of the late Roman army, calculated a similar total of 600,000 (exc. fleets) by applying his own estimates of unit-strengths to the units listed in the Notitia Dignitatum. However, Jones' figure of 600,000 is based on assumptions about limitanei unit strengths which may be too high. Jones calculated unit-strengths in Egypt under Diocletian using papyrus evidence of unit payrolls. But a rigorous reassessment of that evidence by R. Duncan-Jones concluded that Jones had overestimated unit sizes by 2–6 times. For example, Jones estimated legions on the frontiers at c. 3,000 men and other units at c. 500. But Duncan-Jones' revisions found frontier legions of around 500 men, an ala of just 160 and an equites unit of 80. Even allowing for the possibility that some of these units were detachments from larger units, it is likely that Diocletianic unit-strengths were far lower than earlier. More recently, Treadgold (1995) has endorsed the "Large Late Army" position in a detailed examination of the Byzantine army's strength (1995). Treadgold argues that John Lydus' figure of 389,704 soldiers represents the army's strength in 285, while Zosimus' figures totalling 581,000 soldiers account for the army in 312. Treadgold estimates that the army's size was roughly constant during the period 235-285, followed by a rapid increase of over 50% between 285-305, and again remained roughly constant 305-395. But Treadgold's analysis can be criticised on a number of grounds: The conclusion that the army's size remained constant between 235 and 285 appears implausible, as this period saw the Third Century Crisis, during which the army's recruitment capacity was severely diminished by the impact of the Plague of Cyprian, numerous civil wars and devastating barbarian invasions. The assumption that John of Lydus' figure of 390,000 for the Diocletian's army refers to the beginning of that emperor's reign is dubious as it would seem more natural for the chronicler to report the army's peak strength under that emperor. Treadgold's claim that Diocletian increased the army's numbers by over 50% is considered implausible by Heather, who points out that even 33% would have required a Herculean effort. Treadgold's estimates are based on figures for Constantine's army provided by Zosimus, who is notorious among scholars as an unreliable chronicler, both in general and as regards figures in particular: e.g. he reports that 60,000 Alamanni were killed at the Battle of Strasbourg in 357, an absurd inflation of the 6,000 reported by