There is an old cemetery on the north side of Second street, in this city (New York), between First and Second Avenues, separated from the sidewalk by a tall iron fence, placed upon a granite foundation. The shrubbery is always clean and vigorous; the grass is always the greenest, and the walks are scrupulously neat. There are many tasteful and appropriate monuments to the dead that sleep within this hallowed inclosure; but to the memory of the most famous of its dumb inhabitants there was no marble shaft, no obelisk, not even a head-stone erected. But upon a simple slab of marble that lies flat, some two feet square, upon the earth, and is almost covered by grass, is the following inscription: JAMES MONROE, ROBERT TILLOTSON, Vault No. 147. There is nothing to indicate that the James Monroe mentioned is the Monroe who was in the battle of White Plains, and received a ball in the shoulder at the attack on Trenton, who fought by the side of Lafayette at Brandywine, who was Minister to France in 1794, and afterward to England; who was Secretary of State in 1811, and for two full terms President of these United States. Yet such is the fact, and that weather-stained slab of marble, two feet square, covered for many years the grave of Ex-President Monroe. Many years afterward, by order of the Virginia Legislature, the remains of Ex-President Monroe were removed to Richmond, and a monument befitting his fame was erected over his grave. The property of Oak Hill is now owned by Mr. Fairfax, and with it one thousand acres of land. Three hundred acres are comprised in the McGowan estate. The second daughter of President Monroe, Mrs. Maria Gouverneur, died in 1850 at Oak Hill, where she was buried by the side of her mother. The eldest daughter died in Paris, and was buried in Pere la Chaise. There are now living but few descendants of Mrs. Monroe. At this short remove from her day, not many incidents relating to her career are extant. She lived as public a life as did Mrs. John Adams, and was far better acquainted with society in this country and Europe than several of the ladies who preceded her in the semi-official position she filled, but her ill-health and her temperament unfitted her for familiarity with the people, and kept her from being popular in the sense that Mrs. Madison was. The difference between these two women was that the latter was fond of company, enjoyed life and had a healthy, hearty interest in the events transpiring about her. The other lived in retirement as far as possible, and the record of so quiet an existence is not as familiar to the people of this country as is that of those of her contemporaries who occupied the high place she filled.