The Company E, 1st United States Sharpshooters and Companies F & G, 2nd United States Sharpshooters served as a member of Ward’s Brigade in Birney’s Division of the Third Corps, Army of the Potomac, a Fighting 300 Regiment. The unit was commanded by Major Homer R. Stoughton (1836-1902), a resident of Randolph Vermont who enlisted on September 25, 1861 as a Captain. After the War Homer lived in Oberlin, Ohio. He is buried at Elmwood Cemetery, Barre (Washington County), Vermont. Under Homer's command, the sharpshooter had 200 men engaged at Gettysburg and among them, 5 were killed, 23 were wounded and 15 went missing.
The New Hampshire Sharpshooters Monument is located on the west or left side of Hancock Avenue if traveling north, just north of the Pennsylvania State Monument, which is located on the east or right side of the road and both monuments being south of Gettysburg. The Pleasanton Avenue intersection is just 87 feet north of this position. The front inscription faces the east, so you would be facing the west to read it. This location is a hot-bed of activity and one of the best examples of a hands-on history lesson of the Civil War one could hope to find. All along both sides of the road are these types of tablets, memorials, monuments, sculptures, and all manner of cannons, rifles and guns. 
Parking is available at enlarged shoulder cutouts on the right side of the road, directly across from the various monuments. Be sure to keep vehicles off the grass or you will be ticketed by park police. I visited this monument on Thursday, July 5, 2012 at approximately 6:00 P.M. I was at an elevation of 575 feet, ASL. I used a Canon PowerShot 14.1 Megapixel, SX210 IS digital camera for the photos.
The Draw the Sword site helped out by the NPS narrative and the SIRIS site offers the following description: Rectangular sculpture in a horizontal composition with a relief of a uniformed infantry laying face down, propped up on his elbows and firing his musket. The sculpture and base have rough-hewn surfaces. The monument cost $700.00, of which $500.00 was paid by the state of New Hampshire. Monument is a two-part stepped granite shaft with excised inscription on the lower part and a reclining infantryman in bas-relief on the upper part. It is set on a 10.4×3.8 foot rough cut stone base. Flanking markers are 1.4x.6 foot with a polished and smooth finish and chamfered edges.
The monument was dedicated on June 2, 1886 by the State of New Hampshire. The monument is composed of Concord granite and has the following dimensions: The sculpture is approximately 5 feet 1 inch x 8 feet 10 inches x 2 feet 2 inches, the base is approximately 1 foot 3 inches x 10 feet 4 inches x 3 feet 8 inches. Thomas Naun was contracted to work on the monument. I have no idea who sculpted or fabricated the monument.
Through an extensive literature review, I located a first hand account of this monument's dedication in 1886 in a book called Berdan's United States sharpshooters in the Army of the Potomac, 1861-1865. The book was written in 1892 by Charles Augustus Stevens and published out of St. Paul Minnesota. The book contains an 1886 picture of the monument taken at the dedication on July 2, 1886. Below is an excerpt from page 546 of that book concerning this monument:
There is an inscription on the lower front of the monument, right under the relief art which reads:
New Hampshire.
Cos. E, 1st Reg, F & G, 2nd Reg.
Berdan's U.S. Sharpshooters.
2d Brig, 1st Div, 3d Corps.
July 3, 1863.
The New Hampshire Sharpshooters Monument is a contributing feature to the Gettysburg National Military Park Historic District which is nationally significant under NR Criteria A, B, C & D. Areas of Significance: Military, Politics/Government, Landscape Architecture, Conservation, Archeology-Historic. Period of Significance: 1863-1938. The original National Register Nomination was approved by the Keeper March 19, 1975. An update to this nomination was approved by the Keeper on January 23, 2004. The monument is identified as structure number MN262-B.
From the Nomination Form:
1 of 9 Mn to Berdan's sharpshooters of the GBMA Era (1863 - 1895). Indicates position of Co. E, 1st U.S. Sharpshooters of NH, July 3, 1863. Located on Hancock Avenue near intersection of Pleasonton Avenue. LF marker S of Mn, RF marker N of Mn, N side of Pleasonton Ave.
Short Physical Description:
Mn w/ 2 flanking markers. Base 10'4"x3'8" rough-cut stone, 2 part stepped shaft w/ exncised inscription-lower, reclining infantryman bas- relief-upper. RF&LF 1'4"x6"x1'3"H, chamfered edges, polished & smooth finish.
Long Physical Description:
Monument that has two flanking markers. Monument is a two-part stepped granite shaft with excised inscription on the lower part and a reclining infantryman in bas-relief on the upper part. It is set on a 10.4x3.8 foot rough cut stone base. Flanking markers are 1.4x.6 foot with a polished and smooth finish and chamfered edges. Located on Hancock Avenue near the intersection of Pleasonton Avenue.
My Sources
1.
NRHP Nomination Form
2.
SIRIS
3.
Stone Sentinels
4.
Virtual Gettysburg
5.
Draw the Sword
6.
Historical Marker Database