It measures distances by the foot (9)
I believe the answer is:
pedometer
This clue could be a double definition.
'it measures distances' is the first definition.
The definition suggests a singular noun which matches the answer.
'foot' is the second definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Maybe they are linked in a way I don't understand?
'by the' acts as a link.
Can you help me to learn more?
(Other definitions for pedometer that I've seen before include "Tom peered (anag.)" , "Counter of paces" , "It shows distance walked" , "Check on walker" , "It records steps taken" .)