Suppose that our unit for measuring area was not the square foot (the area of a square 1 foot on a side), but the area of a circle with a radius of 1 foot. Call it a “circfoot.” The area of a circle with a radius of 2 feet would be 4 circfeet. But the area of a rectangle 2 feet by 3 feet would be 6/π circfeet. In fact, π would appear as a factor in the area of every rectangle, and not in that of any circle (assuming the radius or side length wasn't a multiple of π).
There is something very disturbing and unnatural about such a state of affairs. One expects π to come up in dealing with circles, but why should it come up with rectangles?
Much the same thing happened with the electrical and magnetic units in the centimeter-gram-second and meter-kilogram-second systems; π kept popping up where it made no sense.
These pop-up π's could be prevented by introducing π into the definition of one or more electromagnetic units. However, one couldn't just simply multiply or divide an existing definition by π, because that would destroy the coherence of the system. Getting π to appear only where it made sense came to be called “rationalizing” the system, and it was extremely controversial.
In a plenary session in 1935 the IEC adopted the Giorgi system. In 1950 it decided to increase the value for the permeability of free space by a factor of 4π (the surface area of a sphere of radius 1), thus rationalizing the system. Expressions concerning spheres would contain “4π”; those concerning coils, “2π”; and those dealing with straight wires would not contain π at all. The resulting “rationalized MKSA system,” was the direct ancestor of SI.
The “circfeet” way of presenting the problem is due to B. A. Massey.
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Last revised: 27 November 2004.