_Size of regiments._ In discussing the size of the auxiliary regiments we have two questions to settle, the numbers of the establishment and the actual strength at which the regiments were maintained. As regards the first question, the evidence of Hyginus[46] and the inscriptions shows us that both _alae_ and _cohortes_ were known as _miliariae_ or _quingenariae_—that is to say, they contained, roughly speaking, 500 or 1,000 men each. The smaller unit seems to have been preferred in the first century, while the larger predominates among the corps raised by Trajan and his successors. The exact theoretical size, both of the regiments themselves and of the centuries and _turmae_ into which they were divided, is more difficult to determine. Hyginus states that an _ala quingenaria_ was divided into sixteen _turmae_, and an _ala miliaria_ into twenty-four.[47] He does not state the number of men in a _turma_ in either case, and it seems impossible to arrive at any certainty on the basis of figures found elsewhere in his treatise. Turning to epigraphical evidence we find an inscription from Coptos which describes the composition of a _vexillatio_ drawn from three alae and seven cohorts, as: ‘_Alarum III: dec(uriones) V, dupl(icarius) I, sesquiplic(arii) IIII, equites CCCCXXIIII. Cohortium VII: centuriones X, eq(uites) LXI, mil(ites) DCCLXXXIIX_’.[48] Von Domaszewski suggests that the cavalry in this detachment are to be divided into ten _turmae_ of 42 men, each commanded by a _decurio_, a _duplicarius_, or a _sesquiplicarius_, and that this figure represents the theoretical strength of the _turma_ in an _ala miliaria_.[49] In an _ala quingenaria_, on the other hand, the _turma_ probably contained only 30 men. This seems to be as near certainty as we are likely to arrive in the present state of our evidence, unless indeed we take literally a statement of Arrian that an _ala_ contained 512 men, a total which would presumably give 32 men to the _turma_.[50] Arrian is, of course, the best authority on the imperial army whom we possess, but the remark in question is a parenthesis inserted into an account of the ideal establishment of a Hellenistic army, and he may have meant no more than that the unit under discussion corresponded roughly with a Roman _ala quingenaria_. More satisfactory and conclusive evidence will perhaps be found when the barracks of an ala in a frontier fort have been accurately planned.[51]