Princeton social physics (1769)
In 1769, James Madison, the "father of the US constitution" was studying a primitive form of "social physics" at Princeton, influenced via his mentor John Witherspoon (his mentor being Charles Montesquieu), and his Newtonian moral philosophy theories, which marks the start of Princeton social physics, a program that was carried through, intermittently, into the mid-20th century (although dormant presently).
In hmolscience, Princeton social physics refers to the study and use of social physics, social mechanics, and or physicochemical sociology at Princeton University.

Overview
The subject of "social physics" and "Princeton", may refer either what one might categorize as "early Princeton social physics", associated with Newtonian mechanics based political economics and government thinking, spearheaded Declaration signatory John Witherspoon (1750s) and his religion-free Newtonian-based moral philosophy predictions, his student James Madison (1769) and his use of Newtonian mechanics to construct the constitution, and later Woodrow Wilson (1912) and Newtonian and Darwinian political campaign platform; the mid-20th century Rockefeller-funded “Princeton social physics project” (or Princeton Department of Social Physics), headed by John Q. Stewart (1939-1955); or the so-called “social physics school”, a precipitate of the latter, in geography circles, via their population potential models, carried forward by William Warntz (1964-1980s), the latter of which being only active form of all three branches.

Early years
In 1769, James Madison, age 18, specifically chose to ride horseback to New Jersey to attend the College of New Jersey, or what is now Princeton University, which he selected, according to historian Irving Brant (1974), specifically for its “hostility to episcopacy”, i.e. a school against the model of educational government by bishops. [2]

At Princeton, Madison, according to John Q. Stewart, was studying a primitive form of Newtonian-based social mechanics (or social physics) at Princeton, under the direction of Scottish-born American John Witherspoon, who was himself mentored by Charles Montesquieu, the logic of which he is said to have used in the construction and debate room floor selling of the penning of the US Constitution (1787); the following are example quotes:

“There can be no question of the fact that, in early Princeton, physics cooperated with politics in a sort of analogical double play, Newton to Witherspoon to Madison.”
John Q. Stewart (1955), on social physics at Princeton [3]

“The eighteenth century was dominated intellectually by the scientific work of Newton, and mechanical metaphors sprang naturally to men’s minds. Men had found a rational order in the universe and they hoped that it could be transferred to politics. Madison spoke in the most precise Newtonian language when he said that such a ‘naturalgovernment must be so constructed ‘that its several constituent parts may, by their mutual relations, be the means of keeping each other in their proper places.’”
— Richard Hofstadter (1967), The American Political Tradition [4]

“The third element—the principle of checks and balances—in the principle of separation of powers is what Madison called ‘partial agency’, which gives each branch enough power over the others to be able to check them. This principle of checks and balances, designed to enable the three branches to protect themselves from each other’s encroachments.”
— Levine and Cornwell (1968), An Introduction to American Government [5]

“The founders were elitists, and realists about human nature. Their task was to make passion subject to reason. If men could be expected to be selfish, or worse, then said James Madison ‘ambition must be made to counteract ambition’. The Newtonian principles of action and reaction were applied to politics.”
— Lance Morrow (1987), “The Ark of America” [6]

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Later years
In circa 1939, John Q. Stewart, in an attempt to rekindle the Princeton social physics flame, over the course of the next decade or so, until 1955, ran the so-called Princeton Department of Social Physics.

In 1940, Stewart, in his “The Gravity of the Princeton Family”, as summarized by William Warntz (1959), reported on his findings that the number of Princeton alumni residing in a given state was directly proportional to the population of the state and inversely proportional to its distance from the Princeton campus. [8]

In 1950, Peter Dodd, a possible relative of Princeton sociologist Stuart Dodd (1950-1975), completed his senior thesis on “Social Physics: Theory and Application of Demographic Gravitation”. [7]

Quotes | Related
The following are example quotes:

“During the year 1951 the Princeton social physics project was hosted in two conferences and benefited by attention and criticism from authorities in the following fields: administration, advertising, anthropology, astronomy, biology, business, chemistry, city planning, demography, economics and econometrics, …”
John Q. Stewart (1952), “A Basis for Social Physics” [1]

See also
Physical sociology falloff problem

References
1. Stewart, John Q. (1952). “A Basis for Social Physics”, Impact of Science on Society, 3:110-133.
2. (a) Brant, Irving. (1974). Encyclopedia Britannica. Publisher.
(b) Haught, James A. (1996). 2000 Years of Disbelief: Famous People with the Courage to Doubt (§:James Madison, pgs. 97-98; episcopacy, pg. 97). Prometheus.
3. Staff. (1955). “Research in Progress: Social Physics”, Princeton Alumni Weekly, 55:17.
4. (a) Hofstadter, Richard. (1967). The American Political Tradition (pg. 8). Jonathan Cape.
(b) Foley, Michael. (1990). Laws, Men and Machines: Modern American Government and the Appeal of Newtonian Mechanics (Hofstadter, pg. 16; Madison, 20+ pgs). Routledge, 2014.
5. (a) Levine, Erwin L. and Cornwell, Erwin L. (1968). An Introduction to American Government (pg. 47). Macmillan.
(b) Foley, Michael. (1990). Laws, Men and Machines: Modern American Government and the Appeal of Newtonian Mechanics (partial agency, pg. 65; Madison, 20+ pgs). Routledge, 2014.
6. (a) Morrow, Lance. (1987). “The Ark of America” (abs), Time, Jul 6,
(b) Foley, Michael. (1990). Laws, Men and Machines: Modern American Government and the Appeal of Newtonian Mechanics (Morrow, pg. 4; Madison, 20+ pgs). Routledge, 2014.
7. Dodd, Peter C. (1950). “Social Physics: Theory and Application of Demographic Gravitation” (Ѻ), Woodrow Wilson School of Public and International Affairs, Princeton University.
8. (a) Stewart, John Q. (1940). “The Gravity of the Princeton Family”, Princeton Alumni Weekly, Feb 9.
(b) Warntz, William. (1959). “Social Physics: A Macrographer Takes a Hard Look at College Enrollments” (Ѻ), Princeton Alumni Weekly, 60:8-13, Sep 18.

Further reading
● Bowen, William G. and Shapiro, Harold T. (2000). The Sacred and the Secular University (abs) (Amz). Princeton University Press.

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