A couple of other interesting bits that i've found.
Roy Military Survey of Scotland, 1747-1755If you click on the link, you will find a number of maps of Scotland. If you then click on 'Roy Military Survey of Scotland, 1747-1755' in the list, you will go to the next page, part way down the page click on Full screen map - 'Lowlands'. You will get a full screen map. On the 3rd strip from the right, near to the bottom, is the word 'Cumberland'.
If you zoom in just above the word 'land' in Cumberland, you should be in the Castleton area and be able to see Mangerton and 'Whithaugh Castle'

(you can use the arrows on the left like google maps or the wheel of your mouse to zoom)
A couple of transcripts from the London Gazette.
7th March 1723
James Armstrong, late of Maingertown in the parish of Castletown in the Shire of Roxburgh, Scotland, Gent, is named in the bankruptcy of Edmund Camden.
29th October 1771.
James Armstrong, late of Logan house, and John Armstrong, late of Logan Mains in the Parish of Half Morton in North Britain, (Scotland), but now of the City of Carlisle in the County of Cumberland. Partners, Dealers and Chapmen were declarded bankrupts. All debts to be paid to Mr John Dixon, Attorney at Law, at Brampton in the County of Cumberland.
A couple of bits mentioning the Armstrong's, Elliot's and Whithaugh, from Two Centuries of Border Church Life. 1891.
It is well known that some years of scarcity occurred at the close of the 17th century; and to that period the Session records contain some interesting references.
On the 6th June, 1698, a meeting of heritors and elders was held, conform to intimation from the pulpit, to take into their serious consideration what farther provision could be made for the poor. There were present Mr. Duncan McArthur, bailie of the regality ; Francis Armstrong of Whithaugh ; John Elliot of Thorlishope, with the minister and elders.
It was agreed that Mr. McArthur should send for two bolls of corn, to be ground free of multure at Whithaugh Mill, and to be distributed to the poor by Adam Armstrong and John Beatty, elders, at the rate of a peck of meal to the most needful and half a peck to those less necessitous.
It was also recommended that the Session give a note under their hand to such of the poor as were able to travel about the parish, but that none others should be entertained "under the penalty imposed by acts of Council." The meal was ground and distributed according to this agreement.
In the same book Mr. Elliot writes in 1749 — "I got three guineas from Sister Helen, that she got from John Armstrong, rowed in a bit paper to give me ;" and, again, "Received from my mother, which she received from John Armstrong, Whithaugh, to give me, three pounds." The worthy farmer had a large holding, but had difficulties not a few in keeping clear of debt, though he struggled manfully to be honest and honourable.
There are frequent intimations that " all accounts are cleared " between him and one or another of his customers, a consummation which is always noted with great apparent satisfaction. Often he adds the words, " We are free ;" and on the 27th June, 1750, having stated that all accounts with John Armstrong, in Whithaugh, were settled, he Adds, " And all money payd betwixt us both, so we are free till more bargains be made."