¹ I am indebted to Alan Bowman, Duncan Foley, Jean Gascou, and the Editorial Committee for helpful comments and suggestions at various stages.

² It is, of course, only one of the determinants and symptoms of particular social structures, and it is true that similar distributions of wealth may result from different social and economic situations, as M. Lewuillon-Blume points out (Proc. XVIII Int. Congr. of Papyrology 11 (1988), 279 n. 5).

³ Probably more in inventories at various stages of production than in equipment or plant.

⁴ See Pleket, H. W., ‘Urban elites and the economy in the Greek cities of the Roman Empire’, Münstersche Beiträge z. antiken Handelsgeschichte 3 (1984), 3–36Google Scholar for a balanced discussion and extensive bibliography of this vexed question.

⁵ We have no means of controlling the accuracy of such records as do survive, and one might well be suspicious of the great precision with which they record holdings, down to minute fractions of an aroura. But landowners had a powerful incentive to see that their holdings were neither overstated (too high a tax bill would result) nor understated (the register might be evidence against their ownership), and there is abundant surviving evidence of protests on both counts when owners thought the official records were wrong.

⁶ Zwei Landlisten aus dem Hermupolites (P. Land-listen), Stud.Amst. 7 (1978)Google Scholar. The two codices are referred to below as F (P.Flor. 171) and G (P.Giss.inv. 4).

⁷ ‘Landholding in the Hermopolite Nome in the fourth century A.D.’, JRS 75 (1985), 137–63,Google Scholar where other reviews and literature are cited. The results of a simultaneous investigation by Marianne Lewuillon-Blume are published in the article cited above (n. 2), and in Cd'E 60 (1985), 138–46.

⁸ See Bowman's discussion of this pagus, op. cit. (n. 7), 152–3; it is difficult to know how much an accounting of the land in it might alter some of the conclusions about the distribution of land, but I argue below that the effect for the entire nome would not be material.

⁹ Bowman cites Dollar, C. M. and Jensen, R. J., Historian's Guide to Statistics (1971)Google Scholar for a description of the index; pp. 121–5 describe it and show how to compute it. As they put it (122–3): ‘The first step in drawing the Lorenz curve and calculating the Gini index is to arrange the sections in ascending order, from poorest to richest on the basis of the ratio Y/P [Y = income, P = population], … Two new values are shown for each section, CumP_i and CumY_i, which are the cumulative subtotals of P and Y for all sections poorer than section i, together with i. … The Lorenz curve is drawn by plotting the … points CumP_i and CumYⁱ on a square graph, with CumPⁱ (the population factor) always on the horizontal axis, and CumY_i, (the good that is distributed) always along the vertical axis.’ The Gini index is arrived at by summing all the figures for P_iCumY_i; and for P _iY _i (simple multiplications for each item in the list) and computing R = 1 – (2ΣP_iCumY_i) + (ΣP_iY_i).

¹⁰ op. cit. (n.9), 122.

¹¹ See Atkinson, A. B., The Economics of Inequality (1975), 45–7Google Scholar with graphic illustration of just this point. His claim that the Gini therefore embodies ‘implicit judgements about the weight to be attached to inequality at different points on the income scale’ seems to me unjustified. Rather, it is the use of the Gini for policymaking that carries the implicit value-judgement that all inequality is equal, so to speak. (Atkinson's book, like much of the literature on inequality, assumes both that it is a bad thing and that it is the business of government to reduce it, particularly at the bottom of the scale.) The problem with the Gini is not that it has judgemental freight but that (being a single figure) it cannot express complexities.

¹² ‘Some configurations of landholding in the Roman Empire’, in Finley, M. I. (ed.). Studies in Roman Property (1976), 7–33CrossRefGoogle Scholar, now reworked in Structure and Scale in the Roman Economy (1990), 121–42CrossRefGoogle Scholar; cited by Bowman, op. cit. (n. 7), 151. His results will be referred to below for comparative purposes. The reworked version does not replace the figures for the Hermopolite registers, drawn from the earlier edition, with those computed by Bowman.

¹³ Duncan-Jones, , Structure and Scale (n. 12), 129 n. 40Google Scholar, remarks of the Gini: ‘Though widely used, the Gini coefficient is a crude measure which takes no account of the shape of the curve. In the present figures, histograms are used as the form of illustration because they reveal more details.’ He does, however, give the Gini along with the histograms.

¹⁴ These will show why Duncan-Jones' caution about comparisons of land registers, though rejected by Bowman, op. cit. (n. 7), 150 n. 75, has some validity.

¹⁵ See Atkinson, op. cit. (n. 11), 27 and 237–51. These figures come from Nafziger, E. W., The Economics of Developing Countries (1984), 85Google Scholar.

