The Fredericton correspondent of the St. John 'Globe' writes: Dow VANDINE of the Custom House, is home from a trip to New York, convinced he is one of the rightful heir to valuable lands in the heart of Long Island City, now in the occupation of Wm K. Vanderbilt. Mr. Vandine claims that his great-grandfather emigrated from Holland, 156 years ago with three sons and three daughtersm settling in Long Island, where he many years afterward acquired an immence amount of land, comprising the track now claimed by his descendants, and that he leased the land for a long term of years to Commodore Vanderbilt, grandfather of Wm K. Vanderbilt and who also emigrated from Holland and in time married one of Mr. Vandine's daughters. When the Revolutionary war broke out, Mr. Vandine, with his three sons and two remaining daughters, came to New Brunswick and in time located at Grand Lake (Queens Co.) where he died and was buried. After his death his three sons and two daughters went back to Long Island. But one of them, Arthur VANDINE, returned in a short time to Grand Lake, where he passed the remainder of his life. He left seven sons, of whom Joseph VANDINE, father of Dow Vandine, of this city and Arthur Vandine of Detroit were two. The lease of the land in question is about expiring and Dow Vandine is cmmunicating with the other surviving descendants of the alleged lease with a view of taking steps to secure the property.