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The United States Abbreviation Theory
One of the most popular theories is that the dollar sign is derived from the initials of the United States. If you superimpose a capital "U" on a capital "S" then drop the lower part of the "U", what you end up with is a version of the dollar symbol with two strokes. This theory was endorsed by the American libertarian philosopher and staunch defender of capitalism, Ayn Rand, in her novel Atlas Shrugged. Chapter 10 is entitled the Sign of the Dollar. Rand claimed the dollar sign was the symbol not only of the currency, but also the nation, a free economy, and a free mind.
The Peso Abbreviation and Piece of Eight Theories
However, a more widely accepted theory nowadays is that the sign owes its origins to the Spanish peso.
One version of this theory is that the standard abbreviation of "peso" was simply "P", but the plural form was a large "P" with a small "s" above it and to its right. This was simplified by retaining only the upward stroke of the "P" and superimposing the "S" upon it. Hence the symbol of the dollar.
If the peso abbreviation theory is the correct one why is the US dollar sign sometimes written with two vertical strokes? A possible explanation is that the best known Spanish Peso coin had two pillars engraved on the reverse side to symbolize the "Pillars of Hercules" at Gibraltar and the words "Plus Ultra" indicating that beyond the Pillars of Hercules there were other lands. That coin was called the Pillar Dollar in the British colonies in North America and the two pillars may have become the two strokes in the Dollar sign.
There is another version of the theory linking the sign to the Spanish peso. As mentioned earlier the peso was subdivided into eight reals, hence the name piece of eight. This was represented as P8 or /8/. Eventually it became customary to write the oblique strokes across the figure 8. In the past precious metal coins were sometimes split into pieces to provide small change. The use in America of the expression two bits for 25 cents is a legacy of this since if a Spanish dollar or peso or piece of eight was split into quarters each part would consist of two of the original eight pieces or reals.
The 8 with two strokes became a letter S with two strokes since S looks like an 8 that has been split, as when a peso was broken to provide change in reals. Eventually a further simplification was introduced by dropping one of the strokes.
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