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A Probabilistic Approach to the Causes of Coups d'Etat

Published online by Cambridge University Press:  27 January 2009

Rosemary H. T. O'Kane
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‘In the last ten years on my individual reckoning’, observes S. E. Finer, ‘there have been seventy-three coups in forty-six countries’. ‘Coups’, Gurr comments, ‘can alter political processes and social institutions as drastically as any classic revolutions’. Yet the incidence and importance of coups are hardly reflected in the sparse literature proposing generalizations about their causes. Certainly, many case studies of individual coups have been undertaken, but the choice of the country has usually been decided by availability of data rather than its significance for a general theory. Given that coups have occurred all over the world, they clearly are a general phenomenon. Existing general explanations for them, however, are open to criticism. These suggest that essentially there is room for a theory which is about coups in particular rather than about wider forms of political instability, or about the narrower, military, coup; which is capable of falsification, avoiding inherently untestable hypotheses or concepts that are defined so loosely as to invite accusations of tautology; and which is, of course, able to withstand appropriate empirical examination.

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Articles
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British Journal of Political Science , Volume 11 , Issue 3 , July 1981 , pp. 287 - 308
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Copyright © Cambridge University Press 1981

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References

1 Luttwak, Edward, Coup d'Etat: A Practical Handbook (Harmondsworth, Middx.: Penguin, 1969), p. 9.Google Scholar

2 Gurr, Ted R., ‘Psychological Factors of Civil Violence’, World Politics, XX (1967–1968), 245–78, p. 246.Google Scholar

3 For full criticisms of these theories see O'Kane, Rosemary H. T., The Coup d'Etat – A Probabilistic Theory (Ph.D. dissertation, Lancaster University, 1978).Google Scholar

4 For example, see Eckstein, Harry H., ‘On the Etiology of Internal Wars’, History and Theory, IV (1964–1965), 113–63Google Scholar, who, by attempting to explain all forms of political disorder, is unable to suggest why coups, which unlike the rest do not always involve mass participation or violence leading to loss of life, should occur.

5 See, for example, Janowitz, Morris, The Military in the Political Development of New Nations: An Essay in Comparative Analysis (Chicago: Chicago University Press, 1964)Google Scholar and Pye, Lucian W., ‘Armies in the Process of Political Modernization’Google Scholar in Johnson, , The Role of the Military in Underdeveloped Countries, pp. 69–89Google Scholar, who are unable to provide an explanation for civilian coups where the military plays at most only a secondary role, or to recognize forms of military intervention which, unlike the coup, are not physical. It is this lack of appreciation of the possibility that the military can intervene when not actually holding office that prevents Von Der Mehden, Fred and Anderson, Charles W. (‘Political Action by the Military in Developing Areas’. Social Research, XXVIII (1961), 459–97)Google Scholar from recognizing that in order to demonstrate ‘Caretaker Governments’ to be evidence of the military being modernizers, they must also show that power and not just office have been handed over. In view of the subsequent evidence that military governments in new nations have demonstrated notably few ‘modernizing’ achievements and have a tendency to be overthrown themselves, these functional approaches are particularly unsatisfactory.

6 See, especially, Murray, Roger, ‘Militarism in Africa’, New Left Review, XXXVIII (1966), 35–59Google Scholar, who emphasizes the importance of the conspiracy of imperialist institutions like the IMF in encouraging coups. See also First, Ruth, The Barrel of a Gun (Harmondsworth, Middx.: Penguin, 1970)Google Scholar, who shares some of Murray's sentiments, particularly in the case of Ghana. Any documented alternative explanation to the role of imperialist institutions in deliberately engineering coups would be countered by the claim that the real truth had been deliberately ‘covered up’.

7 For example, see Gurr, , ‘Psychological Factors of Ci vil Violence’Google Scholar, where ‘civil strife’ is explained by the population's frustration and aggression, which sounds very like the description of a situation of civil strife. For numerous further examples see Dowse, Robert E., ‘The Military in Political Development’ in Leys, Colin, ed., Politics and Change in Developing Countries (Cambridge: Cambridge University Press, 1969), pp. 213–46Google Scholar, who is worried about the ‘woolliness’ of concepts throughout the literature. Fortunately the use of dichotomous variables can help.

