Irish births, deaths and marriages are not viewable on-line anywhere. You have to order a copy from the registrar, either in Belfats or Roscommon. Roscommon is cheaper. You can order a photocopy of that 1866 death cert from GRO Roscommon for ?4. Put the place, year, volume & page number on the application form (anywhere). http://www.groireland.ie/ You have to post or fax the form to them but they will e-mail the copy certificate to you if you wish. Put ?please e-mail to?..? clearly on the top of the form.
The only on-line directory for the area and time is Pigot?s for 1824. It lists about 4 towns in Co Armagh but no mills and no Pattersons are listed that I can see:
http://www.failteromhat.com/pigotu.htm
I am not sure whether a weaving mill in Armagh would have been commonplace in the 1830s. Originally most weaving was done at home, on small hand looms. Often in the winter when the family had spare time from other work. They would make up lengths of linen which they would then take to markets in places like Armagh or Markethill, and sell for cash (so providing a little ready money in an economy that was otherwise largely based on barter). Cash came in useful for purchasing things you couldn?t obtain by barter eg tobacco or a ticket to Australia, and this linen money was a reason why the standard of life in Ulster (where most linen was made) was slightly better than in the rest of Ireland. As the 1800s progressed big mechanised linen mills, powered by water or steam, were built. There were some in Co. Armagh eg in Bessbrook, Lurgan & Portadown. But I don?t think they were built till about the 1850s. These factories could make linen much more quickly than home weaving, and they also provided thousands of new and comparatively reasonably paid jobs, especially for women. So this basically killed off home based hand loom weaving, though some people continued right up until about 1900. So were there linen mills in Armagh in the 1830s? I am not sure. There would of course have been corn mills etc, every 10 miles or so, to grind all the corn and wheat grown by local farmers. Perhaps that?s what the Patterson?s had?
There?s a museum to linen making in Ulster, based in Lisburn, Co Antrim. I imagine they might be able to help you. You could e-mail them and ask if they know of any mills owned by Pattersons in Co. Armagh:
http://www.lisburncity.gov.uk/irish-linen-centre-and-lisburn-museum/
Here?s a link giving a little history about linen making in Armagh.
http://www.culturenorthernireland.org/article/703/the-industrial-herita…
Here?s another link that tells you a bit more about linen making:
http://www.irish-genealogy-toolkit.com/flax-plant.html
Yes I would say your Pattersons are likely to be descended from Scottish settlers. The name is Scottish, they were evidently protestant, and they lived in one of the counties that was heavily settled during the Plantation. If they turned out to have been Presbyterian at any time that would clinch it.
In the 1600s some 100,000 Scots settled in Ireland (representing about 10% of the entire Scottish population at the time). There are no records of the individuals who moved, save for the major land owners (known as undertakers because they undertook to build roads, houses and forts etc, as well as bring an agreed number of their Scottish & English tenants with them.) Many of those who settled in Co Armagh are known to have come from East Lothian and Midlothian (ie around Edinburgh). See:
http://www.thereformation.info/plantnire1610.htm