Below is an old map of the area I'm interested in. As you can see, a boundary line is shown along a general south-east to north-west route (with a southerly loop just before the line meets the Mallsmire Burn) to the north of Hundredacre Hill.
Below is the same map as above but with some added annotation by myself. The solid blue lines are burns that definitely exist/existed (i.e. the Mallsmire to the west side of the plan and an unnamed burn in the south-east corner).
I've previously been able to establish that the unnamed burn ran up to the property called Westhouse, which was located at the existing junction of Curtis Avenue / Westhouse Avenue (I wonder how the council came up with the name for the latter?) - I haven't been able to determine the direction the burn flowed from this point though. There is an existing culverted watercourse a few hundred metres along Cathcart Road (which is the continuation of Curtis Avenue) so it's possible/likely that this is the downstream end of the unnamed burn. I'm hoping (for work-related reasons) that it ran in the opposite direction though and followed the boundary line to the Mallsmire.
I hope this makes the focus of my 'investigation' more clear.