8 The actual techniques employed may diner dramatically. See Rustow, Dankwart A., ‘The Military in Middle Eastern Society and Polities’, in Finkle, J. L. and Gable, R. W., eds., Political Development and Social Change (New York: Wiley, 1966), pp. 386–96, at p. 392Google Scholar, where techniques from a whisper in an ear (Iraq, 1938) to the dropping of bombs (Baghdad, 1958) are discussed. He agrees, however, that the more common step is for army units to occupy key communication points. See especially Luttwak's delightful book, Coup d'Etat: A Practical Handbook.

9 See Eckstein, , ‘On the Etiology of Internal War’Google Scholar and Luttwak, , Coup d'Etat: A Practical HandbookGoogle Scholar, who suggest similar structures for explanations.

10 See Decalo, Samuel, Coups and Army Rule in Africa: Studies in Military Style (New Haven, Conn.: Yale University Press, 1976).Google Scholar

11 For expansion of the arguments which follow, see in particular Helleiner, G. K., International Trade and Economic Development (Harmondsworth, Middx.: Penguin, 1972)Google Scholar and MacBean, Alasdair J., Export Instability and Economic Development (London: Allen and Unwin, 1966).Google Scholar

12 See United Nations Yearbook of Internal Trade Statistics, 1969. Even Brazil contributes less than one-third of total coffee production.

13 For evidence of continued price fluctuations in commodities subject to international agreements see United Nations World Economic Survey, 1969–1970 (New York: United Nations Organization, 1971), p. 171Google Scholar, Table 6. For discussion of the problems faced by such agreements see Helleiner, , International Trade and Economic Development, Chap. 3 and pp. 91–3Google Scholar, and MacBean, , Export Instability and Economic DevelopmentGoogle Scholar, Chap. 12.

14 For example, the formation of OPEC, the Organization of Petroleum Exporting Countries, was followed by the formation of OPIC, the Organization of Petroleum Importing Countries.

15 For a list of twenty-four goods with close industrial or natural substitutes see United Nations World Economic Survey, 1963 (New York: United Nations Organization, 1963), pp. 116–18.Google Scholar

16 Myrdal, Gunnar, Asian Drama: An Inquiry into the Poverty of Nations, abridged by Seth King, S. (London: Allen Lane, Penguin Press, 1972), p. 91.Google Scholar

17 Myrdal, , Asian Drama, p. 92.Google Scholar In support of Myrdal see, for example, Singer, Hans W., ‘The Distribution of Gains Between Investing and Borrowing Countries’, American Economic Review, XL (1950), 473–85.Google Scholar

18 Helleiner, , International Trade and Economic Development, p. 85.Google Scholar

19 Helleiner, , International Trade and Economic Development, p. 86.Google Scholar

20 The 1964 coup in Brazil is illustrative. Before the coup the government received enormous foreign loans and encouraged direct investment from foreign countries, largely in order to fulfil promised development programmes in the face of declining coffee exports and revenues (coffee representing 41 per cent of the value of the total export revenue). At first per capita growth expanded by 3–4 per cent but by 1962 it had fallen to 0·7 per cent, and by 1964 to –6 per cent. See Frank, Andre Gunder, Capitalism and Underdevelopment in Latin America (Harmondsworth, Middx.: Penguin, 1969), pp. 211–12.Google Scholar

21 As in the case of Brazil, Ghana acquired an enormous foreign debt in the face of growing balance of payments deficits and, due to declining prices, diminishing cocoa export proceeds. After 1961 high inflation occurred, the consumer price index rising by 65 per cent in three years. See Kraus, Jon, ‘Ghana, 1966’ in Andrews, William G. and Ra'anan, Uri, The Politics of the Coup d'Etat (New York: Van Nostrand Reinhold, 1969), Chap. IV, p. 105Google Scholar, and Dowse, , ‘The Military in Political Development’, p. 234.Google Scholar

22 MacBean, , Export Instability and Economic Development, p. 28Google Scholar. The 1966 Nigerian coup serves as a good example. Tribal tensions were already high, being exacerbated by price fluctuations in the major exports, each concentrated in particular areas. The increasingly valuable revenues from oil, located mainly in the Eastern regions, were used to benefit the North, from which area the Government largely came. See First, , The Barrel of a Gun, p. 148.Google Scholar

