Arthur obviously was not born after the 14th Amendment
Sorry, my stupid error.
although I suppose he could have been a citizen of Vermont as well as the British Empire as Ireland was ruled over for hundreds of years in actual fact.
He was a citizen of the State of Vermont and a United States citizen at birth. Whether he also had a claim to Be a British citizen or subject is a matter of British law which has no effect on United State citizenship.
Ireland has never been part of Great Britain. Ireland was ruled by the British but that did not make them part of GB. GB is England, Scotland and Wales. UK is the union of GB and NI. The term British is thrown around for the UK as there is no term such as UKer.
In discussing British citizenship determinations, such distinctions have to be considered.
Until the Republic of Ireland changed its constitution after the Good Friday agreement, the Republic had always claimed all 32 counties, considering the six counties to be British occupied Ireland. Anyone having been born in the six counties was able to go south and obtain an Irish passport, as the Republic considered them to have been born in the Republic.
OK, I thought they were considered part of the British Empire.