Use diffusion: An extension and critique

TECHNOLOGICAL

FORECASTING

AND SOCIAL CHANGE

16, 331-341

(1980)

Use Diffusion: An Extension and Critique* STEPHEN 0. MURRAY and JOSEPH H. RANKIN

ABSTRACT This study demonstrates that exponential modeling applies to the diffusion of foods. By using per capita data rather than gross consumption data, we show that this exponential process is not an artifact of a simultaneous population increase. However, whereas previous researchers predict that use diffusion continues indefinitely though at decreasing rates from one time period to the next, the present study demonstrates that it can end or even reverse, as well as attenuate. The extension of reinforcement theory in psychology to “social learning” theory is rejected as an explanation of this change, and the alternative “technological substitution” model is discussed.

Introduction

Two basic forms of “diffusion” are discussed in Hamblin, Jacobsen, and Miller’s [lo] description of social change as quantitative processes: binary adoption and use diffusion. The former refers to discrete decisions on whether or not to adopt an innovation and can be described by logistic curves that reach an asymptote whenever diffusion is completed. The decision to purchase a television set is binary; one either buys the set or one does not. On the other hand, use diffusion is a continuous exponential process. For example, television viewing is not a simple dichotomy, since an individual can watch TV for varying periods of time up to 24 hours a day. The integrated form of the exponential equation for this latter process is X = ue”, where X is the quantity being compounded, a is a scalar constant, e is a constant equal to the base of natural logarithms, k is the compound interest rate, and t is time. Transformed to natural logarithms, this equation becomes log X = log a + kt and linear regression analysis can be performed [2, lo]. Although binary adoption can reach an upper limit or asymptote, Hamblin et al. [lo] and others (e.g., Hart [ 121) fail to *An earlier version of this paper was presented at the 72nd annual meeting of the American Association, Chicago, 1977.

Sociological

STEPHEN 0. MURRAY received his Ph.D. in sociology from the University of Toronto in 1979. His dissertation is concerned with the history of social networks in American linguistics and anthropology and is being published under the title, Group Formation in Social Science. He is currently associated with Social Network Consultants, Berkeley, California. JOSEPH H. RANKIN received his Ph.D. from the University of Arizona in 1978 and is now an Assistant Professor of Sociology at Purdue University. His major research interests include social change, juvenile delmquency, and various attitudes toward punishment and other aspects of the criminal justice system. His most recent article, “School Factors and Delinquency: Interactions by Age and Sex,” is forthcoming (1980) in Sociology and Social Research.

@ S. 0. Murray et al., 1980

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STEPHEN 0. MURRAY AND JOSEPH H. RANKIN

note such limits (e.g., the total number of hours in a day) in describing use diffusion-a process they see as continuing indefinitely. The present study demonstrates that both forms of diffusion can end. The Exponential Modeling Controversy Ogburn [20], the pioneer in mathematical approaches to social change, realized that exponential processes do not continue indefinitely. In his study of dramatic increases in domestic air travel, Ogburn warned against the facile projection of curves from the past into the future.’ Nevertheless, Hart [ 121 maintained that a single exponential curve could continue at the same rate into the future. Air passenger miles continued to increase rapidly during the years immediately subsequent to Ogbum’s [20] study, and in 1949 Hart demonstrated that for the years 1930-1948 a single exponential curve accurately described the data (r2 = 0.99+). Thus, Hart chided Ogbum for predicting that the rate of (use) diffusion would decrease with time. However, Ogbum [21] noted that Hart’s predictions were absurd and reasserted that a decrease in the diffusion process would have to be the long-range trend. Even as the Hart-Ogbum controversy raged in the pages of the American Sociological Review, the particular diffusion process they were discussing was slowing down. In the period subsequent to Ogburn’s research (i.e., 1949- 1968)) the data on air passenger miles was best described (r2 = 0.99) by an exponential equation with an exponent only half as large as that in the preceding period, not by one continuous exponential process beginning in 1930 as Hart had predicted [IO]. By demonstrating that Ogbum 1201 was correct in predicting that the high rate of exponential growth could not continue indefinitely, Hamblin et al. [IO] “rescued” exponential modeling from absurd predictions like Hart’s [ 121. Adopting von Bertalanffy’s [23] suggestion that the original accelerating exponential increase is combined “by multiplication with a decaying exponential increase,” Hamblin et al. [lo] recognized that the rate of diffusion decreases with time. That is, the exponent or compound rate diminishes with subsequent time spans called epochs. The rate of diffusion must diminish with time, or outcomes of infinite use would have to be posited. Although Hamblin et al. [lo] recognize that the diffusion process slows down, an asymptote or level of unchanging adoption was never posited. Perhaps because gross consumption data rather than per capita data (which by definition control for population growth) were used, Hamblin et al. [lo] fail to recognize that use diffusion may reach a steady state. Hamblin et al. [lo] found that some historical data such as the number of passenger miles traveled by a variety of vehicles, gasoline consumption, number of higher education degrees granted, automobile and truck registrations, and number of marriages and divorces were described nicely (median r2 about 0.98) as exponential processes (with decreasing k values or exponents for subsequent epochs). However, such time-series analyses did not control for exponential increases in population growth. Since an exponentially increasing population tends to consume things in exponentially increasing quantities, the diffusion process may be, at least in part, a function of population increase. However, Hamblin et al. [lo] did not plot per capita rates. The present research examines the diffusion of canned, frozen and citrus food con’ Hamblin et al.‘s [lo] account of the Hart-Ogbum polemic attributes Hart’s position to Ogbum, position to Hart, and then miscites Hart (cf. Murray [ 161).