¹⁶ Obviously this may not be true in any given case; the wealthy extremes will stand above the overall R, as Hermopolis does over the nome as a whole. The smallness of the samples may also cause some individual units to deviate from the overall pattern. The R for wealth in Wisconsin, measured county by county, ranged from .520 to .900, when the state R was .750. A map in Soltow, Lee, Patterns of Wealthholding in Wisconsin since 1850 (1971), 63Google Scholar, shows three concentrations of counties which had higher averages than the state as a whole. Only eight had .800 or higher, out of fifty-six total counties. The Wisconsin data are discussed more fully in VII, below.

¹⁷ It should be pointed out that this figure does not distinguish between land owned by village residents and that owned by absentee landlords. A fairly full description of this papyrus was given by Oates, J. F. in Atti dell'XI Congresso Internazionale di Papirologia (1966), 451–74Google Scholar, at which time publication was foreseen in P.Yale I.

¹⁸ Bowman's own recalculations now agree (letter of 18 March 1991); the source of the original error is obscure to both of us, but it was unique to this calculation, as my own computations calculations. have confirmed all of his other calculation.

¹⁹ That does not necessarily mean any simple, egalitarian pattern of leaseholds by ‘peasants'. More than two centuries of Roman rule had given plenty of time for the rights to such land to have been divided, subleased, or ceded in ways that will have made the situation with this land very complicated, and some owners of private land may also have leased public land.

²⁰ As Bowman points out to me, the low percentages (under 20 per cent) of ‘public’ land in the Hermopolite and Oxyrhynchite in the fourth century are difficult to accept as accurate reflections of how much land was owned by the crown in earlier centuries.

²¹ P.Cair.Isid. 6 is such a register, from perhaps five to ten years earlier, but a much smaller part of the population is represented there and a very substantial part of the numbers are missing, so that no useful conclusions about distribution seem to me possible.

²² These terms meant only different tax rates in this period, see Bowman, op. cit. (n.7), 148–9. The barley tax rate is given in P.Cair.Isid. 11.25; cf. the editors' introduction for the computation of the barley taxes for the village as a whole.

²³ This formula and the others are derived in detail in my article on ‘Bullion purchases and landholding in the fourth century’, Cd'E 52 (1977), 322–36, at 330 n. 1. I calculated the landholdings only for members of Isidoros' family in that article.

²⁴ For example, I computed Gini indexes including the four with no data and excluding them; the difference was only .022.

²⁵ It may be worth adding that I will gladly make any of the spreadsheets for data presented in this article available on standard diskette on request; they were prepared on Borland's Quattro Pro and should be usable on any Lotus-compatible spreadsheet programme for an IBM or compatible computer.

²⁶ By the same token, of course, the reservations expressed about the metropolitan data from Karanis are irrelevant to the Hermopolite figures.

²⁷ See Bagnall, ‘Property-holdings of liturgists in fourth-century Karanis’, BASP 15 (1978), 9–16.

²⁸ cf. my ‘Agricultural productivity and taxation in fourth-century Egypt’, TAPA 115 (1985), 290–308 for a detailed discussion of this problem.

²⁹ It is entirely possible that this is too pessimistic, as Alan Bowman points out to me. No doubt the actual figure fluctuated substantially from year to year. If the correct figure were instead 15 per cent (for example), the consequences would be that the village holdings in the nome model (below, IV) would be increased in size by about 21 per cent from the figures I have used, lowering R for the nome to some degree. The figures for R within the village, however, do not depend on any assumption about unproductive land, being computed from the gross holdings.

³⁰ ‘Allocation of risk and investment on the estates of Pliny the Younger’, Chiron 18 (1988), 15–42. Some of the same attitudes can be found in the British landed élite in early modern times; see Stone, Lawrence and Stone, Jeanne C. Fawtier, An Open Elite? England 1540–1880 (1984), 11–15 for the landowners' willingness to accept a low return in exchange for security and prestigeGoogle Scholar.

³¹ It is true that some metropolitans or Alexandrian citizens may have been resident at some time in a village where they had landholdings. There is very little evidence for this in the fourth century, but it may have been more common a century earlier.

³² Gascou, Jean and MacCoull, Leslie S. B., ‘Le cadastre d'Aphroditô’, Travaux et Mémoires 10 (1987), 103–58,Google Scholar pls 1–10.

³³ eidem, 113.

³⁴ The extensive struggle of the village of Aphrodito to maintain its autopragia, of course, shows that it took the matter seriously. Even though the taxes ultimately wound up in the same place, there were considerable consequences for control of the flow and for responsibility implicit in the distinction.