23 This seems to have been the case in Ghana. Nkrumah's Convention People's Party, having founded the Cocoa Purchasing Company to assist poorer farms, effectively put itself in direct competition with important cocoa farmers and local cocoa-brokers. Not surprisingly it was in the Ashanti area, the main cocoa-producing area, that the National Liberation Movement was formed to stage the coup. See First, , The Barrel of a Gun, p. 178.Google Scholar

24 This was the case in Nigeria and also, for example, in Libya in 1969, when the stark riches and poverty in the feudal society were sharply highlighted by the flood of oil revenues. Again, see First, , The Barrel of a Gun, p. 158.Google Scholar

25 It follows that the motive for removing the government and the source of conspirators would be likely to differ according to the nature of the society, structure of the economy, and pattern of economic instability engendered. They might sometimes be intent on being ‘modernizers’ (see, for example, Pye, Lucian W., ‘Armies in the Process of Political Modernization’)Google Scholar. They might equally (as First, , The Barrel of a Gun, pp. 429–32 suggests)Google Scholar be intent on increasing their own share of the spoils, or as Decalo suggests in Coups and Army Rule in Africa: Studies in Military Style, p. 21Google Scholar, be seeking vain personal glory. If it is the military that most often stages coups this surely reflects their peculiar advantages for staging them (rather than the importance of special modernizing characteristics); their monopoly of coercion; and the fact that their neutrality or support would have to be gained before a civilian group could stage a coup. In this latter case the military would be likely either to be provoked into pre-empting a civilian attempt or to join forces with the civilians, so masking the real civilian nature of the coup. Potential coup situations will often involve several groups of plotters. Certainly it is unlikely that motives for the military to intervene will be purely military ones. Most coups are likely to be staged by a combination of military and civilian personnel for a combination of motives which, although compatible at the time of the coup, are likely to create problems for the new government.

26 This obstacle is closely influenced by Zolberg's discussion of the importance of ‘the passing of time’ and his statement that, ‘coups are more likely to occur after a few years of independence than initially because it takes some time for a government to use up its political capital and for opponents to test the government's strength’. See Zolberg, Aristide R., ‘The Structure of Political Conflict in the New States of Tropical Africa’, American Political Science Review, LXII (1968), 70–87, p. 78.CrossRefGoogle Scholar

27 Another reason why this may be important is because countries recently made independent rarely possess experienced armies, so that at least one possible source for likely conspirators will not exist. The correlation between recent independence and not having an army is high (r = 0·605). This interpretation is also supported by the fact that Algeria, which succumbed to a coup only three years after independence, had a particularly highly trained and well-established army.

28 This obstacle is also stimulated by Zolberg's suggestions (see fn. 26): ‘within one country also coups engender other coups. The success of one set of claimants encourages others to try’ (p. 80).

29 It is perhaps for this reason that in some parts of Latin America the ‘illegal’ coup has almost become an institution. See also Rustow, , ‘The Military in Middle Eastern Society and Polities’, p. 391Google Scholar, who argues that military coups are encouraged by repression. The increasing reliance of the government on the military, whilst contributing to the ‘army's skills in domestic coercion’, argues Rustow, makes the civilian government ‘a more vulnerable and tempting target’.

30 That this might be an obstacle was inspired partly by First, , The Barrel of a Gun, pp. 413–23Google Scholar, where she discusses the role played by foreign armies in Africa and in particular by the French, especially in Gabon. But it was largely developed from Luttwak's argument that the presence of a foreign army indicated that the host country was not truly independent (see Coup d'Etat: A Practical Handbook, p. 44)Google Scholar. To some extent the presence of foreign troops may indicate that power does not entirely rest with the internal government. This is particularly likely if the forces are those of the ex-colonial power and especially if they still hold command positions in the country's own army or police force. If power were not considered to exist in the hands of the government then people would be less likely to blame that government for incompetence, and therefore a coup would be less likely to be attempted. However, this would seem to be a special case of the more general argument proposed.

31 See Murray, , ‘Militarism in Africa’Google Scholar, and First, , The Barrel of a Gun, pp. 413–23.Google Scholar

32 For a detailed explanation of discriminant analysis, see Rogers, K. G., Townsent, G. M. and Metcalf, A. E., ‘Planning for the Work Journey’, Local Government Operational Research Unit Report, No. C 67, pp. 47–51Google Scholar. The dependent variable, Z, is calculated from

where Y = had a coup 1950–70 = 1,

and not = 0;

n1 = the number of countries having had coups;

n2 = the number of countries not having had one.