Ogbum’s

USE DIFFUSION:

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sumption* in the United States and Canada using per capita data rather than the gross consumption data used in previous research. Per capita data can be used to determine whether increasing consumption is an artifact of population increase. If an increase in the consumption of particular goods is solely a result of population increase, no exponential pattern will emerge when using per capita data. On the other hand, if exponential patterns do emerge in the per capita data, population increase can be eliminated as an explanation of the increased consumption patterns. After demonstrating that use diffusion remains an exponential process even when controlling for population increase, we will show that use diffusion (like the binary adoption process) can also end (i.e., reach an asymptote so the exponent in the diffusion equation approximates zero) or reverse (i.e., have a negative exponent) as well as attenuate (i.e., have diminishing exponents for subsequent epochs). Finally, Ogbum’s [20] most important question-what accounts for the exponential diffusion process?-will be discussed. United States and Canadian per Capita Consumption Patterns The process of preserving food by heating and sealing in glass jars was invented in 1809 by the Frenchman, Francois Appert. However, a large-scale canning industry did not appear in the United States until after 1874, when Andrew Shriver patented a process that eliminated the problem of bursting cans. Unfortunately, consumption data for canned foods are not available for the period prior to 1909, by which time the initial diffusion process was well under way. Thus, the original level of per capital consumption of canned foods in the available data was already several pounds [22]. The diffusion of frozen foods began later than canned goods. Mechanical refrigeration was first developed in Australia and New Zealand in the late nineteenth century for exporting meat. Although the first commercial freezing plant was constructed in 1891 in New Zealand, the first North American plant was not built until 1904 in Pittsburgh [5]. In the mid-1920s refrigerators with freezing compartments initially replaced ice boxes in North American homes. Per capita consumption of citrus fruit constitutes the final set of diffusion data. During the first half of this century improved storage and transportation permitted the American population wider access to fresh citrus fruit grown far from the major population centers. In fact, per capita consumption of fresh citrus fruits increased fivefold between 1909 and 1945 [22]. Results As indicated in Table 1, even without data from the initial stage of the diffusion process, consumption of U.S. canned vegetables is an exponential process (r’ = 0.93). Whereas the consumption of U.S. canned vegetables is described as one continuous exponential process beginning in 1909, the consumption patterns of U.S. and Canadian frozen vegetables are each described by two epochs of decaying exponential increases; that is, the exponent (the compound rate or k value) decreases for subsequent time periods

*The available data are labeled “apparent” civilian consumption of foods by both the U.S. Bureau of the Census [22] and the Canadian Bureau of Statistics ([3], 1978-1979) because calculations are made at the retail (rather than the consumer) level of distribution. “Amounts of food actually consumed would be lower than that shown because of losses and waste occurring after the products reach the consumer” [3, 1978-1979, p. 4781. However, these data are used in the present study because they “are the only available estimates of consumption” [22, p. 3141.

