The Natural History Society was organized 18 April 1836 as a predominantly undergraduate organization for the investigation and promotion of various departments of natural science. The original constitution and by-laws were adopted in April 1836 and were revised 29 May 1841. The constitution provided for the election of officers at an annual meeting of the society: President, Vice President, Corresponding Secretary (always a faculty member), Recording Secretary, and Curator/Librarian. Members were designated as Resident (students of Wesleyan and residents of Middletown); Corresponding (students who had graduated); Honorary (elected if deemed worthy, for their attainments in Natural Science); and Faculty (ex-officio resident members). It was voted at the second meeting of the society (26 April 1836) to include juniors in the ranks of members, and at the meeting of 18 August 1840, the society voted to amend the constitution to include freshmen and sophomores.

In order to collect money for a treasury, it was decided at the meeting of 25 August 1836 that A tax of 12 1/2 cents was levied on each of the members to defray certain incidental expenses. Whenever extra money was needed, a similar tax was voted upon by the society.

Although the society was originally known as the Natural History Society of the Wesleyan University, its name was changed (apparently not in a formal way, i.e., no evidence of a vote by members) to the Cuvierian Society, presumably after Baron Georges Léopold Chrétien Frédéric Dagobert Cuvier (1769-1832), French zoologist and geologist, a founder of comparative anatomy and paleontology. The first evidence of a name change is seen in the minutes of the meeting of 30 September 1837: A regular meeting of the Natural History Society, alias Cuvierian Society was held this day. After this date it was always referred to as the Cuvierian Society in the meeting minutes. Both versions of the constitution refer to it as the Cuvierian Society.

The last minutes in this record book are for the meeting of 30 May 1846. Essayists were appointed to speak at the next meeting, but it is not known if any further meetings were held.

At each monthly meeting, essays on some aspect of science were expected to be read to the society by members who had been chosen at the previous meeting. Many, however, were not prepared with essays, prompting a resolution at the meeting of 14 November 1838, that persons having essays to write and failing in the duties devolving upon them shall be fined 25 cents each. Even this stern measure apparently did little to motivate the appointed essayists; recording secretary B. F. Mudge, in the minutes for 26 February 1842, editorialized somewhat on the situation: Essayists upon being called upon were found deficient as usual. Some of the topics of the papers included ; ; ; ; ; ; and Local natural phenomena were also discussed at meetings: e.g., the Great Comet of 1843 (25 March and 24 April 1843), a locust colony (27 May 1843), and a bald eagle lately taken in Meriden (27 July 1844).

An address to the Society on the subject of natural science on 31 July 1838 by William H. Allen, professor of chemistry and experimental philosophy in Dickinson College, was printed in New York in 1838.

The Cuvierian Society maintained a cabinet and, later, a room, to hold various specimens which the members had collected or which had been donated. The minutes of 25 August 1836 read: A rattlesnake was received and a vote of thanks returned to the donor H. W. Smith. Also a Shark's Skeleton. It was noted on 19 May 1837 that the society was given the use of the room over the labratory [sic] for the preservation and exhibition of their collections and specimens in Nat. His., as long as none of the specimens were removed from the University. It was also understood that the collection would be donated to the University in the event that the Cuvierian Society should cease to exist; the collection eventually became part of the Museum in Judd Hall.

Several non-students had a great influence on the Cuvierian Society. Professor John Johnston served as corresponding secretary for most of the society's existence, and was elected president at the meeting of 25 July 1845. Prof. Johnston was an active participant at nearly every meeting. Dr. Joseph Barratt of Middletown was elected an honorary member of the society 8 June 1836. The minutes of 19 September 1836 read, It was . . . voted that the thanks of this society be presented through the corresponding secretary to Dr. Barratt for the interest he has taken in behalf of said society. Dr. Barratt was also an active member, delivering essays or papers and making remarks on various topics of natural science at many meetings. He was elected president 29 June 1844, and served until the election of Prof. Johnston. Augustus Smith, professor of mathematics and astronomy, 1831-1857, was also involved in the society during its last years.