Environmental Engineering Reference
In-Depth Information
by considering the legendary origins of the yard as a unit of length. Legend has
it that the yard was originally defined to be the distance from tip of King Henry I
of England's nose to the end of his thumb. Clearly the direct use of this standard
of measurement would have been a little inconvenient; you can be sure that pretty
soon a rod would have been cut to the correct length and used as a substitute for
the King's own person. The use of this rod for measurement is an example of
indirect measurement, though still using the same standard yard it doesn't require
the King to be present. Desirable characteristics of a standard are reproducibility and
precision. Reproducibility means that the standard can be used over and over again
to give a consistent definition of the unit, one which doesn't vary with time. If the
English people had reason to suspect that the King had grown or shrunk (perhaps
by later comparisons with the rod) then they might have faced a dilemma: reject
the King as the means to define the standard yard (in favour of the rod) or keep the
definition using the King and face the problems associated with their not choosing
a reproducible standard of length. Furthermore, the distance from the tip of the
King's nose to the end of his thumb is not a terribly precise standard. Just consider
the question of how he should hold his head while the measurement is taking place.
The yard defined in this way clearly can only be expected to be accurate at the
level of a few percent. It is easy to think of standards for length that are both more
reproducible and more precise than this legendary definition.
Units are either fundamental, as is the case with the second (s), the kilogram
(kg) and the metre (m), or they are derived units, such as the unit of velocity
(m s
−
1
). For each of the fundamental units, there must be a precise and reproducible
laboratory standard. In the case of the S.I. unit of mass, the kilogram, the standard
is a lump of platinum-iridium alloy kept at the International Bureau of Weights
and Measures (BIPM), at Sevres in France. The SI unit of time, the second, was
originally 1/86,400 of the mean solar day, and then later defined as a fraction of
the mean tropical year. Neither of these standards could approach the accuracy of
those based on the frequency of radiation emitted by certain atoms and in 1967
the second was redefined as exactly 9,192,631,770 cycles of the transition between
two hyperfine levels in
133
Cs. In practice this standard uses a cavity filled with an
ionised vapour of
133
Cs. Standing electromagnetic waves are created in the cavity
using a radio-frequency oscillator circuit. When the frequency of the oscillator
matches that of the atomic transition a resonance is observed. At resonance the
oscillator circuit will then, by definition, make precisely 9,192,631,770 cycles in
one second. Clocks based on sophisticated versions of this technique, such as those
at the National Institute of Standards and Technology in the USA, are capable of
measuring time to an accuracy of better than one nanosecond in a day.
The standard unit of length, the metre was once defined as one ten-millionth
of the distance on the Meridian through Paris from the pole to the equator. This
standard was replaced in 1874 and 1889 by standards based on the length, at zero
degrees centigrade, of a prototype platinum-iridium bar. In 1984, standards based
on prototype bars were superseded by the current standard distance that light travels
in vacuum during a time interval of exactly 1/299,792,458 of a second. The effect
of this definition is to fix the speed of light in vacuum at exactly 299,792,458 ms
−
1
.
The justification for this choice of standard relies on our belief in the constancy of
the speed of light in vacuum, a phenomenon that will be discussed in later chapters.
