In Origin of the Phrase “Indian Summer”, published in Notes and Queries (Oxford University Press) of September 2017, Matthew R. Halley, of the Academy of Natural Sciences of Drexel University (ANSP – Philadelphia, Pennsylvania), presents what he calls “a novel origin story for ‘Indian Summer’ from a credible source”.

He explains that, in the papers of the Quaker naturalist Reuben Haines (1786-1831), of Philadelphia, Pennsylvania, he discovered a clipping from an undated issue [see note] of Poulson’s American Daily Advertiser, a newspaper published in Philadelphia from 1800 to 1839; he writes that the clipping was tucked between the pages of one of Haines’s meteorology journals, and that it comprises a letter to the editor, probably written by Haines, explaining that the phrase Indian Summer originated in Philadelphia; this letter is as follows:

Mr. Poulson:—We believe the present is the legitimate Indian summer week. The best account of the origin of Indian summer was given the writer by an old German friend, more than thirty years ago. Many of our elder citizens remember when there was an annual fair held in Philadelphia for three days, beginning on the last Wednesday in November.—The last of these fairs was held about the year 1788. To these fairs the Indians used to resort in great numbers, with their peltry and other articles to exchange for some of the variety of articles exhibited at the fair. In those days, as ever since about this season, there generally happened a few very pleasant days: these pleasant days frequently coming at the time the Indians came to the fair, gave the idea that they brought the summer with them. The fairs having been discontinued, there is no specific time for the Indian summer; consequently, when a few pleasant days occur the term is applied to them. Perhaps this may induce some other person further to explain the subject.
A Friend to Investigation.

Although this theory is interesting, the problem is that it is based on an account that is at the same time indirect, undated and isolated: Reuben Haines reported at an unknown date [see note] what someone else had told him “more than thirty years” before, and no other account has as yet been found that would support the theory that Indian summer originated in the annual fair held in Philadelphia.

I still regard as convincing the theory that I have put forward in origin of ‘Indian summer’ and French ‘l’été sauvage’, because it is based on linguistic facts, not on external facts difficult to prove such as traditions that have disappeared.

My theory is that, in Indian summer, the adjective Indian merely denotes something other than that normally denoted in Europe by the simple noun summer—as in other terms specific to the New World, such as Indian corn. In other words, the periods of dry, warm weather occurring in North America in late autumn did not fit in the usual, normal, pattern of calendar seasons to which the Europeans living in the New World had been accustomed in the Old World.

(cf. also European precursors of the American ‘Indian summer’ and 18^th-century instances of ‘Indian summer’)

Note: I have asked Matthew R. Halley whether he knows in which issue of Poulson’s American Daily Advertiser the letter was published; he has answered that he guesses “sometime between 1815-1831”.