In phenomena, physical sociology falloff problem refers to puzzling phenomenon of the apparent rise to prominence of the so-called “mechanistic school” of sociology—one based explicitly on physics, chemistry, and mechanics—to the apex of contemporary early 20th century American sociology, according to Pitirim Sorokin (1928), to the further rise and formation of the Gibbs-Pareto based so-called Harvard Pareto circle (1932-1942), epicentered the efforts of American physical chemist Lawrence Henderson, to the further historical beginnings (e.g. Princeton school, 1796) and later formation of the Rockefeller-funded Princeton department of social physics (1945-1955), anchored around the one nature vision of American physicist John Q. Stewart, after which the overall physical sociology program in America ceased abruptly.

Overview
Consensus, from a number of sources, indicates that sociology, in the early 20th century was growing into the form of a "true science", mathematical and based in the natural sciences, but that with the event of WWII (1939-1945), and or up-till circa 1955, or sometime there, it peaked as a striving-to-be true science, and fell off. The following are few quotes evidence to this view:

“The leading contemporary sociological theory—of the last sixty or seventy years—has been the mechanistic school, which may be classified as all sociological theories which interpret social phenomena in the terminology and concepts of physics, chemistry, and mechanics.”
Pitirim Sorokin (1928), Contemporary Sociological Theories (pgs. xvii + 3) [1]

“The school dominating present day sociology at least in America is the neopositivist one. It is best represented by G. Lundberg’s Foundations of Sociology (1939), in its companion volume which is S.C. Dodd’s Dimensions of Sociology (1942), but also in such works as G.K. Zipf’s Human Behavior and the Principle of Least Effort (1949), in N. Rashevsky’s Mathematical Theory of Human Relations (1947), and in innumerable articles appearing in the sociological journals.”
— Nicholas Timasheff (1950), “Sociological Theory Today” [2]

“For about twenty-five years prior to the middle 1950s it was widely held in America that sociology was rapidly becoming a true science.”
Richard Brown (1977), per citation of Talcott Parsons (1954) and George Lundberg (1955) [3]

“The clarion call for a return to the dream of a social physics does not, at this moment, seem to be winning the day. Many social theorists are now more inclined to turn to historical and literary studies than to physics and chemistry for inspiration. Whether new developments in the natural sciences can breathe new life into the dream of a social physics is an open-ended and uncertain prospect. Nineteenth-century social theorists favored metaphors that mimicked the more successful natural sciences, selecting analogies mainly from biology, chemistry, and physics. Social scientists, modeling themselves after physical scientists, sought to discover the natural ‘laws’ of society and history. In recent decades, however, the ground has shifted. Today, the positivist dream of a social physics seems, if not dead, at least dormant.”
Daniel Rigney (2001), The Metaphorical Society (pgs. 49+197) [4]

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Void period
American sociology historian Jonathan Turner, in his 2012 Theoretical Sociology: 1830 to the Present, states that a theoretical void existed, in sociology, between the late 1920s and 1950s, and that Pitirim Sorokin was such theorist who flourished as a “giant” during this period. [9]

Reasoning | Discussion
In 1968, as per reasoning behind this apparent falloff, American sociologist Barbara Heyl, in respect to the Harvard Pareto circle, specifically, argued that the impact of WWII enacted a switch to Marxism-focused American sociology. [5] Alternatively, that same year, American sociologist Talcott Parsons stated that the reason for the fall off of physics and chemistry based sociology, of the Pareto-variety, after WWII, was scientific limitation: [6]

“Most of the neglect of Pareto stems from the scientific limitations of subsequent generations of sociologist rather than from his irrelevance to their interests.”

American sociologists Joseph Lopreato and Sandra Rusher, in their “Vilfredo Pareto’s Influence on USA Sociology” (1983), call this a mordant and justified sentence. [7]

In 2013, American anti-reductionist sociologist Leon Warshay, in response to a query, by Libb Thims, about why the mechanistic school is not being taught in American sociology, attempted to give a semblance of an opinionated answer, in a series of email responses, amounting to the effect that the subject of physicochemical based sociology (see: physicochemical sociology) is now seen as foreign matter to modern sociologists, whose minds are absorbed in the prevalence of Weberian, Parsonian, Interactionist, Functionalist, and similar sociological approaches. [8]

Among these supplied reasonings, the "scientific limitations" answer seems to be the main reason, which is evidenced by the fact that Harvard's "Sociology 23", a physical chemistry based sociology, steered by physical chemist Lawrence Henderson, and "Mathematical Economics", a steam engine and physical chemistry based economics, steered by Gibbs-trained Edwin Wilson, are no longer in operation, now that no one with the proper training and qualifications are available to run the show. This would seem to have something to have to do with the intellectual hydraism-effect.

References
1. Sorokin, Pitirim. (1928). Contemporary Sociological Theories (§1: The Mechanistic School (pdf), pgs. 4-62). Harper & Brothers.
2. (a) Timasheff, Nicholas S. (1950). “Sociological Theory Today”, American Catholic Sociological Review, 11(26), Mar.
(b) Nicholas Timasheff – Wikipedia.
(c) Lundberg, George. (1955). “The Natural Science Trend in Sociology” (abs), American Journal of Sociology, 61(3):191-202.
3. (a) Brown, Richard H. (1977). A Poetic for Sociology: Toward a Logic of Discovery for the Human Sciences (pg. 12). University of Chicago Press, 1989.
(b) Parsons, Talcott. (1954). Essays in Sociological Theory (366-67). Simon and Schuster, 2010.
(c) Lundberg, George. (1955). “The Natural Science Trend in Sociology” (abs), American Journal of Sociology, 61(3):191-202.
4. Rigney, Daniel. (2001). The Metaphorical Society: an Invitation to Social Theory (pg. 49+197). Rowman & Littlefield.
5. Heyl, Barbara. (1968). “The Harvard ‘Pareto Circle’.” Journal of the History of the Behavioral Sciences, 4:316-34; in: Talcott Parsons: Critical Assessments, Volume 1 (editor: Peter Hamilton) (§2, pgs. 29-49). Taylor & Francis.
6. (a) Parsons, Talcott. (1968). “Vilfredo Pareto: Contributions to Sociology”, International Encyclopedia of the Social Sciences, 11:411-16.
(b) Lopreato, Joseph and Rusher, Sandra. (1983). “Vilfredo Pareto’s Influence on USA Sociology” (abs), Revue Europenne des Sciences Sociales, 21(65):69-122; in: Vilfredo Pareto: Critical Assessments of Leading Economists, Volume 3 (editors: John Wood and Michael McLure) (§74, pgs. 187-237). Taylor & Francis, 1999.
7. Lopreato, Joseph and Rusher, Sandra. (1983). “Vilfredo Pareto’s Influence on USA Sociology” (abs), Revue Europenne des Sciences Sociales, 21(65):69-122; in: Vilfredo Pareto: Critical Assessments of Leading Economists, Volume 3 (editors: John Wood and Michael McLure) (§74, pgs. 187-237). Taylor & Francis, 1999.
8. Warshay, Leon. (2013). “Email communications to Libb Thims” Mar 5, 8; May 14.
9. (a) Turner, Jonathan H. (2012). Theoretical Sociology: 1830 to the Present (pg. 292). Sage.
(b) Jonathan H. Turner – Wikipedia.

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