Quinarian system
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The Quinarian system was a method of zoological classification which had a brief period of popularity in the mid 19th century, especially among British naturalists. It was largely developed by W. S. MacLeay and adopted for a time by some influential writers, notably William Swainson.
The quinarian system sought to identify a pattern of natural order among animal groups, based on the principle of grouping by fives. Presumably this arose as a chance observation of some accidental analogies between different groups, but it was erected into a guiding principle by the quinarians. It became increasingly elaborate, proposing that each group of five classes could be arranged in a circle, with relatively advanced groups at the top and degenerate forms towards the bottom. Each circle could overlap with adjacent circles (a phenomenon called 'osculation').
Quinarianism was not widely popular outside the United Kingdom; it had become more or less unfashionable by the 1840s, and was eventually discarded in favour of principles of classification based on evolutionary relationship.
"Classification, Evolution, and the Nature of Biology", Alec L. Panchen (Cambridge 1992)