Mr. Kenyon of the British Museum had slightly the priority in briefly declaring that these "Enrollments" obeyed a cycle of fourteen years; but Dr. Wilcken followed him within a month or two with an elaborate paper, and shortly afterwards Dr. Viereck with another, discussing their period, nature and purpose.  The three papers are the authority for what is here stated on the subject.
The facts relating to the "Enrollments" in Egypt are deduced from the actual census papers, many of which have been found (usually in a more or less fragmentary condition). The census was always taken after the end of the year to which it belongs; thus, for example, a census paper dated in the end of the year AD.90-91 contains a statement of the facts required for the enrollment of 89-90, and so on. The purpose evidently was to include in each enrollment all children born before the end of the first year of the census period, which we shall henceforth call the periodic year. All dates in these documents are given according to the Egyptian way of reckoning; and the Egyptian year, which began on the twenty-ninth day of August, was at the basis of the whole census system in Egypt. It is proved that enrollments were made for the years ending in the summer of AD.90, 104, 118, 132 and so on till 230. An enrollment also took place under Vespasian, but its date is not fixed by the evidence. There can, however, be no doubt that Dr. Viereck is right in placing it for the year 75-76. 
Though the Egyptian year was employed, the census was carried out by Roman officials, and formed part of the Imperial system of administration.
It was the habit of the Romans in the East to adapt their arrangements to the custom of the country. They did not force the natives to adopt the Roman system of arranging the year and the months, but rather modified their practice to suit the native year, using an Asian year in the Province Asia, an Egyptian year in the Province Egypt, and so on. As the beginning and end of the years varied greatly in different Eastern provinces -- all, however, being now solar years, like the Roman -- we shall throughout these pages speak of the Roman year; and the reader will understand that in each province it has to be translated into the native year there employed. Censorinus mentions, as was to be expected, that the years of the Imperial system -- anni Augustorum -- were counted from the first of January: they differed in this from the years of any individual emperor's reign, which during the first century were usually reckoned from the day on which the reign began, though during the second century the habit of reckoning them from the first of January became general.
Accordingly, instead of mentioning the enrollment for the Egyptian year falling in AD.89-90, we shall call it the enrollment for the Roman year AD.90. The periodic years, then, are as follows: BC.23, BC.9, AD.6, 20, 34, 48, 62, 76, 90, 104, 118, 132, 146, 160, 174, 188, 202, 216, 230, 244, 258, 272, 286, 300, 314, 328.
In every case, of course, the actual enumeration began after the periodic year was ended, though the enumeration is called in the documents the enrollment of the past (periodic) year. Usually the enrollment paper is dated late in the following year; people were allowed to make their declaration at any time during the following year, and as human nature will have it, most people delayed until the year was approaching its end.
It appears, therefore, that already under Vespasian a system of periodical enrollments was the rule of Roman administration in Egypt. The existing documents establish its existence from AD.76 to 230; but the failure of documents attesting its previous or subsequent existence affords no evidence that it began under Vespasian or ended under Alexander Severus. The preservation of papyri is so accidental and precarious, that imperfection and lacunae are the rule in every department which they touch upon. We must be grateful for the light they throw on any subject, but it would be absurd to reason, because no fragment of papyrus has been found to attest a fact, that therefore the fact did not occur. The argument a silentio, always a dangerous one, is especially dangerous where papyrusfragments are concerned.
On this point Mr. Grenfell writes: "I should admit that the argument a silentio cannot yet be used as regards the first century after Christ. About the second and third centuries it is, however, worth something, and also, I think, about the Ptolemaic period." The silence of the papyri about the period before AD.76 therefore constitutes no argument that the periodic enrollments began in that year.
At the last moment Mr. Grenfell, in a letter dated 12th Sept., 1898, brings to my knowledge, and the courtesy of the discoverer permits me to mention, that Mr. Kenyon has found, and is on the point of publishing in the forthcoming volume of the Catalogue of British Museum Papyri, a document  which mentions the enrollment for the eighth year of Nero, AD.61-62. Mr. Kenyon thinks that it implies also still earlier enrollments. This important discovery will be regarded as a strong confirmation of the theory set forth in the following pages, and printed before I heard of the new evidence. The only argument that could be brought forward against the theory lay in the silence of the papyri; and already that silence is broken for part of the period. [Enrollment of AD.20, see Preface]
The question, then, must be put -- at what time and through whose organizing initiative is the Roman series of enrollments likely to have been begun? The answer to that question is not doubtful. We may appeal with confidence to the students of Roman history, and put the question in this way. We find that under Vespasian a system of periodical enrollments formed a fundamental part of the government of Egypt: these enrollments gave a basis on which a statistical account of the population according to households and place of residence at the beginning of each period could be drawn up. Whom should we expect to have introduced the system?
