I've attempted to follow ATQ Stewart's amd Mary McNeill's references and would urge caution in accepting what Stewart says - namely that "somewhere along the road Hope stuck up another air, a popular song called the 'Swinish Multitude.'" This is because, in Hopes memoirs, - of which I am giving my memory - he denies an account (by the Rev Dr McCartney who was a Yeomanry Commander at the Battle of Antrim) that the rebels played "The Lass of Richmond Hill" on their way to Antrim because they had no instruments. He does say that they sang the Marseillaise and that he, thinking the air a dreary one (by the way they probably sang the words to this air given in Paddy's Resource, a songbook of 1795) struck up (and I think I quote) "a merry Irish song" - he does not mention The Lass of Richmond Hill, which seems odd if he used its air. Charles Teeling in his Memoirs states only that the Marseillaise was sung. Still further confusion is spread by the inclusion of another set of verses called "The Placeman and Pensioner's Address to the Swinish Multitude" in RR Madden: Literary Remains of the United Irishmen and by the fact that Madden who was also Hope's biographer included the Marseillaise in this book and said that "This song was sung by J Hope going to Antrim, and all the people joined in the chorus."
Having helped everyone else share my confusion, I'll conclude, inconclusively.