Hence, the two ideal scores were Z1 = 0·648 for countries having had a coup and Z2 = –0·352 for countries not having had one. The technique essentially consists of the procedure for multiple regression analysis employing a dummy dependent variable (see van de Geer, John P., Introduction to Multivariate Analysis for the Social Sciences (San Francisco: W. H. Freeman, 1971))Google Scholar. It differs from it in that the dependent variable, rather than being 0 to 1, is either positive or negative, the calculation of the dependent variable scores being determined by the size of the two populations. The effect of this on the function generated is to change the constant term, reflecting the shift in the range of scores on the Y axis.

33 See. for example, the ‘Military Intervention Index’, constructed by Putnam, Robert D., ‘Toward Explaining Military Intervention in Latin American Polities’, World Politics, XX (1967–1968), 83–110CrossRefGoogle Scholar, which succeeds only in constructing an ordinal scale and not the interval scale necessary for the calculation of the correlations which he undertakes. For elaboration of this problem see Blalock, Hubert M. Jr, Social Statistics (New York: McGraw-Hill, 1960), pp. 13–16Google Scholar. For a detailed explanation of the use of dummy or binary variables, see Johnston, J., Econometric Methods (New York: McGraw-Hill, 1963), pp. 221–8.Google Scholar

34 The use of cross-section data can be criticized for representing the conditions which existed after a coup, when the hypothesis refers to preconditions. However, the majority of developing countries had not changed the scores of their socio-economic variables much in relation to the rest of the world since the Second World War. In any case, as Ferguson points out, ‘in general the effect of unreliability in measurement of variables is to reduce the obtained correlation coefficients slightly below the values that would be expected if there were no such measurement error’ (see Ferguson, George A., The Statistical Analysis in Psychology and Education (New York: McGraw-Hill, 1966), p. 289)Google Scholar. Given that the problem of errors in variables would be expected to increase the likelihood of the hypothesis being falsified, this difficulty could not be said to bias the data in favour of the theory.

35 Reliable data for 1970 eventually became available in 1976 in the 1974 United Nations Statistical Yearbook (New York: United Nations Organization, 1975)Google Scholar. In this volume a particular effort had been made to collect a complete set of data for 1970. For all the more recent years, missing data, especially for the ‘developing countries’, continued to be a major problem. Employing the more recent data it was found that no significant differences resulted. This was confirmed by a test for structural stability (see fn. 56). See also fn. 52 for discussion of its predictions. Even when taking 1968 statistics there remained some independent countries for which data were unavailable: Communist China, North Vietnam, North Korea, Albania, the Yemen, Nepal, Oman, San Marino, Liechtenstein, the Vatican City, Andorra, Nauru, Western Samoa, Maldives and Equatorial Guinea. The loss of the latter small countries was not really worrying, because their size would tend to make their statistics unreliable even where available. The four communist countries were a particularly unfortunate loss, however, because it would not be unreasonable to expect that they might be possible exceptions to the generalization proposed. Nevertheless, their low dependence on world market trade and the fact that none of them have had coups is consistent with the arguments presented. The cases of the Yemen, Oman and Nepal would not be expected to represent significant deviations, but it was nevertheless unfortunate that they could not be included.

36 Countries having had at least one coup were then the following: Algeria, Argentina, Bolivia, Brazil, Burma, Burundi, Cambodia, Central African Republic, Colombia, Congo Brazzaville, Cuba, Dahomey, Dominican Republic, Ecuador, Egypt, El Salvador, Ghana, Greece, Guatemala, Haiti, Honduras, Indonesia, Iraq, Laos, Libya, Malta, Nigeria, Pakistan, Panama, Paraguay, Peru, Sierra Leone, Somalia, South Korea, South Vietnam, Sudan, Syria, Thailand, Togo, Turkey, Uganda, Upper Volta, Venezuela, Zaire.

37 The countries were the following: Argentina, Bolivia, Burma, Columbia, Dahomey, Dominican Republic, Ecuador, El Salvador, Guatemala, Iraq, Panama, Peru, Sierra Leone, Sudan, Syria, Thailand, Togo.

