I have posted a map of the Lisburn area, which if you are not familiar with the geography of the north of Ireland, lies about 8 miles SW of Belfast, on the river Lagan which here forms the boundary between counties Antrim and Down.
The north side of the valley rises to mountains of about 1,000 feet, while the southern slopes are more rolling hills rising to about 5 or 600 feet and cultivated to the top. The result of this is that the Drumbo church where David Fulton, son of James, was baptized in 1719, though it is in another county is on high ground and practically within sight of the Belsize farm where the Fultons first settled. Lisburn, formerly known as Lisnagarvey, and Blaris parish in which it lay, was of importance as a town before reaches of of the Lagan. The port in those days was Carrickfergus, about 7 or 8 miles north east of Belfast, protected by a Norman castle. Lisburn was of significance as there was a bridge over the Lagan there also protected by a castle, so when the Fultons settled at Belsize on what was then probably the main route from Lisburn ot the port of Carrickfergus, they were going to an area which was of some importance at the time. The map sections are taken from a map of Co. Antrim at a scale of one inch to the mile, showing parishes and town lands ( a subdivision of land used in Ireland, which can be useful in pinpointing where people lived). I have sketched on the location of Drumbo and Hillsborough parishes in Co. Down as they come into the story. Drumbo was later divided and part is now the parish of Drumbebeg.
Belsize itself is in the parish of Derriaghy, east of Lisburn, but the property is quite close to Lisburn town. It appears to have been one of the larger holdings in the parish at over 70 acres, and seems to have passed from the Fultons (or perhaps sublet) around the 1730's. By 1767, it was occupied by a Mr. Hudson who ran the Classical School in Lisburn, and it was destroyed during the 1798 rebellion and never rebuilt. I am coming to think that the reason for the property passing from the family was not because the lease expired, as Hope suggested, but because the family had either moved into business in Lisburn - well documented - or emigrated, while younger sons had found other land in nearby parishes. The decision may also have been influenced by the Belfast Lisburn road becoming a turnpike i.e. tolls had to be paid for its use, which happened in 1 733. Though by then the main road to Belfast did not appear to pass Belsize, they would have had to pass a toll house on the way. If their interests had begun to center on Lisburn they may have thought it better to move into the town rather than pay a toll for every journey.
We are fortunate that the parish records for the area have survived better than most Irish parishes.. Blaris/Lisburn records exist form about 1650, more or less, after a siege and fire in 1642 and this parish also kept the records of Derriaghy parish, where the church was derelict through the 17th century until around 1700, after which most of the Derriagy records remain available though some tantalizing gaps. To the north the records of the three parishes of Tullyrusk, Camlin and Glenavy were all kept by Glenavy and these also survive from around 1700, and the Presbyterian records of Lisburn and Drumbo though by no means complete do give a number of years in the early 18th century.
Briefly, the history of the area is that in about 1608 the land from Derriaghy parish to Lough Neagh comprising the manors (another old division of land) of Killultagh and Kilwarlin was acquired by Sir Fulke Conway, and passed by succession in the Conway family, who later were honoured with the hereditary title Lord Conway until there were no male heirs when the last Conway bequeathed it to a Seymour who was about to marry his daughter when the lady died suddenly. The Seymours were raised to the peerage as first Earl and then Marquess of Hertford and the property remained in the family until the Irish Land Purchase Acts of around 1900. At the end the property had been divided between several parts of the family and in fact the Lisburn Estates were held by the Wallace who is remembered as the man who presented the Wallace Collection (art gallery) in London to the nation.
I have enclosed a note of the information which I have collected about the Conway/Hertford families relating to their interests in the land around Lisburn. I have some more information and this note needs to be updated but will give you a general idea.
Returning to the general history of the area, in 1608, Ireland had been subject to wars and rebellions for may years and was in a poor state, so probably the area around Lisburn was sparsely populated. It was settled by Sir Fulke Conway with mostly English and Welsh settlers so the fact that the Fultons came to this area and not to the areas of the Plantation proper which was further north and west, tends to support Hope's theory that the (Scottish) Fultons were moving in Court circles in London perhaps having come from Edinburgh with the Court of King James VI of Scotland who succeeded to the English throne on the death of Queen Elizabeth in 1603.
The "old English" (i.e. settlers in Ireland from earlier centuries) and native Irish rose in rebellion in 1641 and Lisburn was attacked and severely damaged hence the lack of records for the early 1600's. The unsettled state of the country also encouraged some of the settlers to leave again so the movement of population in Ireland during the 1600's was two way. In 1690, the army of King William passed through the town on the way to the Battle of the Boyne
In the late 1600's and onwards Lisburn was a major centre of the Irish linen industry (linen was one of the few products which the law allowed to be exported) and during the 18th century the Fultons were closely associated with this business.
Lisburn was one of the main centres in Ireland where the Huguenots (French protestant refugees) settled after the revocation in France of the Edict of Nantes in 1685, bringing with them skills with which to develop the local linen industry and it was also one of the principal areas where Quakers were to be found.
The town was destroyed by fire again in 1707, this time started accidentally. Economic conditions rose and fell several times during the 1700's leading to increased emigration in the periods 1720-30 and again around 1770. This emigration was also encouraged by discrimination against the Presbyterians who were strongest in the north of Ireland - the ruling classes tended to be of the Established Episcopalian Church of Ireland. The Fultons who remained in Lisburn seem to have been business men first and sectarian believers second, as they seem to appear indiscriminately in the records of the Presbyterian and Church of Ireland records. Perhaps those of strongest religious conviction were the ones who emigrated.
Political agitation was again in the air in the 1780's and 1790's with the separate Irish parliament, which sat in Dublin, agitating for more autonomy. This resulted in the rebellion of the United Irishmen in 1798., followed by the abolition of the Dublin Parliament and the Union of Great Britain and Ireland in one Parliament in London. Battles were again fought in the Lisburn area during which Belsize, the first known home of the Fultons in this area, were destroyed. The move of the seat of government to London perhaps also was the reason for the move of those members of the "Hope" Fultons who had not gone further afield to move to London, for shortly after 1800 that branch of the family had almost gone from around Lisburn.
The big cause of 19th century emigration, the potato famine, did not affect the area around Lisburn to the same extent as elsewhere because linen workers were not so dependent on the potato for survival.