Measure a curve easy way

Tim,
Take a 62 foot long string and mark the ends and the center of it. Then get two helpers and have each hold the end while you have a ruller in inches at the center. Have each end held at the flange side of the outside rail and when tight, you measure the distance in inches from the straight string to the rail and that distance in inches will be the same as the degrees of the curve.
To do a entire curve, mark it every 31 feet from back in the tangent track and all around the curve and you can see if you have a compound curve or a simple, one radius curve. This is how you fix a curve and reline it so it is all even at the same degree.
If you had a curve out of line, you would measure it as above for each station (31' markings) and record the off-set, then drive staked several feet out from each station, then compute the swings that need to me made at each station. (swing being amount of distance track has to be moved in or out). It is very complicated add and subtract at each station to get it all worked out. It will take hours of trial and error on paper. If you subtract 8 units at one station, you change each adjacent station by -4. You have to figure plus and minus to even the curve.
Then you line the track to the stakes that are on the sides. Lot of luck as it is the hated job called String-lining done by engineering lackies in the winter when the gangs are off. It is now done in the computer in the track liner machine, run over the curve in one pass, and return and move the rails in the next pass.
Let me know if that helps your question.