OBITUARY Gen. J. Egbert Farnum. Gen. J. Egbert Farnum, who died yester- day morning at his residence in this City, was born in 1824 in New-Jersey, but was brought up in Pennsylvania. Displaying early in life an adventurous disposition and a love for a military career, when the Mexican war broke out he joined the First Regiment of Pennsylvania Volunteers, with which he served as Sergeant-Major until the close of the war. During the war he was distinguished for his great personal courage. His service in Mexico served only to increase his love for adventure, and subsequently he was connected with WALKER in the Nic- araguan expedition. At the outbreak of the re- bellion, Gen. Farnum was one of the first to offer his services to his country, and joining the Excelsior Brigade as Major he rose, step by step, until attained the rank of Major-General. He was, during his service, once or twice wounded, and finally so severely as to be incapable for further active service, and he was transferred to the Reserve Corps, in which he served until 1864, when he was mustered out and returned home. He afterward, for some time, held a posi- tion in the Custom-house of the City. Gen. FARNUM, at the time of his death, was about forty-six years of age.