While studying medicine at the University of Edinburgh under William Cullen (1710-1790) he became a Freemason and was initiated in the Lodge Holyrood House (Saint Luke), No.44 in 1763.
The need for accommodation of insane people soon became evident and an asylum to house lunatics was constructed in 1782 but remained vacant until 1794 because of financial problems.
When the asylum opened for patients, Arnold, James Vaughn, and later Robert Bree were appointed physicians.
His son, Thomas Graham Arnold received his Medicinae Doctor (MD) at Cambridge University in 1795 and appointed physician to the asylum that same year serving with his father until 1800.
Another son, William Withering Arnold, received his MD at Cambridge and served on the asylum staff from 1800 to 1840.
Arnold published a two-volume work titled Observations on the Nature, Kinds, Causes and Prevention of Insanity, the first volume appearing in 1782 and the second in 1806.
A set of rules for patients’ treatment included firm management, temperance in food and drink, sleep, exercise, regulation of passions, rational views of God and religion, and attention to the imagination.
He described notional insanity as "that state of mind in which a person sees, hears or otherwise perceives external objects as they really exist as objects of sense, yet conceives such notions of powers, properties … as often grossly erroneous or unreasonable to the common sense of the sober and judicious import of mankind."