He studied law with Thomas H. Crawford, and in 1825 moved to Indiana, seeking a place to recruit his health, and with the hope of finding a favorable location to follow his profession.
He gained admission to the bar at Greensburg, Indiana, on September 26, 1825, and entered the practice of law there, "in a short time becoming a leader in his profession".
[2] Davison was elected from the Second district in 1852, defeating over Charles Dewey, and taking his seat on the Supreme bench of Indiana on January 3, 1853.
He was re-elected in the fall of 1858, and continued in office until January 2, 1865, a total of twelve years.
[2] Davison died in Greensburg at the age of 70, six years after retiring from the Supreme bench.