³⁵ The basic figure is derived from Karl W. Butzer, Early Hydraulic Civilization in Egypt. A Study in Cultural Ecology (1976), 74, but adjusted for the fact that most of the territory of the Kynopolite nome on the West Bank was divided between the Oxyrhynchite and Hermopolite by the Roman period. Factors of uncertainty are the precise dividing point and shifts in the Nile's bed in this period.

³⁶ R. S. Bagnall and K. A. Worp, ‘Grain land in the Oxyrhynchite nome’, ZPE 37 (1980), 263–4.

³⁷ These are somewhat lower than the figures offered by Bowman, op. cit. (n. 7), 147, who does not subtract for the difference between gross and net area.

³⁸ The relatively high Greek settlement in the Fayum may have had some impact on patterns, but it is hard to know precisely what that may have been.

³⁹ I have computed it in two ways. A 10 per cent sample of this hypothetical population was constructed, using 1 in 8 of the Antinoites, 2 in 5 Hermopolites, and 7 times the Karanidians; that yielded R = .558. A simple calculation weighting the separate R's yielded .561. (Herm., .829, weighted at .309; Ant., .631, weighted at .0363; Kar., .431, weighted at .6545.)

⁴⁰ Within the computational error range induced by different sampling procedures.

⁴¹ Assuming a lower percentage of urban-owned land, of course, would lower it further, perhaps another .020 if the real split were 25 per cent urban, 75 per cent village.

⁴² Remembering that this does not include public land.

⁴³ This figure is derived by adding the holdings of those with more than 10 ar., subtracting the number of individuals multiplied by 10, and dividing the remainder by total holdings.

⁴⁴ I have used 11 as a floor for urban residents, since their net yield was no doubt lower than that of villagers who actually worked much more of their own land. Moreover, 10 ar. at Karanis is equivalent to 7 ar. of productive land, probably close to what it actually took to support a family.

⁴⁵ The other figures for R in the Roman Empire derived by Duncan-Jones, op. cit. (n. 12), do not seem to me very useful, for reasons he pointed out himself, quoted above (at n. 13). The best of the lot is probably that from Ligures Baebiani, which gives R = .435, close to that of Karanis.

⁴⁶ Soltow, op. cit. (n. 16).

⁴⁷ idem, 121–4. It was .410 in 1870 and .380 in 1910. These are for not quite comparable sets; that for 1860 is ‘improved’ land; the Gini for all farmland was .364 (p. 57).

⁴⁸ idem, 124; his table there for Milwaukee County alone shows a similar rise from .380 to .640 when zero cases are included.

⁴⁹ Their absence significantly limits the significance of the Gini index; cf. Soltow, op. cit. (n. 16), 11.

⁵⁰ The average native-born farmer aged twenty or higher had 169 per cent of the wealth of the average foreign-born farmer aged twenty or higher. See Soltow, op. cit. (n. 16), 47.

⁵¹ Soltow, op. cit. (n. 16), 127, makes the general point that Wisconsin in the middle of the last century was not yet a stable society. On the other hand, his overall findings are that income inequality has decreased greatly (by a half, roughly) since then, while wealth inequality has decreased very little (p. 139).

⁵² idem, 5–7.

⁵³ There are 234 Hermopolite owners recorded in one quarter of the city; quadrupling would give at most about 1,000. For an estimate of 7,000 houses in Hermopolis, see Roeder, G., Hermopolis, 1929–1939 (1959), 107Google Scholar. Since two quarters are known to have had over 4,200 (East and West City, see SPP v 101), that estimate may be too low. But we do not know how far women listed as landholders may be part of the same households as listed men. And some houses held multiple households. At all events, a total urban population of 35,000 (perhaps too high) would imply 7,000 households.

⁵⁴ Soltow, op. cit. (n. 16), 126. The exclusions comprise 73 per cent of the landowners. These were, to be sure, ‘cottagers’, not farmers, averaging about a fifth of an acre each.

⁵⁵ See Soltow, Lee, Toward Income Equality in Norway (1965), 61Google Scholar.

⁵⁶ Within these groups there are also distinctions (not recoverable with present evidence) between those who own urban property and those who do not, and even those who own property other than their residence and those who own just a place to live.

⁵⁷ cf. Atkinson, op. cit. (n. 11), 247.

⁵⁸ See Soltow, op. cit. (n. 55); Soltow, op. cit. (n. 16), 128–39; Atkinson, op. cit. (n. n), esp. 22–7, 251; Tinbergen, Jan, Income Distribution, Analysis and Policies (1975), 17Google Scholar. For example, various Norwegian towns’ income Ginis fell from .470–.560 in 1865 to .280–.293 in 1960 (Soltow, op. cit. (n. 55), 17). The US in 1967 is estimated by Atkinson at .380 (income from all sources); Tinbergen (17) gives a drop from .500 to .330 for the US (wages only) from 1903 to 1956, essentially in line with data for other developed countries. Atkinson (25–6) points out that the US and UK had essentially similar income inequality, but the UK had a higher inequality of wealth.

