He served as a captain under General George Armstrong Custer in the Indian Territory in present-day Oklahoma, where he died at the age of 24 while leading a charge in the Battle of Washita River.

At the age of seventeen, in June 1862, Hamilton enlisted as a volunteer private in the 22nd New York State Militia, serving for three months at Harper's Ferry, West Virginia.

[3] As a result of his conspicuous "gallant and meritorious conduct" during the passage of the river, he was placed the next day on the staff of General Romeyn B. Ayres, who commanded the division.

[5]: 101 [7] The next day, November 27, 1868, Hamilton became the first casualty in the Battle of Washita River, killed while leading the first charge of the troops in Custer's attack on Black Kettle's Cheyenne encampment.

"[6] He marshalled his squadron "in splendid style right up to the enemy's lodges," where he "fell dead from his horse, shot through the heart by a bullet from a Lancaster rifle" in the hands of a combatant concealed in a wigwam.

[7] An army surgeon later wrote that the "ball entered about five inches below the left nipple, and emerged near inferior angle of right scapula.

While he was susceptible of the perfect phrensy of enthusiasm, and would brave danger and death in every form of duty, yet, in the quiet hours of life, he was gentle and winsome as a maiden.

His strong intellect, refined by careful culture, enabled him to comprehend the "fluctuations and vast concerns" of life with rare intelligence and discrimination.

Thus attuned and trained, he lived a noble and blameless life, an honor to his profession and a worthy possessor of the great name which he inherited.