Harry Thurston Peck, Harpers Dictionary of Classical Antiquities (1898)

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Turma

（ἴλη). A subdivision of the Roman cavalry. The 300 knights originally belonging to each legion were divided into ten turmae of thirty men: each of these had three decuriones, the first of whom commanded the whole turma, and three optiones (adjutants). The divisions of allied cavalry called alae (see Ala), each consisting of 300 men, contained five turmae of sixty men each. Under the Empire the independent divisions of cavalry of 500 or 1000 men, which were also called alae, consisted of sixteen or twenty-four turmae. The cavalry divisions of 120 horsemen in a cohort of 500 strong, which formed the unit in many cohorts, and of 240 horsemen in a cohort of 1000 strong, were divided into six and ten turmae respectively. See Cohors; Exercitus.