334

STEPHEN 0. MURRAY AND JOSEPH H. RANKIN TABLE 1 Canadian and U.S. Per Capita Consumption Item

U.S. Canned Vegetables U.S. Frozen Vegetables Canadian

Frozen Vegetables

’ Parameters

of Selected Foods

Epoch

a (lbs)”

k

1909-1970 1937-1952 1953-1970 1947- 1957 1958-1972

16.22 0.37 5.53 0.28 2.16

0.02 0.18 0.08 0.19 0.08

0.93 0.97 0.99 0.98 0.84

for the equation log X = log a + kt

Sources. From refs. [22] and [3]

or epochs. Thus, even when controlling for population growth by using per capita data rather than gross consumption data, these results support the predictions of Hamblin et al. [lo]. The consumption of canned and frozen vegetables increased exponentially. However, Table 2 indicates that Canadian and U.S. consumption patterns can also reach upper limits (asymptotes). Whereas Hamblin et al. [lo] hypothesize a series of exponential epochs with diminishing exponents, use diffusion appears to have ended altogether in these particular consumption patterns (see Figs. 1 and 2). The exponents become minuscule in subsequent epochs (0.01 for all the items in Table 2). Thus far, the data presented in Tables 1 and 2 support the predictions of Hamblin et al. [lo] (i.e., that the exponents for subsequent epochs should diminish, but remain positive). Although the patterns in Table 2 do indicate a final “leveling off” of consumption patterns, the exponents still me positive (albeit minuscule). Moreover, since exponential equations describe the data rather well, the alternative hypothesis that population growth solely accounts for the increased consumption of these foods is implausible. However, Table 3 reveals that use diffusion can also reverse. That is, the exponents for the integrated form of the equation describing the trend of per capita consumption of Canadian canned and frozen fruit and U.S. citrus fruit become negative in the later years of the diffusion process. The downward trend of these data (median r* = 0.89) indicates a clear reversal (see Figs. 3 and 4). Reinforcement as an Explanation of Social Change Hamblin and Miller [ 1I] state that “one of the most significant theoretical problems in sociology is what influences the beginnings, the rate, and the extent of macro social TABLE 2 Canadian and U.S. Per Capita Consumption Item U.S. Canned Fruit Juice Canadian Canned Vegetables U.S. Frozen Fruits and Juices U.S. Canned Fruit

” Parameters Sources.

Epoch

a (lbs)”

k

p

1925- 1945 1946-1970 1949- I972 1925-1954 1955-1970 1909%1920 1921-1930 193lL1946 1947- 1970

0.12 14.68 18.10 0.20 8.49 3.09 7.94 11.92 19.89

0.25 0.01 0.01 0.12 0.01 0.11 0.06 0.02 0.01

0.82 0.02 0.04 0.98 0.09 0.96 0.83 0.24 0.61

for the equation log X = log u + kt.

From refs. [22] and 131.

of Selected Foods

USE DIFFUSION: AN EXTENSION

335

AND CRITIQUE

l** i?

:**-•-

Canadian Canned Vegetables

I

1930

Fig. 1. Per capita consumption

I

I

1940

I

I

1950 YEAR

I

I

1960

I

I 1970

of Canadian canned vegetables and U.S. frozen fruits and juices.

processes.” Although they have clearly expressed the problem confronting this line of research, there is little in their work that could be characterized as explanation of the many origins, rates, or extent of the diffusion processes they document. “Epochs” are ad hoc creations, drawn in whatever manner maximizes the r* values. Sometimes the epochs coincide with the Depression or World War II, but Hamblin et al. [lo] fail to explain why some diffusion processes are affected by these events while others are not. Moreover, their appeal to Skinnerian learning theory is tautological, assuming that an individual adopts an innovation because it is rewarding and then arguing that the innovation is rewarding because the individual adopts it. Their concept of “reward” is elastic-either assumed a priori or tautologically claimed post hoc [4]. Specifying the meaning of “reward” is difficult for individuals. When similar explanations are posited for groups of individuals, who or what is being rewarded is even more puzzling. Hamblin et

336

STEPHEN 0. MURRAY AND JOSEPH H. RANKIN 4 0,

2 O-

o?5-

!-

U.S. Canned Fruit

>

"I I I

1 I

.EI/

.C,I 00

L

U.S. Canned Fruit Juice

I00

.4I-

.i ,-

00 I I I

I 1910

1

I 1920

1 01

I

1930

Fig. 2. Per capita consumption

I 1940 YFAR

1

I 1950

I

I 1960

1 0

of U.S. canned fruit and canned fruit juice.

to prevent hijackers, bank failures, and al. [lo] present societies supposedly “learning” so on. Not only is this reification, but the measure of societal reward is left unspecified (and is probably unspecifiable) .3 Hamblin et al. [lo] posit but do not measure rewards, nor do they specify whom is to be rewarded. In a recent article reinterpreting Griliches’s [9] data on the diffusion of 3There are theories of learning other than those based on Hull and Skinner (e.g., Dunn [6]). However, the point is simply that if one espouses Skinnerian learning, the reward must be specified. Since Dunn [6] is not concerned with reinforcement, this criticism does not apply to him.

