OBITUARY. GEN. ADDISON FARNSWORTH. Gen. Addison Farnsworth died on Sunday last at his residence, No. 229 Putnam-avenue, Brooklyn, in the 52d year of his age. The deseased gentleman was a brave soldier, and did good service for his country in two wars. He was born in Albany in the year 1825, and resided there until the outbreak of the Mexican War. He then entered the volunteer service as a second lieutenant, and by his bravery won rapid promotion. At the close of the conflict he held the rank of Major. He was then offered a com- missionin the regular Army, but declined it. Returning to civilian life, Major Farns- worth became a journalist, and founded a paper called the Albany Dutchman. This venture did not succeed, and he obtained the position of a storekeeper in the Custom-house of this City, which place he held at the beginning of the rebellion. At the first note of war he en- gaged in the organization of the Thirty-eighth Regi- ment of New-York Volunteers, and became its Lieutenant-Colonel. He did not retain this position long, but was advanced to the Col- onelcy of the Seventy-ninth Regiment. With this command he participated in the battle of Bull-Run, in which conflict he was severely wounded. Re- covering in a measure from his wounds Col. Farnsworth was appointed Commander of the First Regiment, Veteran Reserve Corps, with the rank of Brevet-Brigadier-General. At the close of the war he was again employed in the Custom-house, where he held a position at the time of his death. Gen. Farnsworth's body will be taken to Albany for interment this afternoon.