There is an interesting story related in Edward R. Dewey's book, "Cycles: The Mysterious Forces that Trigger Events" about a group of investors on Wall Street in 1912. They had heard that Rothschild had analysed Consol prices and found in their fluctuations a secret series of curves which he used for forecasting price movements. The group engaged a mathematician to replicate the Rothschild formula. Reputedly success followed, particularly when the group adapted their investment strategy to a 41-month stock cycle.
While this story has all the hallmarks of one of those early investing myths, the periodicity is interesting. In 1923, Joseph Kitchin published in the Harvard University Press an article entitled "Review of Economic Statistics," outlining his discovery of a 40-month cycle resulting from a study of U.S. and UK statistics from 1890 to 1922, At the same time as Kitchin was carrying out his investigation, a fellow Harvard professor, W.L.Crurn, found a cycle of 39, 40 or 41 months in commercial paper rates in New York. The Kitchin cycle is sometimes said to be based on a stocking/destocking cycle.
Richard Mogey of the Foundation for the Study of Cycles determined a cycle of 40.68 months over the entire history of US stock prices.