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That "s" is for "sign", as in the "signs" of the zodiac. Although they are today exclusively associated with astrology, up through the early 19th century signs were still sometimes used in astronomical literature. Each sign is exactly 30° and represents a 30° band of ecliptic longitude. There's a little ambiguity over zero and one based counting, but historically the signs seem to have been one-based. If a planet was listed as 1° Taurus that implied that it was in the first degree of the sign called Taurus. The signs were named 2000 years ago so they no longer align with the constellations of the same name, but this is not really a problem when you get used to it.

Why use signs? Tradition, tradition, tradition. That's three reasons. Signs were highly traditional in astronomy (and astrology). Also they provided a nice way of specifying an object's position at the convenient approximate level of the nearest degree. If I tell you that Jupiter is at 13° Gemini and Saturn is at 18° Virgo, then you can picture their locations easily in the sky and also (with basic knowledge of the list of signs) quickly determine the angle between them. The angle between two planets has minimal relevance to astronomy, but it's critical in astrology. Still another reason for counting in signs... you can see this as an extension of sexagesimal counting. While 60° bands would give a clean sequence of sixties (each sign would have 60°, each degree would have 60 minutes, each minute 60 seconds, and each second 60 thirds), 30°-wide bands are a reasonable extension that mostly retain the arithmetic conveniences of the number 60 (sixty has lots of factors so it's easy to divide in half, thirds, quarters, fifths, sixths... but let's not talk about sevenths!).

Frank Reed