failed to bring about this adjustment, the censors must have found it necessary continually to advance the citizens from the lower to the higher divisions. The ratings mentioned above as established on the basis of the sextantarian standard, namely 100,000, 75,000, 50,000, 25,000, and 11,000 asses for the five classes respectively, are those given by Livy.[509] Several variations affecting the highest and lowest classes are offered by other writers. Dionysius[510] states the appraisement of the fifth class at 12½ minae, which would be 12,500 asses. The usual explanation is that he is dealing in round numbers without especial regard to accuracy, for which reason Livy should be given the preference. It is doubtful however whether Dionysius was so inexact. More probably his estimate depended ultimately on the idea that the minimal number of iugera of the highest class was twenty-five,[511] taken in connection with the decimal ratio between the extreme classes—an interpretation which would help explain variations in the rating of the highest class to be mentioned hereafter; or with less reason we might assume that the statements of Dionysius and Livy represent earlier and later conditions.[512] The limit of 400 drachmas given by Polybius[513] proves a lowering of the minimal rating between 269 and the publication of his history.[514] It may have been made in 217, when the money system was again changed. As Polybius probably considered the drachma, or denarius, to be worth ten asses,[515] the limit which he mentions would be 4000 asses. Cicero states the minimal limit at 1500 asses,[516] and a still lower sum of 375, mentioned by Gellius,[517] marked the line of division between the taxable proletarians and the capite censi, who were exempt from taxation. As the differentiation between the two groups last named must have been effected before 167, when the Romans were relieved of the tributum,[518] the rating given by Cicero could not have been later than that vouched for by Polybius. The limit of 4000 asses, accordingly, had reference merely to military service, whereas 1500 marked at once the political and tributary line of separation between the fifth class and the taxable proletarians.[519] The limit of 375 asses, on the other hand, was far below the fifth class, and had nothing to do with it.[520] The relation of these numbers to one another may be summarized as follows: Those assessed at 4000 or more asses belonged to the fifth class, enjoyed the political rights of that class, and were subject to military service as well as to taxation (tributum); those rated at 1500-4000 asses also belonged to the fifth class, enjoyed the political rights of that class, and were subject to taxation but exempt from military service; those rated at 375-1500 asses were proletarians, below the fifth class but subject to taxation; those rated below 375 asses, the capite censi, were exempt from taxation.