These calculations show that during the period in question the auxiliary troops amounted to 47,500 cavalry, 15,375 mounted infantry, and 129,925 infantry, giving a total establishment of 191,800 men. It is probable, however, that this puts the proportion of mounted men too low. Arrian’s _Ectaxis_ shows that nearly every cohort of the Cappadocian garrison was _equitata_, and although the proportion of mounted men was doubtless higher on the eastern frontier than on the Rhine or in Britain, it is probable that if we possessed more documents similar to the _Ectaxis_ dealing with the other garrisons we should find a higher proportion of _cohortes equitatae_ than our present evidence suggests. It is equally probable that the total figure arrived at falls below the reality. For no province is it likely that the list is complete; in some cases, such as Mauretania Tingitana and Africa, the garrison is obviously put far below its real establishment, while for Arabia and Cyrenaica we have no evidence at all. The deficiency is certainly too great to be made good by the few regiments of uncertain habitation which conclude the list. Probably we may reckon on a total figure of about 220,000 men, of whom at least 80,000 would be mounted. The twenty-eight legions in existence at this time, if we follow Suetonius in assigning 5,600 men to a legion,[504] would only have a total establishment of 156,800, so that clearly in dealing with the army at this period we must disregard Tacitus’s statement that the auxilia were approximately equal in number to the legionaries. The total military establishment of the Empire at the accession of Marcus including the Household Troops, that is to say the ten Praetorian and six Urban[505] cohorts and the Equites Singulares, and the complement of the fleets in the Mediterranean and the Channel and on the Rhine, Danube, and Euphrates, must thus have amounted to some 420,000 men. This total, however, was to be still further increased before the decline began. At the beginning of the third century when additions had been made to the Household Troops, when the legions had been increased to thirty-three[506] and scores of _numeri_ added to the frontier guards, there may have been nearly half a million men serving with the colours, a larger disciplined force than was at the disposal of any one state before the nineteenth century, and the largest professional army which the world has ever seen. Footnotes: [446] See above, pp. 53-5. [447] Any one desirous of further information on any particular regiment will find a summary of the evidence, in so far as it was then available, in Cichorius’s articles in Pauly-Wissowa., s.v. _ala_ and _cohors_, to which I am deeply indebted.