Plural of convulsionary; people who are subject to or characterized by convulsions, or historically, members of a religious sect associated with ecstatic convulsions.
From convulsionary plus the plural suffix -ies, referring to either medical subjects experiencing seizures or, historically, followers of Jansenism in 18th-century France known for their spasmodic movements.
In 18th-century Paris, crowds gathered to watch 'convulsionaries'—people who had religious experiences causing violent convulsions—the crowds were so large police had to disperse them!
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