USE DIFFUSION:

AN EXTENSION

337

AND CRITIQUE

TABLE 3 Canadian and U.S. Per Capita Consumption Epoch

Item Canadian Canned Fruit

Canadian

U.S. Citrus Fruit U.S. Total Fruit

R Parameters Sources.

a(lbs)"

1949-1965 1966- 1972 1946- 1963 1964- 1972 1909- 1944 1945- 1970 1909- 1947 1948-1970

Frozen Fruit

of Selected Foods

13.95 39.76 0.27 3.48 16.55 57.66 139.62 121.23

k

9

0.07 -0.03 0.15 - .03 0.04 -0.03 -0.01 -0.02

0.74 0.98 0.89 0.45 0.95 0.89 0.02 0.91

for the equation log X = log a + kt.

From refs.[22] and [3].

2oo, .

.*

150-

.

.

l

.

..*

.

l

. . .

l

l .

. .

. . .

.

loo-

U.S. Total Fruit

80-

U.S. Citrus Fruit

I

1910

L

I

1920

d

I 1930

1

Fig. 3. Per capita consumption

I 1940 YEAR

1

I 1950

I

1

1960

of U.S. citrus and total fruit.

I

1970

338

STEPHEN 0. MURRAY AND JOSEPH H. RANKIN

Canadian Canned Fruit

Canadian Frozen Fruit

.2

1945

1950

1955

Fig. 4. Per capita consumption

1960 YEAR

of Canadian

1965

1970

canned and frozen fruit.

hybrid corn, Hamblin and Miller [ 1 l] initially suggest that the reward is increased yield per acre.4 Nonetheless, “expected reward” was subsequently presented as their explanation for the adoption of hybrid corn, but survey data on midwestem farmers’ expectations 4This fits into a hedonic calculus that they assume governs human behavior. However, concern solely with output would be expected only in areas where farming produces corn for exchange, not for subsistence. Apodaca’s [l] study on the resistance to seemingly rational innovations demonstrated that hybrid corn was not accepted by farmers who produced corn for their own use (making tortillas). Since the geographic regions in the United States in which agriculture was less capitalized [ 13, 141 also appear to be the areas where hybrid corn was less markedly superior, generalizations based on the assumption that increased yield is the sole or even primary motivation for farmers are suspect.

USE DIFFUSION:

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in the 1930s are, of course, not available. Furthermore, Hamblin and Miller [ 111 cannot decide whether it was the farmers or the seed companies who were rewarded for adopting the innovation. Yet, this is their attempt to rectify the vagueness of Skinnerian reinforcement. The End of Diffusion It was demonstrated that exponential modeling as used by Hamblin et al. [lo] applies to the diffusion of processed foods. By using per capita data rather than gross consumption data, it was shown that the exponential processes were not artifacts of simultaneous population increases. Finally, it was revealed that use diffusion (like binary adoption) is a finite process. Whereas Hart [ 121 projected continuing exponential increases at an unflagging rate, Hamblin et al. [lo] modified such an unrealistic approach by demonstrating that the diffusion process continues, but at a decreasing rate from epoch to epoch. However, the results of this investigation suggest that diffusion may end altogether. Thus, the modification of Hamblin et al. [lo] is insufficient. The rate of diffusion may not only decrease with time, it can also cease or reverse. Negative exponential processes are not unknown. Several, including bus passenger miles, movie attendance, and consumption of chewing tobacco, were discussed by Hamblin et al. [ 10, Chap. 61. Some negative exponential processes result from legislative action (e.g., a decrease in the consumption of alcoholic beverages resulting from Prohibition; a decreasing number of bank failures due to the inauguration of the F.D.I.C.), while others follow social catastrophes such as depressions and wars (cf. Nisbet [19]). However, none of these explanations can adequately account for a decrease in U.S. and Canadian consumption patterns after the end of World War II. THE EMERGENCE

