A new free app is available to download, and it enables you to walk around identifying the Meadows & Links trees using your smartphone.
I should mention first that your starting point for all things in this park are the fine folks of the Friends of the Meadows and Bruntsfield Links.
But if you want to name that tree, then I recommend the excellent TiCL app. You can download it here for iPhone and Android.
At the moment, the first Tree Trail for the Meadows and Bruntsfield Links is a small trial version, which you can also partly preview on its TicL webpage. This mini-trail is based in the little fenced-off children's park beside Alvanley Terrace, on Whitehouse Loan.
As you'll see from the app, there are some huge mature trees and some attractive new plantings here. Among the young trees, look out especially for the five young Magnolias. The varieties are Galaxy, Heaven Scent, Kobus, Saucer and Spectrum. (In Autumn 2017, we'll also be getting some bird-friendly Rowans, kindly donated by a neighbour.)
Among the old trees, look especially for a towering example of what's said to be Britain's rarest type of elm, the Plot Elm. It appears to be surviving the threat of Dutch Elm disease.