Karen: I will follow your postings with interest. I would like to inform you of a matter regarding a possible 17th century link between the Meachams/Mechams from this Jeremiah line and my own line. We have traced our Mechams back to Athlone, co.Westmeath, Ireland, about 1695. Robert Mecham arrives there; origins unknown, but born 1675. His family prospered in Athlone for 150 years. He seems to have been English and certainly Protestant and settled in the east of the town, amongst English-origin families. One of his grandsons was Lt. and Quartermaster William Mecham (often spelt Meacham)of the 28th Foot. This regiment had extensive service in America and Canada 1757-1778 (with a break of 10 yrs home).
I have it from a very reliable source that there was a reported meeting in Canada in the 1770s, between an officer serving with the 28th Regiment of Foot, and an American Mecham. They had a discussion about common ancestry and it was mentioned that "Robert Mecham was living on the old family homestead" (that I expect meant Robert Meacham c1700-1783 and father of the 28th Foot Wm. Mecham, living at Kilmacuagh, near Athlone). This meeting was reported, I'm told, "in an 1852 New York Genealogical Register". I haven't been able to find out any more, as yet. I'd be pleased if you came across any reference to the above.
In researching, I've come across another Jeremiah Meacham, who may fit in your lineup somewhere. Source: 'Canadian Military Institute Officers of the British Forces in Canada During War 1812-15', by L.Homfray Irving 1908. Page 173 has Capt.Jeremiah Meacham, Ridge (serving in Lower Canadian Militiar, District of Montreal, Argenteuil Division. Page 174 has 'deserted during the war (Canadian Archives). I would think he was an American who decided to return home.
I have discussed the foregoing with Pam MacDonald, who has also posted here. Maybe this is not exactly a response to your topic, but I wanted you to be aware of the matter. Good luck with your project: Mick Mecham, Aust.