I saw a leaflet from the Eastwood Ramblers (http://www.eastwood-ramblers.org.uk/) that talked about a walk coming up that was from Busby to Netherlee. I didn't want to wait for their walk but wondered about its route.
I figured that it had to follow the River Cart and end up at the Linn Park. I had a look at Google maps
http://maps.google.co.uk/maps?f=q&source=s_q&hl=en&geocode=&q=clarkston&sll=56.419076,-3.571157&sspn=0.017186,0.066047&g=busby&ie=UTF8&hq=&hnear=Clarkston,+Glasgow,+Lanarkshire,+United+Kingdom&ll=55.796794,-4.248877&spn=0.034932,0.132093&t=h&z=14
and basically we are talking about the green area in the middle between the two roads.
Searching a bit further I came across a short description of part of the walk
http://www.s1play.com/out-and-about/recommendation-Walk-the-White-Cart-Way-1229.html
although that was on the south side of the river and didn't really show a round trip which was what I was after.
Hunting with Google maps I came across a bridge
http://maps.google.co.uk/maps?hl=en&ie=UTF8&ll=55.791303,-4.267698&spn=0.001132,0.004128&t=h&z=19
at the end of Moray Gardens and then I thought that I had a round trip.
And so, with a rough plan I set off for my expedition.
Unfortunately the interpretation of the right to roam legislation in East Renfrewshire has interesting nuances.

So I had to modify my route.
I went back to Mr C. Walker's route and found the access from Alyth Crescent to the riverbank.
A lovely route and got to the Linn Park quickly.
Crossed the bridge, but there isn't a path on the north side of the river, so you have to divert away.
The grass was wet so instead of heading up the hill, I followed the path up past the equestrian centre and then round to the right and found myself crossing out of the park and into the grounds of the Linn Crematorium. Leaving from the main exit I crossed the road and into the cemetery. Initially I went round to the right to get closer to the river, but no sign of a path so i wandered back to the left and round the whole cemetery. It was the first time I had been there, very touched by the number of still-birth or early infant deaths that are commemorated. Very sad and moving.
At the end of the cemetery there was a little almost play park with toys and other mementos.
And just beyond it was a path exiting onto Netherton Braes. The path was a bit slippy and in the early part has three burnt-out car wrecks so it was a bit spooky, but it soon settles down and again is a lovely walk and before I knew it I was at the other end of the Moray Gardens bridge.
Oh, why couldn't it be open as that would make a lovely round trip?
Or maybe just during daylight on certain days of the week so that the overall community could get the benefit without the local residents having too many drawbacks.
Oh well, I moved on.
(please don't copy this route, I got it right in a later walk, so this red herring route is just included as its what I did the first time).
The path following the river was wide and well maintained, however after a while it stopped.
I double-backed and found a smaller path going up the hill, so I following it.
It got a bit wild then disappeared, then started again.
After I had gone too far, it then appeared that the paths may have been made by deer or something similar.
I made my way back down to the river where I was now on the bank of the Kittoch Water (although I didn't know it until I checked it on the map later) and it was easy to cross over the water using stepping-stone rocks in the waterfall. From there I came round onto nice paths then led under the railway viaduct and onto Cartside Drive in Busby.
then back by the main road to where I started.
A great fun walk, but not the gentle stroll that the Eastwood ramblers were suggesting.
Next time I would try not to get lost and follow the right path.