Using Ayling's Revised Register and the History of Pittsfield, I've added the soldier's unit and cause of death to their memorial.
John Brooks - Co. H, 3rd NH; wd 6/16/64 Ware Bottom Church, VA; d. 6/17/64, Bermuda Hundred
Henry Plummer Brooks - Co. H, 3rd NH; died of dis, 4/14/65 Wilmington, NC
William Campbell - Co. G, 7th NH; KIA 7/18/1863, Fort Wagner, SC
John Cate - Co. G, 15th NH; wd 5/27/63, Port Hudson, LA; d. wnds 6/8/63, Baton Rouge
Joseph M. Chesley - Co. E, 2nd NH; KIA Gettysburg, 7/2 or 7/3
Willard K. Cobb - Co. E, 4th NH; KIA 9/29/64, New Market Heights, VA
George W. Davis - Co. E, 4th NH; a POW, d. after being paroled in Annapolis, MD
Joseph C. Dennett - Co E., 4th NH; d. of sickness, Hilton Head, Jan '64
Justice C. Drake - Co. B, 1st NH Cavl d. 8/14/64, Andersonville Prison
John J. Drake - Co. D, 11th NH; d. of dis. 11/10/64
Israel Drew - Co. G, 8th NH; died Camp Parapet, LA, 8/23/62
John S. Eaton - Co. E, 8th NH; disch for illness, died on voyage home, 11/2/62 and bur at sea
Lewis E. Edgerly - Co. G, 7th NH; missing at Fort Wagner, 7/18/63
Samuel R. Green - Co. A, 5th NH; wd at Gettysburg, 7/2/63, died 7/29/63
William T. Knight - Co. E, 2nd NH and Co. B, 12th NH; KIA 7/2/63 at Gettysburg
Henry B. Leavitt - Co. G, 7th NH; wd at Fort Wagner; died after amputation of leg, 7/22/63, Charleston, SC
Jeremiah Marston - Co. F, 12th NH; wd/killed 6/3/64, Cold Harbor, VA
John C. Mason - Co. G, 15th NH; died 8/3/63 Sandusky, OH, on way home due to sickness
John B. Merrill - Co. F, 12th NH; KIA Chancellorsville, 5/3/63
George F. Meserve - Co. F, 12th NH; captured at Petersburg 5/16/64; died in Andersonville Prison
James D. Meserve - Co. B, 7th NH; killed at Fort Wagner, 7/18/63
George H. Reynolds - Co. F, 12th NH; KIA Chancellorsville, 5/3/63
Isaiah Swain - Co. G, 15th NH; sick on return home, died at Mound City, IL, 8/5/63
Daniel P. Tilton - Co. G, 7th NH; captured at Olustee, FL; died at Andersonville, 7/26/64
William H.H. Watson - 14th NH; died of fever 5/30/64, New Orleans
Hazen W. Willey - Co. G, 7th NH; wnd at Fort Wagner 7/18/63 and captured; died in Charleston, SC, 7/20 or 7/21
George Winkley - Co. F, 12th NH; died at Falmouth, VA, 5/24/63, of disease
Enoch M. Young - Co. G, 15th NH; died at New Orleans, 6/2/63, from exhaustion/sickness
THE UNION IN THE CIVIL WAR, BUT DID NOT
RETURN; WHOSE SAD PORTION WAS A SOLDIER'S
DEATH AND AN OBSCURE SOUTHERN GRAVE.
CAPT. ASA W. BARTLETT Camp No. 39, S. of V.
History of Pittsfield, N.H. in the Great Rebellion on [Internet Archive], for excellent biographies of all the men who served from Pittsfield, including those engraved on the above memorial.
The Sons of (Union) Veterans Camp No. 39 was named for Asa W. Bartlett, who was captain of Co. C, 12th NH Infantry (prev 2nd Lieut of Co. G, and 1st Lt of Co. K). He was author of the History of the Twelfth NH Regiment. Camp information, such as charter date, is not known at this time.