Individual Details

I have no proof that the John who served with Edom Adamson is the same man as his brother, but that would be a reasonable assumption and is incorrect since that John survived the war.
Civil War: 130th Indiana Regiment Infantry - Company A
ADAMSON Edom Private Tampico 30 Dec 1863 mustered out 22 May 1865
ADAMSON John N. Private Tampico 30 Dec 1863 mustered out 2 Dec 1865 as Corporal

THere was also a John Adamson in Co. G of the 57th Regt. along with Enoch Adamson, another brother. In fact there may have been two of them in the 57th Regt. Private John Adamson of Kokomo was killed in battle at Stone River, on 31 Dec 1863. And John W. Adamson of Kokomo was killed in battle at Kenesaw Mountain on 23 Jun 1864. It is true that John is listed as John W. Adamson in the 1850 Census - so I have chosen this as the most likely date of death.

The John W. Adamson that died at Kenesaw on 23 Jun 1864 is buried Marietta Natl. Cemetery, Marietta, Cobb Co, GA per the US Veteran's Affairs. He enlisted 18 Nov 1861, Co G, 57th Regt, Union Army. He was from Kokomo, IN. One of the records lists his middle name as Wesley.
Find A Grave Memorial# 3946034 and Civil War Soldier Records and Profiles, Ancestry.com

John was not mentioned in the will of his father in 1869, so apparently he died in the War without heirs.

But there were still other John Adamsons in the Civil War. John N. Adamson was a son of Simon Adamson and Anna Elliott. He lived in Quincy, Adams Co IL, and filed for his Civil War Pension. AND John R. Adamson, son of David & Mary Ann Roberts Adamson, died at the Battle of Fort Gibson in Mississippi, 1 May 1863 - his widow filed for his pension. He served as a 1st Sgt, Company D of the 69th Indiana Volunteers. A John Wesley Adamson served in Capt. J. H. Mooney's Co, Matchel's Battalion, Missouri Volunteers - he enlisted 9 Aug 1862, Oregon Co, MO at age 18.

Birth	1843	Indiana
Death	23 Jun 1864	Battle of Kennesaw Mountain, Georgia

Father	ANDREW JACKSON ADAMSON (1817 - 1869)
Mother	RACHEL ANN GARNER (1816 - 1898)
Sibling	Edom Adamson (1835 - 1885)
Sibling	ENOCH REUBEN ADAMSON (1841 - 1910)
Sibling	Sarah E. ADAMSON (1846 - 1907)
Sibling	Mary Emily ADAMSON (1847 - 1929)
Sibling	Rachel Ellen ADAMSON (1851 - 1855)
Sibling	Andrew Fredrick Adamson (1855 - 1913)
Sibling	Hester "Hattie" ADAMSON (1857 - 1890)