I did a Fold3 search and found only two Silas [nmn] Harringtons in Federal service, 7th Michigan Cavalry and 179th New York Infantry. All other Silas' had middle initials other than 'W'.

I did not find in the American CW Research Database Silas in the 7th Michigan.

Ages seem to match with that of the Silas in the 179th

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Silas W. Harrington, Private, Capt. J. B. Brockenbrough's Co. (Baltimore Light Artillery),* enlisted August 15, 1861 at Richmond for the war, recorded on the December, 1862 Company Return as absent, wounded, writes to Sec. of War, Dec. 26, 1862, I entered the service at the age of 16 and have been in the service of the Confederate States more that 12 months and after being engaged in many Battles was wounded twice in the same foot, an endorsement on his letter, dated January 18, 1863 notes, desires discharge from Baltimore Artillery on the grounds that he is under 18, discharged February 4, 1863 being a minor

* This company subsequently became the 2nd Maryland Battery

M321: Compiled Service Records of Confederate Soldiers Who Served in Organizations From the State of Maryland.

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Silas Harringrton

Residence was not listed; 18 years old.
Enlisted on 5/31/1864 at Urbana, NY as a Private.
On 7/20/1864 he mustered into "A" Co. NY 180th Infantry
He was transferred out on 7/23/1864
On 7/23/1864 he transferred into "G" Co. NY 179th Infantry
He was Mustered Out on 6/8/1865 at Alexandria, VA

Sources used by Historical Data Systems, Inc.:
- New York: Report of the Adjutant-General