November 6, 1837
The second session of the first legislative assembly of the Territory began at Burlington (now in Iowa); at this session the seat of Government was located at Madison, and the session continued until January 20, 1838.
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The evidence
“The first session of the Legislature, in 1836, by a proclamation of General Dodge, who was the first Governor, was convened at Belmont, now in Lafayette county, on the 25th day of October, of that year. The second session was held at Burlington, now in the State of Iowa, November 6th, 1837, at which session the seat of Government was located at Madison, where the third session of the Legislature was held November 26th, 1838.”
1856-history-of-rock-county/01-wisconsin.md, PDF p. 21 / book p. 3
Guernsey, Orrin, and Josiah F. Willard, editors. History of Rock County, and Transactions of the Rock County Agricultural Society and Mechanics' Institute. Janesville, Wis.: William M. Doty & Brother, 1856. Cornell University Library via the Internet Archive, archive.org/details/cu31924028871593.
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On the printed page (PDF p. 21 / book p. 3) · open the whole page