Dear Brad,
The escapement of the Centigraphe beats at 21600 and counts 6 stops per second. If there was nothing else to regulate the speed of the hand, it would look like the movement of a "foudroyante".
Thus, on the axis of the hand there is a 30 teeth wheel which works with a free lever.
This free lever slows down the speed of the axis of the hand 60 times per second; furthermore this axis is slowed down 6 times per second by the escapement of the watch.
The cinema taught us that to have a fluid image, 24 images are enough. There are 60 images/second in the vision of the movement of the hand, it is sufficient to see a fluid flow which we can stop at any moment.
Best regards,
FPJ