Occasionally we get an old bike in the workshop, and this four speed retrodirect from around 1925 is special enough to be shown here. This post-war quality bike has two forward gears and two in reverse! Not that the reverse gears result in driving backwards, as the crossed chain restored drive in the preferred direction. The front changer follows the trend in providing upshift if you pedal forward, and in allowing downshifts if you pedal back and doubles the gears provided by the two freewheels!

The frame is, as with more french bikes from this era, constructed in lugless gaswelded construction, and the finish was nickel plated, as you can see on chainwheel which was protected by lubricant.

Here you can see how the driveline works. Pedal forward and the chain rotates the smallest freewheel in the normal manner. The chain then runs over the idler and back over the larger freewheel towards the chainwheel up front. As the large freewheel spins slower than the smaller one, the freewheelpawls will do their thing.

Pedal backwards and the situation is reversed and the crossed chain will drive the largest freewheel. The small freewheel will spin backwards 

On this picture you can see the curved chainstay, necessary to clear the crossed chain

The rearbrake must have inspired later designs

There is also a front changer: this is the control lever

And here are the mechanics. The arm rotates around the bracketshell and is provided with two conical protrusions which lift the chain from one chaiwheel and direct it to the next one. To change up you rotate the arm up while pedalling forward, to change down you reverse the procedure while pedalling backwards.