Centimetre–gram–second system of units facts for kids

The centimetre–gram–second system of units (often shortened to CGS or cgs) is an older way of measuring things in science. It's like a special set of rules for units, built around three main measurements: the centimetre for length, the gram for mass, and the second for time.

While CGS was very important for a long time, it has mostly been replaced by the International System of Units (SI), which uses the metre, kilogram, and second. You probably use SI units every day! Even though SI is now the main system, CGS is still used in some special areas of science, especially in theoretical physics and astrophysics.

For simple things like measuring force, energy, or pressure, CGS and SI units are pretty similar. The main difference is just the size of the units. For example, 1 metre is 100 centimetres, and 1 kilogram is 1000 grams. So, converting between them usually just involves multiplying or dividing by powers of 10. For instance, the CGS unit of force is the dyne, and the SI unit is the newton. One newton is equal to 100,000 dynes!

However, when it comes to measuring things like electric charge or magnetic fields, converting between CGS and SI can be a bit trickier. This is because the rules for defining these electrical and magnetic quantities are different in CGS compared to SI. Plus, within the CGS system itself, there were a few different ways to define these units, leading to different "sub-systems" like Gaussian units.

History of CGS

The idea for the CGS system started in 1832 with a German mathematician named Carl Friedrich Gauss. He suggested creating a system of units based on length, mass, and time. He originally thought of using millimetres, milligrams, and seconds.

Later, in 1873, a group of important scientists from the British Association for the Advancement of Science, including famous physicists like James Clerk Maxwell and William Thomson, recommended using the centimetre, gram, and second as the main units. They also suggested that all other units, especially those for electricity and magnetism, should be based on these three.

But, many CGS units turned out to be a bit awkward for everyday use. For example, measuring a person's height in centimetres is fine, but measuring a room or a building in thousands of centimetres can be a bit much! Because of this, the CGS system wasn't widely used outside of scientific labs.

Starting in the 1880s, and especially by the middle of the 20th century, the MKS system (metre–kilogram–second) began to take over. This MKS system then grew into the modern SI standard that we use today.

Since the SI system became the international standard in the 1960s, the use of CGS units has slowly decreased. Today, SI units are used in most engineering jobs and in physics classes. However, CGS units, especially Gaussian CGS units, are still common in theoretical physics, like when scientists study very tiny systems, electrodynamics (how electricity and magnetism work together), and astrophysics (the physics of space). You might still see CGS units in astronomy journals, like The Astrophysical Journal.

Even though CGS isn't the main system anymore, the gram and centimetre are still very useful as smaller units within the SI system, just like other units with prefixes (like millimetres or kilograms).

CGS Units in Mechanics

In mechanics, which is the study of how things move and the forces that make them move, the CGS and SI systems define quantities in the same way. The only difference is the size of the basic units: centimetres instead of metres, and grams instead of kilograms. The second (for time) is the same in both systems.

Because the basic rules of mechanics are the same in both systems, the definitions of other units (called "derived units") are also the same. This means there's a clear way to switch between CGS and SI for mechanical units.

For example, the CGS unit for pressure is the barye (Ba). It's defined as 1 gram divided by (centimetre times second squared). The SI unit for pressure is the pascal (Pa), defined as 1 kilogram divided by (metre times second squared).

To convert a barye to a pascal, you just use the conversion factors for grams to kilograms and centimetres to metres:

• 1 gram = 0.001 kilogram (10⁻³ kg)
• 1 centimetre = 0.01 metre (10⁻² m)

So, 1 barye = 1 g / (cm ⋅ s²) = (10⁻³ kg) / (10⁻² m ⋅ s²) = 10⁻¹ kg / (m ⋅ s²) = 0.1 pascal.

Here are some common CGS mechanical units and how they relate to SI units:

CGS Units in Electromagnetism

When it comes to electromagnetism (the study of electricity and magnetism), the CGS system gets a bit more complicated. This is because the way electric and magnetic forces are defined is different from the SI system.

In SI, the unit of electric current, the ampere, is one of the basic units, just like the metre, kilogram, and second. This means that when we write down the laws of electromagnetism in SI, we sometimes need extra constants (like the permeability of free space) to make the units work out.

However, the CGS system tries to define all electromagnetic quantities directly from the centimetre, gram, and second, without adding new basic units. This means that the formulas for electromagnetism can look different in CGS compared to SI.

There are a few different ways to define electromagnetic units within the CGS system. These different ways led to different "sub-systems":

• Electrostatic Units (ESU): This system defines electric charge based on Coulomb's law, which describes the force between two electric charges. In ESU, the unit of charge is the franklin (Fr), also called a statcoulomb. One franklin is defined as the amount of charge that, when placed 1 centimetre away from an equal charge, creates a force of 1 dyne between them.
• Electromagnetic Units (EMU): This system defines electric current based on the force between two parallel wires carrying current (similar to how the SI ampere is defined). In EMU, the unit of current is the biot (Bi), also called an abampere. One biot is defined as the current that, when flowing in two long parallel wires 1 centimetre apart, creates a force of 2 dynes per centimetre of wire length.
• Gaussian CGS: This system is a mix of ESU and EMU. It uses ESU for electric units and EMU for magnetic units. This is the most common CGS system used today, especially in theoretical physics.
• Heaviside–Lorentz CGS: This is another mixed system, similar to Gaussian, but it's "rationalized." This means that certain factors of 4π (a mathematical constant) are moved around in the equations to make them look simpler in some cases.

Because of these different ways of defining units, converting between CGS electromagnetic units and SI units can be complex. For example, the speed of light (c) often appears in the conversion factors between ESU and EMU units.

Here's a simplified look at how some SI electromagnetic units compare to their CGS (ESU, Gaussian, and EMU) counterparts:

Note: In this table, c is the numerical value of the speed of light in centimetres per second (about 29,979,245,800 cm/s).

Advantages and Disadvantages

One "advantage" of some CGS systems is that the formulas for certain physical laws might look simpler because they don't have extra constants in them. However, this often means that the units themselves are harder to define or measure in experiments. Also, the CGS system can be confusing because many units don't have unique names. For example, "15 emu" could mean 15 abvolts, or 15 units of electric dipole moment, or something else entirely!

The SI system, on the other hand, starts with a unit of current (the ampere) that is easier to measure in experiments. While this means some electromagnetic equations in SI need extra constants, it also means that all SI units have unique names (like 1 henry, 1 ohm, or 1 volt), which avoids confusion.

The CGS-Gaussian system is often liked because electric and magnetic fields have the same units. Also, the only constant that appears in Maxwell's equations (the main equations for electromagnetism) is c, the speed of light. The Heaviside–Lorentz system also has these features and is "rationalized," meaning it tries to simplify the equations by moving factors of 4π around.

In SI, and other rationalized systems, the unit of current was chosen so that equations for spheres have a 4π, equations for wires have a 2π, and equations for flat surfaces have no π. This was helpful for engineers. However, with modern calculators and personal computers, this "advantage" isn't as important anymore. Some scientists, especially in fields like astrophysics, still find the non-rationalized CGS system simpler for certain formulas.

Scientists also use even more specialized unit systems, called natural units, to simplify formulas even further. For example, in particle physics, they often express everything using just one unit of energy, the electronvolt. This makes calculations in particle physics easier, but it wouldn't be practical for everyday measurements.

See also

• International System of Units
• List of metric units
• List of scientific units named after people
• Metre–tonne–second system of units
• United States customary units
• Foot–pound–second system of units