By the time they left the venue, now part of the Mitchell Library, the former members of the National Party of Scotland and the Scottish Party were joined together. The Scottish National Party was born, and they toasted the birth at a reception in the Ca'doro Restaurant.
The Glasgow Herald reported that the party's new constitution said the object of the new SNP was "self-government for Scotland on a basis which will enable Scotland, as a partner in the British Empire with the same status as England, to develop its national life to the fullest advantage".
The report also referred to the tensions caused by the merger of two parties with very different philosophical origins.
"Any differences that might still exist between the members of the former parties were differences arising from point of view or particular environment, and did not affect the one quest on which they were all centred," it said.
The article added that there "had been a disposition to sink all minor personal questions and to concentrate on the task of working out a programme of national reconstruction".
It added: "They believed that they had not only to convince the people of Scotland of the need of self-government, but they had to present them with a practical programme of reconstruction."
There were certainly questions to sink. The NPS, founded by John MacCormick in 1928, had as a central figure the remarkable radical Robert Bontine Cunningham Graham, the former Liberal MP and avowed socialist who had founded the Scottish Labour Party with Keir Hardie.
He became joint president of the SNP alongside the Duke of Montrose, whose Scottish Party could fairly have been described as "Tartan Tories", so there were tensions from the start.
Then, as now, the backdrop was economic depression. Next to the report in the Glasgow Herald that day were the announcement by Ghandi that he was ending the campaign of civil resistance in India, and a report on a speech in Edinburgh by Sir William Beveridge on whether Britain needed its own New Deal.
Historian Dr Peter Lynch, author of a history of the SNP, said of those early founders: "If you had said to them it would take 80 years to get to where we are today I'm sure they would have been stunned and disillusioned.
"Indeed you could probably say the same for those who were involved in other breakthroughs … yet here we are approaching the possible endgame because of what happened in Glasgow 80 years ago."
Professor James Mitchell, of Edinburgh University, said coming together in 1934 involved "almost entirely different entities, a bizarre, fractious collection of individuals."
He added: "Much to most people's surprise they have evolved from a group on the fringe of the fringe, a loose collection of individuals, to the most successful party in Scotland today."
Ahead of the party conference next weekend First Minister and SNP leader Alex Salmond called the 80th anniversary a time to look back on "our many achievements" and becoming "central to Scotland's national life as the party of government."
He said "Even more importantly it is a look-out point to the future, as we approach the referendum and the historic opportunity to achieve independence and equality for Scotland."