A couple of weeks ago @Frenchy and I spotted a previously unknown cyclepath linking Newmills Road and Musselburgh Road in Dalkeith, north of the River South Esk. This was on a map in the Midlothian consultation. Neither of us have seen it in the flesh.
Today I made the effort to divert from my usual commute via Dalkeith Country Park. I found it! On both sides the entrance is a bit hidden. On the west side, the entrance is found through the "car park" where the old school was. You can just see a cycle painted on the ground at the south end. On the other side it comes out by the wee playground near Eskglades.
You can see the route on google satellite view
Now though it is a good wide path not too wiggly with good sight lines. It does have one of those silly barrier gates in the middle but this can be opened without having to go through the kissing gates. On the whole 100 times better than the NCN 1 through from Woodburn to Eskbank.