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The Links are the last section of the burgh muir to remain open space. Using today's street names, it extended from Leven Street, Bruntsfield Place and Morningside Road in the west to Dalkeith Road in the east, and as far south as the Jordan Burn and east to Peffermill, occupying a total area of approximately five square miles. The contemporary names for the roads which bounded the muir were the "Easter Hiegait" (Dalkeith Road) and the "Wester Hiegait" (Morningside Road). The magistrates of the Town Council described the boundaries of the muir as follows in a legal document of 1593:

"Begynnand at the west neuke [corner] of the dyke upoun the south syde of Sanct leonards loneing [lane] qr [where] the grund of the croce stands, and thairfra passand south and south eist as the said dyke gangis be the heids of the airabill landis of Sanctleonards and Preistisfield respectively until it cum to the end of the dyke foresaid, and to the gait that passes to the Priestisfield, Peppermylne, and Nidrie, and fra the south wast syde of the said gait, as ane oyr dyke passes south and south wast, be the sydes of the airable lands of Camroun qll it cum to the south wast neuk of the said dyke, and thairfra doun as the said dyke passes south south eist to the end of the Grene end of the said Commoun Mure by and contigue to the passage and hie street [Dalkeith Road] fra the said burgh of Edr. to the brig end betuix the lone dyke of the said lands of Camroun, and thairfra ascendand the waster lone dyke be the edge of the said commoun mure, and as the said wester lone dyke gannis to the end thairof, quhair it meets at the croce dyke by and upoun the eist syde of the aikers of the said commoun mure pertening to [blank text] and sa linalie be the said dyke qll it cum to the Powburne, and sua up the said Pow burne qll it cum to the loneing that passes to the lands of Newlands pertening to the laird of Braid [bordering the south of the Grange], and thairfra wastwart as the dyke gangis to the south neuk of the dyke situat upone the eister pt of the lands of Tipperlinn, and sua northwart as the said dyke gangis by the yet [gate] of Tipperlinn, and thairfra northwart to the dykes of the corne land heids thairof, passand north as the said dyke gangis to the hie gait that passes by Merchamstoun to the Craighous, and eist be the said gait till it cum to the west dyke of the croft callit the Dow croft [present Albert Terrace], and thairfra sout. to the sout. end of the said dyke and sua nort. eist be the said dyke to the nort. eist neuk thairof, and thairfra nort. wert as the dyke gangis to the nort. west nuk of the same upoun the south syde of the passage that leids fra Edr. by the yett of Merchamstoun, and than begynnand upoun the nort. syde of the said hie passage directlie foiranent [in front of] the nuk of the said dyke be the new yaird dyk laitlie biggit [built] be the laird of Merchamstoun upoun ane pece of the said commoun mure laitlie disponit [transferred in ownership] be the provost baillies and counsall of the said burt. [baronet] for the tyme to him, and sua haldand be the said new dyke and gangand about the samen till it cum to the nort. eist nuk tairof, and thairfra nort. wart and nort. eist be the auld dykes at the heid of the airable lands of Merchimstoun till it cum to the wester gawill [side] of the Coithouses [stone cottages] pertenand to the Laird of Wrytishouses [present Leven Street]."