The phrase "a long discourse" is correct and usable in written English.
It can be used to describe an extended discussion or conversation on a particular topic.
Example: "The professor delivered a long discourse on the implications of climate change during the lecture."
Alternatives: "an extensive discussion" or "a lengthy dialogue."
There was no subject that did not merit a long discourse.
What they played on Thursday were chunks of a long discourse, all of a piece.
Secretary of State Condoleezza Rice gave a long discourse about not letting Russia off the hook.
Alec Baldwin indulged a few brief interviews before disappearing, but his brother Billy Baldwin stopped to provide a long discourse on his opinions of both teams.
A shareholder asks a real stemwinder of a question, which began with a long discourse about Fannie Mae and Freddie Mac.
Mr. Santorum did not miss a beat, launching into a long discourse on how single-parent homes spawn poverty and government intervention.
But maybe if somebody would just let her talk to us about all this for a while, settle in for a good long discourse about women's options and criminal law and the moment when life begins, then the bellicose rhetoric of her final weeks on the campaign trail might yield, for an hour or so, to something the governor of Alaska sounds as if she truly believes.
Instead, he has a tendency to answer emotion with explanation, often launching into a long, rambling discourse laden with facts and figures.
May I suggest that anthropology and its related research fields, including cultural geography, have been strengthened by a long historical discourse about moral relativism?
When Mark began to lecture him on scriptural inerrancy, Jack interrupted to give a long, rambling discourse on early church history, the Greek philosophical tradition versus the Hebrew, and the problems often faced by Protestant theologians.
The document contains an explanation of the sect's religious and moral ideals, a description of its admission ceremony, a long catechetical discourse on its mystical doctrine of the primordial spirits of truth and perversity, organizational and disciplinary statutes, and a final hymn or psalm praising obedience and setting forth the sacred seasons.