OF COMPETITIVE

INNOVATIONS

The “technological substitution” model is a more plausible explanation of these reversals. Fisher and Pry [7] maintain that products of new technologies compete with products of old technologies to satisfy invariant needs. For example, margarine replaces butter, plastic replaces leather, synthetic fibers replace natural fibers, and so on. Increase in the use of one product is correlated with a decrease in the use of another. In fact, Fisher and Pry [7] may correlate these processes too closely, predicting that “if a substitution has progressed as far as a few percent, it will proceed to completion” [7, p. 751; that is, “the substitution will proceed to 100 percent” [7, p. 761. Although products have been known to disappear from the market, the innovations examined by Fisher and Pry [7] did not completely replace the products of an earlier technology. Consumption of butter, leather, and natural fibers appear to have reached asymptotes rather than being totally replaced-just as fresh fruits and vegetables continue to be consumed despite the increased consumption of canned and frozen vegetables. Indeed, decreases in per capita consumption of fresh products (see Fig. 3) cannot be accounted for solely in terms of functional alternatives such as the substitution of frozen and canned fruits and vegetables, since the per capita consumption of these latter products was also declining [22]. Whereas Hamblin et al. [IO] err in predicting that diffusion can continue indefinitely, Fisher and Pry [7] err in another direction. By regarding the market as a zero-sum game in which the gain of one product can come only at the expense of another, Fisher and Pry [7] fail to note that the totul market can expand. New “needs” can be created and manipulated through advertising and other means. Thus, increased per capita (U.S.) consumption of margarine coincided with a 10 percent per capita increase in consumption of total fats

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STEPHEN 0. MURRAY AND JOSEPH H. RANKIN

during the 1950s and early 1960s [22], rather than simply the substirution of margarine for butter and lard. Similarly, increased consumption of gas and oil coincided with an increase in total world energy consumption [ 151 rather than simply a decreased use of wood and coal. Although substitution accounts for some diffusion, it can be overestimated. Complete replacement should not always be predicted5; positive exponential processes may stop short of cornering the entire market. Furthermore, the technological substitution model is not a safeguard against extrapolation. As Ogbum [20, p. 381 noted, “even when a known law describes the past course of social phenomena, it is not known how long that course will be followed in the future.” Similarly, Fisher and Pry [7, p. 811 assert that “The substitution model is fatalistic in the sense that it projects a specific and undeviating future based upon past events.” Nevertheless, Fisher and Pry [7] avoid some of the problems of Hamblin et al. [ 101 by (1) not predicting infinite consumption, (2) correlating decreasing rates of consumption with something other than time,6 and (3) recognizing negative diffusion processes. However, like Hamblin and his associates [lo], Fisher and Pry [7] and Marchetti [15] posit a homo economicus reaching rational decisions without specifying the advantages of the “rational” choice. The use of competing products is clearly one variable in the consideration of how far substitution will proceed, but one must also know what the advantages (rewards) and disadvantages of the substitutes are for the consumers who are supposedly making rational decisions. Conclusion A number of cases considered in this paper (e.g., U.S. canned and citrus fruit) suggest that up until roughly 1945 there were exponential increases in the consumption of fruits and vegetables. Some of these processes then leveled off-not simply to epochs with diminishing exponents, but to equilibria analogous to the steady states of binary diffusion. Whereas some of the exponential curves appear to reach asymptotic levels (see Pigs. 1 and 2), others are clearly negative exponential processes (Figs. 3 and 4). Such results are clearly not anticipated by Hamblin et al. [lo]. Thus, binary adoption and use diffusion are more similar than initially anticipated. Using per capita data rather than gross consumption data, we demonstrated that use diffusion can end, and for the same reason that the binary adoption process ends; that is, consumption has its limits. Once an entire population has adopted an innovation (e.g., television), the diffusion process is over. Similarly, consumption of fruits and vegetables cannot increase indefinitely. Just as people are not now continuously traveling by airplane or watching television 48 hours a day, per capita consumption of frozen orange juice will not exceed five gallons a day by the year 2000. Like Hart [12], Hamblin and his associates overemphasize high r2 values at the expense of explanation. On the other hand, Ogbum [20] was interested in the consequences of diffusion, as witnessed by the title of his book, The Social Effects of Aviation. Fitting curves to maximize r2 values was not an end in itself for Ogburn, who argued that

‘Similarly, not even “outdated” scientific theories are wholly replaced [ 171. Those theories rejected in one discipline may continue to diffuse and prosper in analogies of other disciplines [8, 181. ‘Although Hamblin et al. [IO] demonstrate that various processes are exponentially patterned over time, they do little to explain these processes. The passage of time is presumably not the cause of these social changes. In fact, “time” cannot explain any of the three “theoretical problems” that Hamblin and Miller [I I] positneither the beginning, the rate, nor the extent (nor the end) of social change processes.

