Bridgehill 1753 Roy sheet 17, 5
Bridgehills 1775 Ainslie/Fife
Brigghills 1781 Sasines no. 181 [‘in Brigghills, Muirside, North Spittal, and Sillytoun’]
Bridgehill 1828 SGF
Sc brig + Sc hill
The bridge in question is Bow Bridge over the Ore at NT201948 (Bowbridge 1753 Roy sheet 17, 5; Bow Bridge 1775 Ainslie/Fife). It is called Brigghills Farm on OS Pathf., and will have been coined in Sc, despite the early SSE forms. It was probably a division of the lands of Spittal ADN, that part which lay in the barony of Wester Lochoreshire, hence the pre-1891 parochial anomaly.
This place-name appeared in printed volume 1