Part of the Telfer Wall, Lauriston Place
A surviving stretch of the old town wall, built as an extension to the older Flodden Wall between 1628 and 1636 to enclose the grounds of Heriot's Hospital and the Greyfriars Kirk. It is known as the Telfer Wall, after John Taillefer, the mason who supervised its construction. The town wall enclosed an area of about 140 acres with six ports or gateways (clockwise, starting from the Castle): the New (at the east end of the Nor Loch), the Netherbow at the foot of the High Street, the Cowgate (also known as the Blackfriars or St. Mary's), the Potterrow (also known as the Kirk O' Field), the Bristo (also known as the Greyfriars, and later the Society, after the Brewers' Society that came to own the ground) and the West. A clear space, 24 ft wide, was left outside the wall, creating a line which later roads tended to follow, as seen here.
"The common Council at this time having bought of Tours of Innerleith, ten acres of land at the Grayfriers Port, for the sum of five thousand eight hundred marks, Scottish money; ordered the same to be inclosed with a wall. This piece of ground, which, from its situation, is denominated the High Riggs, is the spot whereon Heriot's Hospital and gardens, the southern part of the Grayfriers church-yard, the charity workhouse and bedlam, with their appurtenances, are situated; and inclosed by the town wall on the western, southern and eastern sides, extending from within a little way of the West Port, to that of Bristow." -- Town Council Minutes 1618*
*This source from Daniel Wilson's Memorials Of Edinburgh, if accurately dated, suggests an earlier building date than that given in most sources, because it's hard to see why it would take ten years before the act of council was implemented