gauge
v.
"ascertain by exact measurements," mid-15c., from Anglo-French gauge (mid-14c.), from Old North French gauger "standardize, calibrate, measure" (Old French jaugier), from gauge "gauging rod," a word of unknown origin. Perhaps from Frankish *galgo "rod, pole for measuring" or another Germanic source (compare Old Norse gelgja "pole, perch," Old High German galgo; see gallows). Related: Gauged; gauging. The figurative use is from 1580s. "The spelling variants gauge and gage have existed since the first recorded uses in Middle English, though in American English gage is found exclusively in technical uses" [Barnhart].
n.
early 15c., "fixed standard of measure" (surname Gageman is early 14c.), from Old North French gauge "gauging rod" (see gauge, v.). Meaning "instrument for measuring" is from 1670s; meaning "distance between rails on a railway" is from 1841.
Railway-gage, the distance between perpendiculars on the insides of the heads of the two rails of a track. Standard gage is 4 feet 8 1/2 inches; anything less than this is narrow gage; anything broader is broad gage. The dimension was fixed for the United States by the wheels of the British locomotive imported from the Stephenson Works in 1829. [Century Dictionary]