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explanation is more impressive than goodness of fit and that social variables must be taken into account to provide this explanation. Finally, since many social processes can be represented by exponential or linear equations, the obvious task for mathematical work on social change is to relate these various processes to each other. The high explained variance in studies such as Hamblin and his associates (and ours) simply demonstrates that temporal patterns exist. The next and more interesting problem is to relate one type of social change to another. Only then will mathematical “theories” of social change provide explanation. Hopefully, controlling for population growth by using per capita data rather than gross consumption data in the present study is a step in the right direction.

The authors wish to acknowledge Frances Allen, Robert Poolman, Hamblin for their helpful comments on earlier drafts of this paper.

and Robert

References 1. Apodaca, Anacleto, Corn and Custom: The Introduction of Hybrid Corn to Spanish American Farmers in New Mexico, in Edward Spicer ed., Human Problems in Technological Change, a Casebook. Russel Sage, New York, 1952, pp. 35-39. 2. Baird, David C., Experimentation: An Introduction to Measurement Theory and Experiment Design. Prentice-Hall, Englewood Cliffs, N.J., 1962. 3. Canadian Bureau of Statistics, 1945-1979 Canada Year Book. Ottawa: Queen’s Printer. 4. Chomsky, Noam, Review of Skinner’s Verbal Behavior. Language 35, 26-58 (1959). 5. Critchell, James T. and Raymond, Joseph, A History of the Frozen Meat Trade. Dawsons, London, 1969. 6. Dunn, Edgar S., Jr., Economic and Social Development. John Hopkins University Press, Baltimore, 1971. 7. Fisher, J. C. and Pry, R. H., A Simple Substitution Model of Technological Change. Technolog. Forecast. Sot. Change 3(l), 75-88 (1971). 8. Gould, Stephen J. Ontogeny and Phylogeny. Harvard University Press, Cambridge, Mass., 1977. 9. Griliches, Zvi, Hybrid Corn: An Exploration in the Economics of Technological Change, Econometrica 25, 501-522 (October 1957). 10. Hamblin, Robert L., Jacobsen, R. Brooke, and Miller, Jerry L. L., A Mathematical Theory of Social Change. Wiley, New York, 1973. 11. Hamblin, Robert L. and Miller, Jerry L. L., Reinforcement and the Origin, Rate and Extent of Cultural Diffusion, Social Forces 54, 743-759 (June 4, 1976). 12. Hart, Homell, Predicting Passenger Miles Flown, Amer. Sociolog. Rev. 14, 1.53-155 (February 1, 1949). 13. Hofstadter, Richard, The Age ofReform: From Bryan to F.D.R. Knopf, New York, 1955. 14. Mann, Susan, The Capitalization of American Agriculture. Unpublished Ph.D. dissertation, University of Toronto, 1979. 1.5. Marchetti, C., Primary Energy Substitution Models: On the Interaction Between Energy and Society. Technolog. Forecast. Sot. Change 10(4), 345-356 (1977). 16. Murray, Stephen O., Round One of the Exponential Modeling Controversy: Hart vs. Ogbum. Unpublished manuscript, 1979. 17. Murray, Stephen O., Gatekeepers and the “Chomskian Revolution,” /. Hist. Behavior. Sciences 16 (forthcoming) (1980a). 18. Murray, Stephen O., Recent Levi-Strauss. Contemp. Sociol. 9 (forthcoming) (1980b). 19. Nisbet, Robert A., Social Change and History. Oxford University Press, New York, 1969. 20. Ogbum, William E, The Social EfSecrs ofAviation. Houghton Mifflin, Boston, 1946. 21. Ogbum, William F., Rejoinder. Amer. Sociolog. Rev. 14, 155-156, (February 1, 1949). 22. U.S. Bureau of the Census, Historical Statistics of the United States. U.S. Government Printing Office, Washington, D.C., 1975. 23. van Bertalanffy, Ludwig, An Outline of General Systems Theory, British J. Philos. Science 1, 134-165 (1950). Received 31 August 1979; revised 23 January 1980