In the first place every one who has studied the history of Roman provincial administration would reply that Augustus was, in all probability, the originator of this Roman system in Egypt. Any important part of Egyptian administration which was in existence under Vespasian is probably as old as the organization of the country by Augustus. It is well known with what peculiar and jealous and minute care: he regarded that country. No Roman of senatorial or equestrian rank was permitten, even to visit it without special leave from the Emperor. It was considered as the granary of Rome; and it was regulated in the most careful way so that its harvests should be reserved for Roman needs, and its resources should be always calculable and certain, as far as care and forethought could make them so.
It is unnecessary to do more than briefly refer to those facts touching the policy and intentions of Augustus which have been skillfully collected and marshaled by a long succession of writers on this subject -- his general survey of the whole empire: the rationes imperii, "a sort of balance sheet published periodically": the libellus or breviarium totius imperii, a compendium of useful statistics about the kingdoms, the provinces, the allies, etc.
These show how carefully and methodically Augustus organized his splendid machinery of government on the basis of accurate, minute and complete knowledge of everything that concerned the subject peoples, and make it probable that the system of periodic enrollments, which alone rendered a complete statistical account of those peoples possible, originated from him, and formed part of his plan of Imperial administration.
In the second place, the system of periodic enrollments is likely to be as old as Augustus, because it probably rested on a pre-Roman foundation. Every year's discoveries strengthen the proof that the organization of Egypt was brought to a very high degree of perfection long before the Romans entered the country, and increase the probability that the germ or even the complete form of almost every detail of administration was found by Augustus already in existence in Egypt, and was merely adapted by him to Roman needs.
Mr. Grenfell notes that the silence of the Ptolemaic papyri about Household-Enrollment -- constitutes an argument against its being an institution of the Ptolemaic period; whereas valuation papers of the class (described later in this chapter) are found not infrequently under the Ptolemies. There must, however, have been in that period some kind of numbering (as Wilcken thinks). Papyri are found c. BC.3000, "a kind of census list of a household," naming the head of the house, resident female relatives, slaves, and young male children.  Two Apographai of unusual character. occur,  resembling the Household-Enrollment papers more than the Valuation papers, and dated BC.19 and 18, before the Periodic Household-Enrollment system was organized.
The probability remains that Augustus originated a new system in Egypt of Periodic Enrollment-by-Households, developing some previously existing system of numbering the population.
In the third place, as we saw in the preceding chapter, Clement of Alexandria believed that the system of enrollments originated from Augustus; and he expresses the general opinion held in Egypt at the end of the second century.
In the fourth place, chronological reasons suggest that the enrollments come down from the organization of Augustus, because the cycle leads us back to the year BC.23, from which dates the Imperial rule of Augustus in the most formal and complete sense. The Roman emperors, beginning from Augustus, reckoned the years of their reign according to their tenure of the tribunicia potestas, which constituted them "Champions of the Commons"; Augustus received the tribunician power on 27th June, BC.23; and the number of years in his Imperial title is reckoned invariably in all later inscriptions from that date. The Coincidence that the EnrollmentCycle was arranged according to the official years of Augustus's reign, is conclusive in favor of the view that Augustus inaugurated the system of periodical enrollments.
This coincidence, also, shows with almost complete certainty that the Fourteen-Years'-Cycle was not devised in Egypt, or for Egypt alone. Mr. Grenfell points out to me that in Egypt the reign of Augustus was invariably reckoned from the taking of Alexandria, the first year being considered to begin on 29th August, BC.30; and there is not a trace of any other reckoning of his reign in the country. Had the Enrollment-Cycle been an Egyptian matter simply, it is in the last degree improbable that it would have been arranged according to the years of the tribunician power.
On the other hand, that was the natural system in general Imperial matters. It was the only method of reckoning which was known universally throughout the empire: it was employed in every official statement of the Emperor's title: it was sometimes used even in dating private inscriptions. 
The use of this epoch, further, proves in all probability that the Enrollment was, as Luke says, actually held first for the year BC.9. It could not be devised until after the reign began, for the epoch was unknown until the epoch-making event had occurred; and, after it had occurred, no time remained to arrange all the details for an Imperial enrollment for the current year. Hence we find a different style of enrollment paper used in Egypt in the years BC.19 and 18.
We see also why the Egyptian year 24-23, and not 23-22, was taken as that correspondent to the Roman year 23. Augustus's reign began during the Egyptian year 24-23, two months before the end of that year on 29th August. Thus the reign of Augustus began officially in the Egyptian year BC.24-23. On the other hand, in any country where the year began in the spring, the official year 1 of Augustus would be the year BC.23-22; and the year 15, which was the first periodic year, would be BC.9-8.
These reasons justify the reasonable confidence that Augustus arranged a system of periodical "enrollments" in Egypt. As the system is fixed according to the year BC.23, in which the fully formed constitutional Principate was organized and the reign of Augustus in the official reckoning began, the arrangement of this system must have taken place later than that year. The system of enrollments must therefore be distinguished from the operation called by Marquardt  the provincial census, which began to be taken in Gaul in BC.27.