38 The countries were as follows: Barbados, Botswana, Guyana, Lesotho, Mauritius, Southern Yemen, Swaziland.

39 Following Wood, David in The Armed Forces of African Slates (Adelphi Papers, No. 27, 04 1966)Google Scholar the countries were the following: (i) Foreign Officers on secondment to local army (or police force where no army exists): Botswana, Cameroon, Gabon, Gambia, Malawi, Mauritius, Zambia, (ii) Foreign armoured divisions (not missile bases): Chad, Ivory Coast, Malagasy Republic, Malaysia, Malta, Mongolia, Niger, Philippines, Senegal, Singapore, South Vietnam, West Germany (NATO) and East Germany, Hungary, Poland and Czechoslovakia (since 1968) (Warsaw Pact troops). Egypt, which did not have such troops at the time of its coup in 1952, was not included, although their presence since may help to explain the absence of a second coup. These European countries were included only reluctantly because it was thought that given their high economic indices and the fact that none of them have had successful coups since 1950, they might bias the results in favour of the theory. However, running the model as if these countries were not subject to this obstacle (X6 = 0), the multiple correlation coefficient, R, actually increased, although by the insignificant level of 0·005. The model remained virtually unchanged, all variables remaining significant at approximately the same level, except this particular variable, the ‘t statistic’ increasing from 3·59 to 3·91.

40 A less simple operationalization – taking the total of the four major exports as a percentage of all exports – was also considered. In practice, however, the two operationalizations were very highly correlated at r = 0·917. In any case, it suffered the disadvantage of being less easily interpreted.

41 This relationship would have probably been better represented by the function log Y = a+b (log x) + c(log X)2. Unfortunately this function could not be used, because of the dummy dependent variable being negative. For discussion and illustration of transformations see Ezekiel, Mordecai J. B., Methods of Correlation Analysis (New York: Wiley, 1949), pp. 75–127, p. 79.Google Scholar

42 For a detailed discussion of multicollinearity, see Johnston, , Econometric Methods, pp. 201–7.Google Scholar

43 For an explanation of students' t distribution, see Blalock, , Social Statistics, pp. 144–9.Google Scholar

44 In general, the eflect of intercorrelation would be to reduce the significance of each variable. When multicollinearity is at a very high level, however, the fraction of explained variance, R2, may be increased. This is clearly a major problem, because this might lead to the hypothesis not being falsified when it should be. However, inclusion of the dummy variable in the regression, ‘whether or not a country produces a primary good as the major export’, which was the most highly intercorrelated of all the variables, increased the multiple correlation coefficient by only 0·002. Additional confirmation comes from the fact that the correlation coefficients are not larger than the multiple correlation coefficient. This is indeed the case with no r being as high as R at 0·741. It was therefore decided to run the regression without fear that the results would be likely to be unduly favourable. Indeed, it was expected that the reduction in the significance scores by the multicollinearity would probably be unfavourable to the hypotheses.

45 Data sources: Variables Y and X 4: Keesing's Contemporary Archives (London: Keesing's Publications, Longman); Europa Yearbooks, 1950–1972 (London: United Nations)Google Scholar; The New York Times Encyclopedic Almanac, 1970, (New York: 1969)Google Scholar; The Statesman's Yearbooks, 1950–1972 (London: Macmillan)Google Scholar; Luttwak, , Coup d'Etat: A Practical Handbook, Appendix C, pp. 194–9Google Scholar; First, , The Barrel of a Gun, pp. xii–ivGoogle Scholar; Niedergang, Marcel, The Twenty Latin Americas, Vols, 1 and 2 (Harmondsworth, Middx.: Penguin, 1971)Google Scholar; X 1: Europa Yearbook, 1970Google Scholar; United Nations, Statistical Yearbook, 1971 (New York: United Nations, 1972)Google Scholar; New York Times Encyclopedic Almanac, 1970Google Scholar; X 2 and X 3: United Nations Yearbooks of International Trade Statistics, 1968 and 1969 (New York: 1970 and 1972)Google Scholar; X5 Europa Yearbooks; X 6, Col. Dupuy, T. N. and Col. Blanchard, Wendell, The Almanac of World Military Power, 2nd ed. (London: Arthur Baker, 1972)Google Scholar; Europa Yearbooks: Hovey, A., United States Military Assistance: A Study of Policies and Practices (New York: Praeger, 1965)Google Scholar; Wood, , The Armed Forces of African States.Google Scholar