⁵⁹ Soltow, op. cit. (n. 55), 42, gives wealth-income ratios for Norwegian towns, showing a decline in the median from 5.4 in 1855 to 1.2 in 1950.

⁶⁰ The Honduran figures are taken from Nafziger, op. cit. (n. 15), 85. The British come from Atkinson, op. cit. (n. 11), 46. Note that income and wealth may diverge considerably; cf. above.

⁶¹ Radwan, Samir, Agrarian Reform and Rural Poverty, Egypt, 1952–1975 (1977). 3–4Google Scholar.

⁶² idem, 4; in Radwan, Samir and Lee, Eddy, Agrarian Change in Egypt (1986), 7Google Scholar, however, the figure is given as .785; one of these is clearly a misprint. Radwan cites (25) a figure of .889 for R of landholdings (separate holdings, not totals held by an individual) in 1950; this is explicitly said to include zero cases, but it is not obvious how that can be true for a set of plots of land rather than of people.

⁶³ Harik, Ilya and Randolph, Susan, Distribution of Land, Employment and Income in Rural Egypt (1979), 22Google Scholar; Radwan, op. cit. (n. 61), 20. This figure, according to Radwan, relates to properties rather than people but includes some aggregation.

⁶⁴ That is, 200 feddan. I use a conversion of 1.5 ar. per feddan here; the feddan is actually .42 ha., or 1.524 aroura.

⁶⁵ Radwan, op. cit. (n. 61), 20; Harik and Randolph, op. cit. (n. 63), 22. For the progress of reform, see Radwan, 14.

⁶⁶ The slide and its consequences are vividly described in Cannadine, David, The Decline and Fall of the British Aristocracy (1990)CrossRefGoogle Scholar.

⁶⁷ Harik and Randolph, op. cit. (n.63), 2: a typical Third World country. On the other hand, Radwan, op. cit. (n. 61), 6 points out that Egypt had already been transformed from subsistence farming to ‘commercialised and profit-maximizing' agriculture by the introduction of cash crops, integration into world markets, the development of transport, trade, and financial structures. In this regard it resembled, mutatis mutandis, the situation in the third and fourth centuries.

⁶⁸ Radwan and Lee, op. cit. (n. 62), 44.

⁶⁹ idem, 46–53.

⁷⁰ Even the nineteenth-century data are often spotty and of doubtful reliability, after all, and we have none at all for antiquity.

⁷¹ cf. above, n. 58, and Soltow, Lee, ‘Long-run changes in British income inequality’, Economic History Review 21 (1968), 22CrossRefGoogle Scholar. Much of the data is insecure, but the gross consistency of the figures obtained from many different sources suggests that the true figures are likely to be in this range.

⁷² Lewuillon-Blume, op. cit. (n. 2); I am accepting the connection of the children of Aelianus to the family of Hyperechios' descendants. Her percentages are based on inaccurate totals and may be disregarded. It is, of course, possible that some of these families include still other landowners who cannot be identified with them given the information provided—husbands of women, for example. Eulalia, daughter of Aelianus, for example, registers some of her land through a Hymnos, known from G to be the son of Deios. Is Dios the bishop (who owns nearly 500 ar.) their son?

⁷³ See my ‘Conversion and onomastics: a reply’, ZPE 69 (1987), 243–50 on recent work concerning the date of this text.

⁷⁴ See R. S. Bagnall and P. J. Sijpesteijn, ‘Currency in the fourth century and the date of CPR V 26’, ZPE 24 (1977), 111–24 for the unit used.

⁷⁵ He remarks on the oddity of this organizational unit in a village; but I cannot offer anything better.

⁷⁶ See my ‘P.Oxy. XVI 1905, SB v 7756, and fourth century taxation’, ZPE 37 (1980), 185–96 and Bagnall, op. cit. (n. 28), for details.

⁷⁷ Assuming that all homonyms are the same person; there are twenty-two appearing in more than one phyle, and some of them might be different, though with some the names are uncommon enough that this is unlikely.

⁷⁸ A brief note on procedures followed: I omitted any amounts for which the entire entry was crossed out, but not numbers if the name was left. Entries in the same name are totalled. In a significant number of cases, names are lost but patronymics preserved. Some of these are probably to be identified with persons appearing else-where, in which case the number of very small holders would diminish (but some medium-sized payments would also be added to existing totals). It is not obvious that small holders would gain if we had more entries; the reverse may in fact be true, since the largest payers appear more often in general and the damaged entries are thus perhaps more likely to be theirs.