RootsChat.Com

Yes - Bellingham Mill (repeated on the next census sheet - separate household)

Newcastle Journal, 6 Oct 1871
BELLINGHAM AGRICULTURAL SOCIETY
Cottagers pig for feeding - 1st Mr John Place, Reedswood; 2nd J Ridley, Bellingham Mill; 3rd Mr Matthews, Bellingham

Looking at the '41 Census, there are 8 households recorded with the address "Shorts, Ide, St. Thomas". 

http://maps.nls.uk/view/101444347

"Higher Whiddon" - check bottom right hand corner

Yet to spot "Shorts".

From Crookshank's 1762 description of the battle

"They (the Covenanters) were scarce formed in this manner when an alarm came that a body of men was approaching them; they found it was Dalziel's van, which had cut through a ridge in the Pentland hills, and came upon them undiscovered, til they were within a quarter of a mile, upon a hill over against them. Colonel Wallace upon this sent Captain Arnot, who repulsed Lieutenant General Drummond, who was sent by the General (Dalziel) with a select party to begin the attack ...... When the Lieutenant General was driven back, there was no small confusion among Dalziel's army, of whom not a few threw down their arms. Major Lamont made the second attack, and repulsed the enemy; Duke Hamilton narrowly escaping. The last encounter was after sunset, when the General's foot, flanked with their horse upon all hands, overpowered the Colonel's little army, and routed them"

https://books.google.co.vi/books?id=04lbAAAAMAAJ&printsec=frontcover&source=gbs_atb#v=onepage&q=learmont&f=false

9 hits for "learmont (no "h") - not all Joseph.

It includes a description of the battle (page 181)