[5] Described as a "powerful orator",[5] and a "steady, consistent, honourable man"[18] who claimed to "always put the interests of my country and cause of reform first"[17] he is credited with 20 recorded contributions in Parliament during his terms of office.

[18] On 20 February 1833, Oswald was appointed with Sir Robert Peel and others to a parliamentary select committee to classify and prepare abstracts for petitions presented to the house.

[20] In February the following year, he was appointed to another select committee to scrutinise the education, practice and usage of the medical profession in the United Kingdom.

In 1835, he was appointed to the acting committee for the management of the affairs of the Radical Whig Association, formed to protect the interests during a surge in conservative activity.

Originally erected in Sandyford Place, off Sauchiehall Street, it was moved to the north-east corner of George Square in 1875, after the council were petitioned by his great-nephew, Richard Alexander Oswald.

It had long been felt by Oswald's friends and family that he should be accorded the same honour as his political opponent Robert Peel, whose monument had been erected in George Square in 1859.