoch**: Epoch signifies the beginning of an era (or event) or the reference date of a system of measurements.

**Julian Day**: Obtained by counting days from the starting point of noon on 1 January 4713 B.C. (Julian Day zero). One way of telling what day it is with the least possible ambiguity. (see Julian Date Converter)

**Modified Julian Day (MJD)** = Julian date – 2400000.5 . MJD zero is 17 November 1858 at 00:00. Examples: 1900-01-01 (NTP epoch) = MJD 15020, 1970-01-01 (Unix epoch) = MJD 40587, 2000-03-01 = MJD 51604.