The latter operation was intended to form the basis on which the taxation of the provinces of the empire should be regulated. It was repeated from time to time throughout the period of the empire, and was an essential part of the orderly working of the Imperial administration. That taxation should be proportionate to wealth was a Roman principle, and without frequent revaluation of property it was impossible to secure a fair apportionment of taxation. Augustus fully recognized the vast importance of making correct valuation of property in the provinces, as securing both fair taxation and a more lucrative revenue for the State.
Such enumeration and valuation of property was confined, as a rule, to Roman provinces, and was often made as soon as any new province was incorporated in the empire. Such, for example, was the case in Palestine when Quirinius, in his second Syrian governorship, made that country part of the empire. The novel proceedings on that occasion, and the strict inquisition into value of property, brought vividly home to the Jews that they were now wholly reduced to servitude under a foreign power, and led to much disorder and rebellion. The name census was used by the Romans to denote this characteristic institution. In modern usage the term census denotes the periodic numbering of the people, without valuation of property. In this study we use the terms "valuation" or "rating" and "enrollment".
But the system of periodic enrollments in Egypt is quite different from the system of rating and valuation. The latter system also existed in Egypt; many census papers are preserved among the papyri, and Wilcken gives several examples of them on pp.231-240 of the article which we have quoted above. These valuations seem to have been made annually;  and it is often stated in the papers that the census is taken according to the orders of the governor of the province. They contain an enumeration and precise definition of all property in land, houses, and live stock  belonging to the enumerator, often also a statement whether the property is free from debt or mortgage, and often an estimate of the money value, of the whole. Where there is no estimate of value, it is understood that the value is unchanged from previous valuations and can be found in the older official registers.
The same verb apographomai is used in both kinds of papyri, and both operations seem to have been termed Apographai. But the periodic enrollment papers are distinguished by other criteria besides the want of statistics about property and money value; they are dated according to the year of the reigning emperor, and contain no reference to the orders of the governor; they state accurately and exactly which periodic enrollment they are intended for; and they always use the phrase "Enrollment-by-Household", apographe kat' oikian. These periodic enrollments according to the Four-teen-Years'-Cycle  were therefore closely connected with the existing households, and served as basis for an enumeration of the total population. This operation obviously corresponds much more closely than the other kind of Egyptian census to the "enrollment" alluded to by Luke; and we shall therefore always allude to it as the enrollment system, or, more accurately, enrollment-by-household.
The enrollment papers were filled up and sent in to the proper official by the heads of households. In the enrollment paper, the householder specified the house, or part of a house, which belonged to him; he declared that he was formally enrolling himself and his family for the house-to-house enrollment of the past year, twenty-eight of the Emperor Commodus, or whatever else the case was. But, if the owner did not live in the house himself, he enrolled only the tenants; if he kept lodgers, he enrolled himself, his family and the lodgers. He gave a complete enumeration of all the individuals who lived in the house, children, relatives, etc. In one case, twenty-seven persons are enumerated in one paper by a householder. No statement of income or of the money value of the house is given in the enrollment papers.
Thus, according to our theory, the nature of the case led the Romans to adopt a double system, which presents a remarkable analogy to our modern methods. We have an enumeration of the people every ten years, the census: the Romans numbered the people every fourteen years. We have an annual making up of the valuation roll, and an annual system of income tax returns. The Romans, likewise, found it expedient to require annual valuation of property; but they did not require any estimate of annual income, for they, like the United States, arranged their taxes, not according to income, but according to property.
The intention of this system of enrollment by households has been investigated by Wilcken. It furnished a complete enumeration of the population of Egypt; both provincials and resident Romans had to fill up their enrollment papers and send them in to the proper official. The papers not merely furnished the total numbers of the population; they were also useful in allotting the various burdens of public service, and especially they facilitated the conscription; and finally they gave information which aided in levying the poll-tax, determining the classes of persons who were free from the tax, and the date at which each male became of age to pay it (fourteen), or reached the age of exemption (sixty). 
According to Marquardt, 2., p.199, a poll-tax was levied by the Romans only in countries where it had been customary from ancient times, or where there was for the time no survey of property available to furnish a standard for a more rational kind of tax. He is disposed to consider the tributum capitis in the province of Syria as not a poll-tax, but a tax on those engaged in an industrial occupation; but Wilcken seems clearly right in regarding the Syrian tax as a poll-tax, exactly similar to the Egyptian poll-tax.
Thus the Egyptian documents, and the inferences founded on them by comparison with other evidence, have revealed two most important and hitherto unsuspected facts.
(1) In some parts at least of the empire the enrollment and numbering of the population according to their households was a distinct and separate process from the census and valuation, which previously was considered to be the only properly Roman kind of census.
(2) The enrollment by households took place periodically, according to a cycle arranged according to the years of the reign of Augustus in Imperial, but not in Egyptian, reckoning. Probably this system was introduced later than 18 BC.