Numbers

IT HAS been a long week. One second longer than normal, to be precise, for at one o'clock on Friday morning an extra second was added to the day. Such 'leap seconds' like extra days in leap years, are added to ensure our time- keeping stays in step with reality.

In ancient times we had sundials. The Middle Ages brought the mechanical clock, which revealed the variability of sun-time and led to the idea of the mean solar day - the average time between one dawn and the next. The second was defined as 1/86,400 of a day.

That served us well until 1967, when scientists invented the 'atomic clock' whereby a second is defined as 'the duration of exactly 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom'.

This enabled time to be measured with an accuracy equal to one second in 300,000 years, but it created a problem. We now had two scales: Universal Time, measured by the earth's rotation, and Atomic Time, measured by the caesium atom. Accordingly, in 1972, 'Co-ordinated Universal Time' was introduced, allowing for the addition or subtraction of leap seconds, at the end of December or June, to keep atomic time in step with variations in the earth's period of rotation. Since then, 19 leap seconds have been added - an indication that the earth is slowing down.

Before shuddering to a halt, however, pause to admire that 9,192,631,770. It may be the largest exact integer you ever meet.