In 1917 the charlatan John R. Brinkley experienced what was truly a seminal moment. This so-called doctor, whose diploma had come from a medical school that was “vague, obliging and long defunct” and whose expertise was dubious at best (“if the white coat reassured people, the healing had begun”), was consulting with a 46-year-old Kansas farmer named Bill Stittsworth. “I’m all in,” Stittsworth said. “No pep. I’m a flat tire.”

Then both farmer and doctor gazed out the office window. They spied livestock. And they experienced a shared brainstorm. Supposedly at his patient’s urging, Brinkley agreed to try to restore the man’s virility via an unorthodox transplant operation. The farmer wound up with two extra testicles courtesy of one luckless goat.

For Dr. Brinkley, whose story is told with uproarious brio in Pope Brock’s heavenly “Charlatan,” this 1917 epiphany was the beginning of a mercenary miracle. “Dimly he had begun to realize that he was gifted beyond the run of doctors,” Brinkley’s adoring authorized biography would one day explain. That book would also credit Brinkley with “this lovable characteristic of genius, that money is not an aim, or an end in itself, but a means of enlarging the central idea of his life-work.”

Image Pope Brock Credit... Lynda Shenkman Curtis

Selflessly or otherwise, Brinkley parlayed his goat-gland breakthrough into a unique place in American history. He was much more than just a mere medical quack. In a book so lively that its wild stories are virtually wall-to-wall, Mr. Brock describes early-20th-century America’s endlessly credulous populace, with “the average citizen as guileless as the wide-mouthed shad.” Brinkley and his virility scheme tapped into the nation’s penchant for mumbo-jumbo and hence into opportunities for salesmanship that had been previously unknown.