The Imperial system

The British Empire, being predominantly a vehicle for trade, had a little more success at imposing its weights and measures upon the world … indeed, that is why the system of feet and inches; ounces and pounds; pints and gallons is called the Imperial system (of, or pertaining to, an empire). Even then, different towns often had differing ideas as to what constituted a pound and what qualified as short measure and, even today, there is a difference between the amount – and spelling – of units: a US gallon is 3.79 liters and a UK gallon, 4.55 litres.

If you think this haphazard, bear in mind that, until the need for conformity was driven by railway timetabling in the mid-19^th century, different towns not only could have different weights and measures but even their clocks were set differently, not just by seconds but by minutes!

The MKS system

Whilst science was still limited to the leisurely pursuit of gentleman amateurs, such variations mattered little as long as there was internal consistency; however, as the pace of scientific and technical advance started to snowball in the early 19th century, scientists began to seek a means of developing international conformity. The first international system devised was called the metre-kilogram-second (MKS) system whereby scientists agreed to use metres for measuring all distances, kilograms for mass and seconds for time. There was, of course, a schism almost straight away with some scientists championing centimetres, grammes and seconds (CGS system), which, as you will see later, explains some of the derived units with which we have been historically endowed.

Importantly though, there was also, for the first time, international agreement as to what the exact definition of these quantities should be.

A metre had already been defined by the French Academy of Science in the post-revolution fervour for change as ¹/_{10 000 000} of the quadrant of the Earth’s circumference running from the North Pole through Paris to the equator. The kilogram was defined as the mass of 1000 cubic centimetres of water, the second as ¹/_{86 400} of the average period of rotation of the Earth on its axis relative to the Sun. Unfortunately, as measurements became ever more precise, the definitions were no longer accurate enough: the Earth’s crust is a dynamic, moving structure subject to alteration at short notice; its rotation is also (very) gradually slowing. The density of water changes according to temperature and pressure (not to mention to regional fluctuations in the Earth’s gravitational field).

The problem was temporarily solved by relating the definitions of mass and length to the parameters of two lumps of platinum and iridium (and thus highly inert and resistant to oxidation) that were kept locked in a Parisian vault … which was fine if you were a Parisian scientist but was a bit tough on anyone else who wanted to calibrate their instruments.

Today, wherever possible, we use highly precise definitions based on constant phenomena that are observable by any scientist working anywhere in the world or, indeed, off it. A metre is now defined as the distance travelled by light in a vacuum in ¹/_{299 792 458} of a second; a second is 9 192 631 770 cycles of radiation associated with the transition between the two hyperfine levels of the ground state of the caesium-133 atom (a statement that will be understandable by the end of Ch. 8). A kilogram, however, remains as the mass of a cylinder of French platinum-iridium until somebody can think of anything better.

The SI system

By this time, three new units had been added, all named after eminent scientists: a unit of force (the newton, N), defined as that force which gives to a mass of one kilogram an acceleration of one metre per second per second; a unit of energy (the joule, J), defined as the work done when the point of application of a newton is displaced one metre in the direction of the force; and a unit of power (the watt, W), which is the power that, in one second, gives rise to energy of one joule.

These additional units, which built upon the MKS system, were called the Système International D’unités, known as the SI system. Since its formal adoption in 1960, many more units have been added. There are now seven basic units (Table 1.1): in addition to the metre, the kilogram and the second, we now have the ampere, A, for electric current; for luminous intensity, the candela, cd; for temperature, kelvin, K; and for quantity of substance, the mole, mol.

Table 1.1 The seven base SI units

The three original derived units have also been built upon considerably; however, all these other SI units can – as Tables 1.2, 1.3 and 1.4 show – be defined in terms of these seven basic units, either directly or indirectly. Many of these units have their own special names (such as the newton and joule). At this stage, there may appear to be an alarming number of these units with peculiar names that define quantities of which you may never have heard – and the lists given are by no means complete, these are merely the units that a health professional is likely to encounter! However, by the time you have finished the book, all these terms should be like regular acquaintances. Do not try to memorize them all at this stage, rather familiarize yourself with the names and use the table as a reference so that, when you encounter a new term or an unfamiliar symbol, you can refer back and learn the detail in its correct context.

Table 1.2 Some derived SI units

Table 1.3 Some derived SI units with special names and symbols

Table 1.4 Some SI units with derived unit names

There is one other trick to know about when it comes to units, which can – and often does – serve as an alternative to scientific nomenclature. In everyday conversation, it becomes a bit tedious to say ‘it’s six times ten to the three metres to the nearest town’ so, instead, we say ‘it’s six kilometres’, ‘kilo’ being a prefix meaning ‘one thousand’. Scientists do the same in their everyday conversation too: there are a stack of these prefixes, some of which – kilo (10³), centi (10⁻²), milli (10⁻³) – you will be familiar with as you will with their common abbreviations: k, c and m respectively. Table 1.5 shows the abbreviations and symbols from 10⁻²⁴ to 10²⁴, which, whilst not exhaustive, is enough for most eventualities that you are likely to encounter. So you are now able to express large and small quantities in two ways, by saying, for example:

Table 1.5 Commonly used prefixes for SI units. Note the use of capital letters for units of 10⁶ and above and lower case for 10³ and below