Inch Infantry Shoulder Belt Plate c1798:

http://www.militarymetalwork.co.uk/proddetail.php?prod=AM200&cat=99

From TMP:

http://theminiaturespage.com/boards/msg.mv?id=368049

I found:

"Names of those proposing to form a cavalry unit to act with the Inch infantry and to be known as Inch Legion, c.1798, 18 names -T/1023/163", and other related items:
http://books.google.com/books?id=3ZJ-kPLnZr8C&pg=PA99

"216 Male Residents of Inch Parish, County Down, 1796":
http://cdn.bbcmagazinesbristol.com/bbcwhodoyouthinkyouare/bonus_content/issue_66/3_Inch_Residents.pdf

"John Martin (not specified) Inch Militia Lists Finnebrogue Estate 1793"
http://freepages.genealogy.rootsweb.ancestry.com/~donaghmore1/donaghmore/tgcmartin.html

And;

"The Volunteers, after the Convention in the Rotunda, Dublin, 10 Nov., 1783, and the rejection of its demands by Grattan's Parliament, disappear for a time. In 1792 there was a great revival. Belfast raised some new corps; Seaforde provided 541 men and two pieces of artillery; Downpatrick raised two new corps — the first, the Inch Infantry, under Maxwell of Finnebrogue, with Thomas Nevin and Thomas Mc Clinchey lieutenants. This corps had scarlet uniform with blue facings. The second corps was commanded by Captain William Hawthorne, and had yellow facings.

These troops were raised, not to repel a foreign foe, but to enforce certain Parliamentary reforms. In many places they evinced a tendency for Republicanism and an admiration for the French Revolution, and accordingly they were suppressed by a proclamation of the Lord Lieutenant. Four years later, a new Volunteer force was called into existence to resist the United Irishmen. About
Downpatrick they took the old names, and it was with a force largely composed of these men that General Nugent defeated the Insurgents at the battle of Ballynahinch. I shall now briefly describe, the eight County Down badges, which have been entrusted to me by Colonel Wallace of the " South Down" Rifles, Mrs. Jordan of Downpatrick, and other friends.

[Illustration not separately downloadable -see article URL below]

1. The Inch Infantry. — This is the largest of the badges, and is of the usual oval shape, with crowned harp in centre and ribbons above and below, with the name " Inch Infantry." " [Note: This is the same style of badge in the picture I posted above.]: "The Down Volunteers" by the Rev. L. A. Pooler, B.D., Ulster Journal of Archaeology, Volume 4 (1898), pp. 152-154:
https://archive.org/stream/ulsterjournalofa04ulst#page/n163/mode/2up

Of possible interest:

List of Irish Volunteer corps:
http://en.wikipedia.org/wiki/List_of_Irish_Volunteer_corps