Re: Question about an old rare pocket watch
The watch pictured is a "crab tooth" or Chinese duplex. The watch balance beats 4 times for each impulse or long drop, so the center second hand appears to beat seconds.
The invention of this form of the escapement is attributed to Charles E. Jacot. Jacot patented another variant with a lobular wheel to improve the dynamics of the escapement, which was one of the earliest watch patents filed with the U.S. Patent Office. Hen also experimented with forms of the duplex escapment with 3 and 4 spokes called the "star duplex.",
The term Chinese duplex derives from the fact that most if not all the crab tooth duplex production was sold in China where the timekeeping system was different from the European hours and minutes. The rapidly moving center hand provided visual entertainment since the indications were meaningless.
The duplex is a frictional rest escapement that locks on a grooved cylinder on the balance staff with the long teeth and gives impulse to an arm attached to the balance staff via the upright teeth. It impulses in one direction only the return swing generates no impulse. With two locking teeth, you get 4 swings per impulse. Since the balance beats 4 beats per second, the center hand moves once each second.