> 112/35.5 = 3.14.....
> Thus I suspect something for deciphering circumference based on 
> diameter.

I picked up what I thought was a typical blacksmith's 2 foot folding 
rule
a few years ago but on closer examination it had a line of measurements 
for
calculating circles, pretty much what you describe (couldn't open the 
photo).
It turned out to be a tinsmith's rule.  Perhaps your rule is for 
tinsmithing.

Mike in Sacto