Originally Posted by
Doohickie
Yes, by definition. If you take out 1 tooth, you end up with one extra 1/2" link, Half of that distance adds to the top of the chain, and half to the bottom, so you end up with the wheel moving 1/4" back.
EDIT: ACK... half that? I gotta read Sheldon's writeup on that.
I'm not sure if he ever showed his work on that, there's just:
Adding or subtracting a link in the chain will move the axle 1/2". Changing either sprocket size by one tooth is the equivalent of moving the axle 1/8" (4 mm).
ON EDIT: Think I figured it out -- one extra tooth increases the circumference of the cog by one half-link. Half of that is on the inside of the chain loop and doesn't contribute to the chain length. The other half contributes equally to the top and bottom of the chain.