We are indebted to the Evening Gazette for the subjoined notice of this remarkable lady : " Cornelia Beeckman was the second daughter of Lieutenant- Governor Pierre Van Cortlandt, by his wife, Joanna Livingston, whose birth took place in the old manor house, by the banks of the Croton, on the 2d of August, 1753. Here her infancy and youth glided away, and but a short time before the war, she left its scenes for a life in New York, whither she removed upon her marriage with General Beeckman. When the Revolutionary troubles ran high, she came back to the old house at Peekskill, where part of her family resided. Exposed, of course, to all manner of insult and aggression, well-known herself, and in connection with her father, subsequently Lieutenant-Governor of this State, under Clinton, (but at that time, president of the Committee of Public Safety.) with her brother serving in the army, and many relatives and intimates, all zealous Whigs and devoted Americans, her unconquerable will and high spirit bore her safely and uncompromisingly through those trying scenes. We copy from a graphic sketch, by an able and we fancy well-known pen the following notice of her life during this disastrous period.

" One little incident we recollect to have read in a letter written by herself, in 1777. A party of royalists, under Colonels Bayard and Fanning, came to the Peekskill house, and commencing their customary course of treatment, one insultingly asked her, ' Are you not the daughter of that old rebel Pierre Van Cortlandt ? ' She replied, ' I am the daughter of Pierre Van Cortlandt, but it becomes not such as you to call my father a rebel.' The tory raised his musket, when she, with great calmness, reproved him for his insolence and bade him begone.