46 For an explanation of the computation of degrees of freedom, their relevance to the t statistic and the statistical table for the distribution of t, see Blalock, Social Statistics, pp. 156, 247 and 442. For support for the use of tests of significance where data are being used for a universe of cases rather than the random sample for which they were designed, see Blalock, , Social Statistics, p. 270Google Scholar, and Gold, D., ‘Some Problems in Generalizing Aggregate Associations’, American Behavioural Scientist, VIII (1969), 6–18.Google Scholar

47 See Blalock, , Social Statistics, p. 274Google Scholar and Johnston, , Econometric Methods, p. 224Google Scholar. See also fn. 34.

48 All of the following coups and events can be checked in Keesing's Contemporary Archives, and the Europa Yearbooks.

49 Data source: Europa Yearbooks and the New York Times Encyclopedic Almanac, 1970Google Scholar. However the variable was constructed (e.g. to exclude ‘constitutional monarchs’) it remained insignificant with a low score.

50 The problem here, as with Putnam's MI index (see fn. 33), is the difficulty of constructing the interval scale necessary for correlation analysis. Attempts to do so soon revealed that there were almost as many different variations of political systems as countries, not to mention the problems of trying to decide, for example, the real power of monarchs, or the meaningfulness of elections. See, for example, the criticisms made against Cutright, Phillips (‘National Political Development: A Measurement and Analysis’, American Sociological Review, XXVIII (1963), 253–64CrossRefGoogle Scholar) by Needier, Martin C. in ‘Political Development and Socio-Economic Development: The Case of Latin America’, American Political Science Review, LXII (1968), 889–97.CrossRefGoogle Scholar

51 As a further check on the generality of the Model and its claim to achieve a ‘best’ explanation, a variety of other variables suggested by existing theories were also included, in turn, in the Model. In no case did they achieve significance. See O'Kane, , The Coup d'Etat: A Probabilistic Theory, Chap. 7.Google Scholar

52 Discriminant analysis applied to the newly collected data for 1970 (see fn. 35), which was expected to suffer from fewer errors, indicated that the apparent deviance of Honduras, Saudi Arabia and Jamaica was the consequence of errors in the data and that Tunisia should have been included amongst the list of predictions for a coup.

53 Nevertheless, the same technique that was used to examine the implications of change in the other two dummies can be usefully applied here in order to examine possible bias. The problem is that only countries which have had coups between 1950 and 1970 can also have had previous ones during that time. It might be argued that this accounts for the high t statistic at 6·24. However, of the forty-four countries having had a coup, only seventeen of them have had more than one during the same period. Furthermore, when the regression was run without this dummy variable only Dahomey, Peru and Togo out of these seventeen countries could not have been explained by the model.

54 In addition to Keesing, 's Contemporary ArchivesGoogle Scholar, see Dupuy, and Blanchard, , The Almanac of World Military Power, pp. 228 and 351.Google Scholar

55 For discussion of this test see Johnston, , Econometric Methods, pp. 136–7.Google Scholar

where Q 1, = ESS (Error sum of squares of the full data set)

Q 2 = ESS1 + ESS2 (ESS of developed countries only + ESS of developing countries only)

Q 3 = Q 1 + Q 2

and n – k = degrees of freedom in the ‘developing countries’ data set,

m – k = degrees of freedom in ‘developed countries’ data set.

If F > F 1 then the hypothesis that the three regressions were the same must be rejected. For 120 degrees of freedom and 8 variables, the score for F 1 = 3·55 at the 0·001 level of probability.

56 Other categories of countries than these have also been suggested as being critically different from the rest. In particular, the countries of Latin America, of Africa, more narrowly of the tropical states of Africa, and more widely the ‘new states’ of Africa and Asia have been suggested as significantly different from other areas of the world with respect to coups. When the test for structural stability was applied in turn to these areas, in no case could a significant difference be found between the coefficients of the two subset functions and those of the model. With the score for P remaining at 3·55, the results were the following: for Latin America, F = 1·458; for Africa, F = 0·945; for tne new states of tropical Africa, F = 0·858; for the new states of Africa and Asia, F = 1·110. The test for structural stability applied to the new model generated by the 1970 data also showed no significant difference between them with F = 0·364.