The unit was also known as Beach’s Battery. During the battle of Gettysburg, it served as a member of Ransom’s Brigade in the Artillery Reserve, Army of the Potomac. The unit was commanded by Lieutenant Evan Thomas (1843-1873), born in Georgetown, District of Columbia. Thomas was killed fighting Modoc Indians. Thomas commanded 112 men (& six Napoleons) at Gettysburg and among them only 1 man was killed in action with 17 wounded.
The Battery C, 4th U.S. Artillery - US Regulars Tablet is located directly across from the gigantic Pennsylvania State Memorial/Monument. The monolith is is on Hancock Avenue, on the left when traveling north, on Cemetery Ridge. Traffic is crazy-ridiculous here. There is an abundance of parking. I would allow up to two hours to seriously tour this area as this is the most concentrated area of monuments, markers, memorials and artillery. Two cannons flank the monument. The cannon to the left of the monument is a 12-pounder Napoleon manufactured at the Alger Foundry, No. 56, and the cannon to the right of the monument is also a 12-pounder Napoleon manufactured at the Hooper Foundry, No. 8. While the monument faces the PA monument and Hancock Avenue in a northeasterly directions, the Two Napoleons face southwest, toward enemy lines concentrated over a mile away at Seminary Ridge along Southwest Confederate Avenue. Be sure to keep vehicles off the grass or you will be ticketed by park police. I visited this monument on the late afternoon of Thursday, July 5, 2012. I was at an elevation of 571 feet, ASL. I used a Canon PowerShot 14.1 Megapixel, SX210 IS digital camera for the photos.
The monument work was done under the direction of the Gettysburg National Park Commission (established by the United States Department of War), after they took over the administration of the park from the Gettysburg Battlefield Memorial Association (whose funds had expired) on March 3, 1893, and whose stewardship was then transferred to the National Park Service in 1933). SOURCE
Draw the Sword, with descriptive help from the NPS site, offers the following description: One of 45 monuments erected to units of the United States regular army on the battlefield. A red polished Jonesboro granite monolith that is set upon a concrete foundation with a descriptive 3’6'x3’7' bronze tablet with the coat of arms of the United States in bronze. At the top of the tablet are the crossed cannon of the artillery, just above the inscription. The inscription on this tablet reads:
coa.gif)
Army of the Potomac
Artillery Reserve
First Regular Brigade
Battery C Fourth U.S. Artillery
Six 12 pounders
Lieut. Evan Thomas commanding
July 2 Arrived and took position on crest of hill near General Meade's Headquarters on the left of the Second Corps and was actively engaged in repelling the attack of the Confederates.
July 3 In position near the left of the Second Corps line.
Casualties. Killed 1 man. Wounded 1 officer and 16 men.
There are hundreds of non-sculpted monumentation for the various Confederate States & Union units which fought at Gettysburg. There are about 10 different variations of tablets, markers & monoliths by my reckoning. Six designs represent brigade (2), division (2), corps (2), & army headquarters (2), each different in a subtle way so as to distinguish between armies. Battalion/battery/advance position markers & regimental monuments for U.S. Regulars & Confederate have their own distinct design (2), bringing the total to 10 designs at the battlefield. The bronze tablets were created by Albert Russell & Sons Co. of Newburyport, Mass. The granite bases which accompany the various tablets were created by the Van Amringe Company from Boston, Mass. The cast iron tablets were manufactured by Calvin Gilbert. The 1910 Gettysburg Commission report lists the awarded contracts to these companies (not Gilbert) for the tablets. All of these tablets were designed by architect Colonel Emmor Bradley Cope (July 23, 1834 - May 28, 1927). He designed pretty much every tablet for both the Union & Rebel armies, each one distinct, w/ several different varieties. He is buried in Evergreen Cemetery 
in Gettysburg, as well he should be as this park and most of the things seen here today were designed by him and as such, are his legacy. These monuments were erected just after the turn of the century during the first & beginning of the second decade of the 20th century. Each one has since been preserved or restored at least twice since the turn of the 21st century. The plaques & tablets were erected by the Gettysburg Park Commission (established by the War Dept.). The Gettysburg Park Commission is also referred to as the Gettysburg National Military Park Commission or the Gettysburg National Park Commission, to clear up any confusions, especially my own.
On October 1, 1898, the Gettysburg National Park Commission in a letter to the Secretary of War set gave recommendations for continuing the task of organizing & progressing the work of the Gettysburg National Military Park. Every November they wrote their annual report which outlined the work of the GNPC for that year. The following is an excerpt from that report relevant to this waymark. The link at the end of the paragraph will take you to the entire report. The method of marking the positions of troops on this field, as approved by the War Department, is to place the principal tablet or monument of each command at the position occupied by the command in the main line of battle, and to mark the several important positions subsequently reached by each command in the course of the battle by subordinate and ancillary tablets, with appropriate brief inscriptions giving interesting details and occurrences and noting the day and hour as nearly as possible. SOURCE
Most of the Commission reports have been digitized and can be found HERE. The initial 1893 report up to & including 1921 can be found here. 1922 to 1926 are missing & have yet to be discovered. The years 1927 to 1933 were discovered in 1996 and are also included. To my knowledge this is the most comprehensive list of documents that illustrated the development and formation of the park.
Information about these specific types of monuments:
UNITED STATES REGULARS TABLETS
Forty-two monuments honor units of the regular army to fight at Gettysburg. Other sources have the amount at forty-four tablets while I have personally counted 48 of these monuments. These regiments and batteries were designated as United States Regulars as opposed to the state volunteer forces. These polished granite monuments with bronze plaques affixed to the front were fabricated by the Van Amringe Granite Company, of Boston and authorized in 1907. They were completed in the autumn of 1908. Each consists of Jonesboro granite, 24 by 50 inches and 7 feet high, set upon concrete foundations, and upon each is fastened a descriptive bronze tablet and the coat of arms of the United States. are similar in appearance to and often mistaken for headquarters, since they have the same curved-and-scrolled top on the bronze tablet as corps and army headquarters. The difference is that instead of being square, the stone comes to a peak in the center on the U.S. Regulars monuments, with a brass Great Seal of the United States centered within the peak. SOURCE & SOURCE
The Battery C, 4th U.S. Artillery - US Regulars Tablet is a contributing feature to the Gettysburg Nat'l Military Park H.D. which is nationally significant under NR Criteria A, B, C & D. Areas of Significance: Military, Politics/Gov't, Landscape Architecture, Conservation, Archeology-Historic. Period of Significance: 1863-1938. The monument is designated as structure no. MN676-B.
From the Nomination Form:
1 of 45 Civil War US Regulars Tablets in Park. Locates position occupied by Thomas Regular Battery during Battle of Gettysburg.
Short Physical Description:
Red granite monolith w/rough-hewn sides & back, 4'2"x2', 7" high. Gable top. Bronze inscription tablet, 3'6"x3'7", mounted on polished face. Bronze seal of US Coat of Arms, 1' in diameter, on face above tablet. Located west side of South Hancock Avenue near Pennsylvania Monument.
Long Physical Description:
N/A
My Sources
1. NRHP Nomination Form
2. Stone Sentinels
3. Virtual Gettysburg
4. Draw the Sword
5. Historical Marker Database