SAM LOYD you will see puzzles had impact on political campaigns too, if you research it.
Here's the disappearing: When you rotate the indicator arrow from pointing at A (as in main pic), to it pointing at B as in 2nd pic, you lose one of the bicyclists. Rotating the dial turns 13 wheelmen into 12! For company name, see next pic. See in following pix, when you rotate even further, more bicyclists just crash over the edge!
It's really not magic, just 1/12 or 1/13 of the puzzle tightens up in a cleverly drawn way.
Full size of piece is 4 3/4 x 5.5". The smaller disc of the two, which is atop the bike wheel image. is 3 1/4" diameter. The parts are of thin card stock, with sturdy metal fastener in the center, allowing the rotation!
This promotional puzzle/enigma was developed by Sam Loyd, famous novelty and puzzle designer, who first published it in 1896 as the "Get off the Earth" puzzle, with the circle represented the earth, losing an inhabitant along the edge as the cyclist in the present puzzle.
As a promotional piece. the company name New Departure is very understated. You can see it in small letters at the hub of the wheel, and also the Co. is mentioned in the promo patter on the reverse side. Many Get off the World type puzzles had an advertising link in, often to Bicycles. The figure disappearing could be another sort of person or object.
Sometimes a store name would be printed on them piece too, to be given promotionally to the public.
The center metal fixture creates a volvelle, rotating wheels upon each other.
This is undated, in great condition. Roughly from 1905-1920, following the company history.