A place where this has annoyed me greatly in the past is the detailed summary she gives of Canandaigua's state of affairs around the time Joseph Smith Sr and family arrived in Palmyra (p.10f), where Brodie writes
But when the buckboard [i.e. the Smiths travel wagon, RCK] came to a stop in Palmyra [in the winter of 1816, RCK], the weary brood looked out upon a town of almost four thousand citizens, twice the size of the village [of Norwich, VT, RCK] they had left. Canandaigua, twelve miles south, was even bigger [than Palmyra, RCK], and boasted a twenty-year old academy, two "respectable private female seminaries", five common schools, three libraries, thirty-nine stores, seventy-six shops, [p.9], three churches, and paved sidewalks. [pp.9-10]It is on page 11 that Brodie has one of her "collector footnotes", where the second entry is William Darby's A Tour of the City of New York to Detroit (...), New York 1819, where on page 133 we find the description of an informal "census" taken by three volunteers, the result of which Darby had copied from an edition of the Ontario Repository. Unfortunately, this "census" is not easy to date; terminus ante quem is most likely 1819. Canadaigua was indeed an old and important city; Gorham and Phelps had made their headquarters there after receiving control of the purchase in 1788.
But this is where things get interesting. The first thing that is odd about this statement is that the part "was even bigger" [p.9] is factually false. If we accept Brodie's claim that Palmyra had almost four thousand citizens in 1816---the census of 1820 gives 3734, as shown here---, then we are surprised to discover that the Ontario Repository's informal census only knows of "1788 souls". This is in fact half the population.
Furthermore, Brodie goes on to castigate Joseph Smith Sr. for selecting a boom town and thus facing boom town land prices, rather than continuing on to Ohio or Indiana for cheap land. In this context she points to a population plateau that was to strike Palmyra while the Smiths were still there.
He [i.e. Joseph Smith Sr, RCK], could not know that he had come at the peak of a speculative spiral, that Palmyra, instead of doubling its population in the next decade, would actually shrink by three hundred citizens and remain even a century later a town of little more than four thousand. [p.10]This claim is clearly based on the US census of 1820 and 1830, where a flat-out comparison of the totals for Palmyra result in a drop of 3734-3276=458. But this is an illusion, also discussed here, created by the spin-off of Palmyra West into Macedon during the organization of Wayne County in 1823. The "greater Palmyra area", which is what Palmyra in the 1820 census was, had increase to 5155 souls by 1830.
Admittedly, this is not a doubling; and Brodie is right that after the completion of the Erie Canal, Palmyra ceded its position of pre-eminence to Rochester, whose feeder Palmyra had always been, deflating the boom for the long run. By 1850---the 1840 data not being easily usable on the web---Macedon had 2834 souls, Palmyra 3893 (that is 6727 for the "greater Palmyra area"), and Canandaigua 6143. Most of that growth, compared to 1830, had come on the Macedon side. But Rochester had now a whopping 36,403!
This "right in principle, wrong in the details" tale then began its path through the footnotes of history; Whitney R. Cross in his influential The Burned Over District: The Social and Intellectual History of Enthusiastic Religion in Western New York, 1800-1850, New York ---London (Cornell University Press), 1950, writes on p.140, dependent on the pages we had just cited,
Palmyra particularly would have a considerable bonanza in the early twenties and evince social restlessness accompanying each rapid expansion. But before the end of that decade the village was destined to come quite suddenly to stability, with even a touch of the doldrums, after the canal had reached Buffalo and Rochester had seized local commercial leadership. (Brodie, No Man Knows, 9-11)The population census shows Rochester's leadership. Following Turner, History of the Pioneer Settlement, p.623, the population was a mere 1502 in 1820, half the size of Palmyra. Then in 1821 work on the aqueduct began: by 1822 the population had risen to 2700 residents, plus another 430 laborers. By 1823, Rochester was connected to the canal. For 1825, we have two census points: in February, 4274, and in August, 5273, a growth rate of almost 1000 souls for that year alone. In 1830, five years after the completion of the canal, Rochester had 9,207 inhabitants; the thousand-souls-per-year rate had continued unabated. Another decade of that rate, and by 1840, the population had doubled to 20,191. The growth rate when super-linear thereafter, increasing by another 80% over the next decade, i.e. 1850 to 36403 souls.
Even though the greater Palmyra area was no longer booming, it was still growing. Perhaps it was a small consolation to the folks in Palmyra that the aristocratic banking center (Cross, p.139f) Canandaigua, even in 1850, was still smaller, contra Brodie, than they.