An appeal to the publick of New-York Forasmuch as a news-paper has appeared in the city of New-York, on the 16th of this instant February, entitled, Weyman's New-York gazette; in which, and by which, the subscriber apprehending himself unjustly and ingratefully dealt by, he is obliged to beg leave to lay the following brief state of the affairs between said Weyman and himself, before the tribunal of an impartial publick