As you suggest, "a driving wheel 58 inches in diameter" is a big clue here. The safety bicycle (basically what we tend to ride nowadays) was invented in 1876, a

As you suggest, "a driving wheel 58 inches in diameter" is a big clue here. The safety bicycle (basically what we tend to ride nowadays) was invented in 1876, at least the version which became most popular. The so-called "penny farthing" bikes were often called just "wheels" by their owners, hence "riding a wheel" and "wheelers". Some modern clubs are still called "Something Wheelers", e.g. "Bolton Wheelers", presumably because they have a history going back to the 19th C. There is a surprising evolution to the bicycle, leading not least to the invention of the first automobiles. See Carlton Reid's book "Roads Were Not Made for Cars" for a history of this from both a UK and US perspective.