Below is information I put together from this board, the Arkansas, Louisiana boards and the Kaufman County board. Tivy was a lieutenant in the 31st. Hardeman's regiment and the 31st were different organizations. You can skip the first and last if your not interested in Tivy.

A Short History of Joseph A. Tivy

Captain Joseph A. Tivy was from Toranto, Canada, born February 25, 1818. He was educated as a surveyor in New York State and came to Texas in 1837. He started out as a chainman and was soon doing his own surveying. Working from San Antonio, he did a lot of the original survey work in Kerr County and along the Guadalupe River. As the Indians were a problem, he also aligned himself with Captain Hayes Ranger Company and rode along on many of their chasing of the Comanche. In 1849 he got a bad case of gold fever, and went to California. He was a miner, a hotel owner, and a legislator. Tiring of that he started back to Texas in 1857, but spent a year in New Mexico. He returned to Karnes County, Texas in 1859.

He joined the 31st Texas Cavalry Regiment which was organized in the Dallas Ft Worth area but which also pulled men from Karnes and Fannin Counties. In May, 1862, and led by Col. Trezevant C. Hawpe, a Dallas businessman, the 31st started moving north. It is at Ft. Washita in August 1862 that the 31st completed its organization. It’s first battles and training were in the Indian Territories. Joseph Tivy was elected 1st Lt of Company A because of his age and military experience. (Captain Hayes ran a rough bunch of Rangers and not a lot of military training.) With the 31st organized it was added to the 22nd and 34th Texas Cavalry Regiments into a new Brigade which is where the name problems begin. There is some problem with the correct name and brigade, but the unit was the 31st Texas Cavalry Regiment, CSA (Hawpe’s Regiment).
All three regiments were in the area of northeastern Oklahoma (Ft. Gibson) on the eastern border with Arkansas (Ft. Smith) in July and August 1862. It seems the 31st was sick and going through that early adjustment period every new regiments went through while their immunities build up to the rigors of camp life. In early August, the 34th, on a reconnaissance mission out of Ft. Gibson, participated in a skirmish at Park Hill with Pin Indians who had sided with the Union. In late August, the brigade stopped at Camp Osage, while the measles epidemic raged through the troops and put 88 men in the hospital.
In early September, the 22nd and 34th Cavalries moved to Camp Caudle near Bentonville, Arkansas, five miles from the Missouri state line and joined Cooper’s Indian Brigade. There was a typhoid outbreak at this time at Camp Myrick near McDonald, Missouri. Part of the 34th and the 31st rode north to attack that camp of the 2nd Indian Home Guard (Union- composed of Osage warriors with a fierce reputation). The Confederates captured wagons and cattle and killed between 60 and 120 men, according to one report.
They continued to move toward Newtonia, Missouri, where the 22nd performed picket duty. On Sept. 27, Col. Cooper sent the 31st and an Indian battalion to Newtonia as an advanced post. The 22nd was ordered to Granby and the 34th marched for Granby to relieve the 22nd on the morning of Sept. 30, the day of the battle of Newtonia. The Union troops withdrew from Newtonia and the 31st was put in charge of securing Newtonia. All three regiments ended up fighting at Newtonia, mostly dismounted. Although the Confederates did well at Newtonia, on October 4th they were forced to withdraw when more Union troops arrived. This was the last of Confederate troops in Missouri for the war.
Though I could go on for a long time concerning the three regiments and their conduct of the war in Louisiana, Arkansas and the Indian Territories, it is enough to say they conducted themselves as did all of our Texas Cavalry. You can get bits & pieces on the 31st when it was a part of reserve units assigned to back up the battle of Yellow Bayou in Louisiana. Some of Anne Bailey's books about Parson's Brigade give little bits & pieces on the 31st."Between the Enemy and Texas: Pasrson's Texas Cavalry in the Civil War" & "In the Saddle With the Texans". The 31st was involved in several battles including Poison Springs, Massard’s Prairie, Sterling Plantation and Newtonia. Other possible battles include Mansfield, Ft DeRussy, Cabin Creek and Prairie Grove.
In February, 1865, Lt. Col. George W. Guess was placed in command of the 31st Texas Cavalry. The dismounted regiment was marched to Rusk, Texas and consolidated with Brig. Gen. Hamilton P. Bee's brigade. In May 1865, Brig. Gen. Bee's Brigade including Lt. Col. George W. Guess' 31st Texas Cavalry Regiment were disbanded.

From all of this I have not discovered anything, except that Joseph A. Tivy was in the 31st Texas Cavalry from the National Park Service Rosters. After the war he returned as a Captain probably to the Karnes County area. He arrived in Kerrville in 1872 to live on property he had obtained in 1842. This land was 640 acres that had been the Thomas Hand military grant. He was in several businesses in Kerrsville and must have been successful at all. He married Ella Lossee Koch on January 7, 1875. In 1877 he was on the County Court. Along about this time Kerrsville became Kerrville. In August 1883 he was a member of the Kerrville School Association and accepted along with others a plot of land for a school given by R.H. Burney Jr. It was needed because the school was being bumped from building to building. The city incorporated in 1889 and Tivy was the Mayor for 7 months until an election could be held. Tivy soon announced he would give some land to the school. On August 16, 1890 he gave 16 ½ acres to the school and 23 city blocks to the city to pay for maintenance on the school. He also donated a city block for a park. All in all he gave over 100 acres to the school system. He passed away July 5, 1892. He asked to be buried on a Hill of his land next to his wife. This became Tivy Mountain. It is told that he paid a young Chester Nemitz one dollar to bury a family cat at the Family plot. I am told there is a stone for a feline. Question about the deed for the cemetery occurred when the property passed from one family member to another and then no one could find out what happened to the deed.