After the Restoration, the hats' squareness was exaggerated yet again to show loyalty to the newly established churches. In order to make that structure possible, the square top was merged with the skullcap into a single hat, like what is worn today.
The American preference for the exaggerated square cap is likely related to our English history. Where the clergy of the 17th century all wore square caps, England started enlarging the square flat top of their hat, where the rest of Europe added material to the sides of the hat. This version of the biretta is still worn by Lutheran clergy, German lawyers, deans and rectors of continental European universities.
In England, Oxford and Cambridge went through several different variations on who wore square caps and round caps, and how to distinguish those with degrees in divinity. In 1636, Oxford's Laudian Code granted the pileus quadratus to pretty much everyone, with the pileus rotundus granted to "commoners and all who were not on the foundation of the colleges." And in 1769, Cambridge's undergrads successfully petitioned to wear the square cap.
In the United States, the popular form of the mortarboard can be traced to a 1950 patent filed by inventor Edward O'Reilly and Joseph Durham, a Catholic priest. The patent introduced a metal filling into the hat, making it more sturdy.
The mortarboard is now worn by most graduates at commencement, there are a few chances to get out of the hat. In England, doctorate holders more commonly wear a round hat called the "Tudor Bonnet." In the United States, doctoral graduates can wear a four-, six-, or eight-cornered velvet tam instead. And, for a while, women had the option of wearing a soft square tam instead.
As shown above, American universities' academic dress is described in the Academic Costume Code, which is the product of the American Council on Education. The first code was written in 1895. Prior to that, every university adopted its own academic costume, with no reference to each other. The 1895 code was the product of an intercollegiate commission consisting of representatives from Columbia, New York University, Princeton, Yale, and "technical adviser" Gardner Cotrell Leonard, whose company manufactured academic dress. Intercollegiate Code of Academic Costume was adopted on March 16, 1895 and was based on Columbia's own academic costume code. In comparison to its European counterparts, the American code had much vaguer descriptions, but it applies to all colleges rather than just each individual school.
The American Council on Education (ACE) got involved in 1932, appointing a committee to determine whether the old code needed revision. The 1932 committee left the 1895 code mostly unchanged. Since then, the ACE has changed the code three times: 1959 (which approved the soft version of the mortarboard for women), 1973, and 1987 (removing the option of the soft hat for women). The 1987 revision was the last, and that's where we get the current general recommendation of the mortarboard.
It should be noted that the American Costume Code is technically just a guide, and schools aren't required to follow it. For example, while the code recommends black robes, many schools will have graduates wear robes in the school colors.
So, the next time you see a student struggling to keep a mortarboard on, know that there's a lot of history behind the choice to put him or her in this stupid, stupid hat.
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