Exactly the last 1/9th of a burning cigarette. The part of the cigarette that is often the least pleasant and least satisfying remainder of a cigarette. When someone cannot afford to buy their own pack of cigarettes but said person's friend is not particularly inclined to give said person a cigarette seeing as said friend has already given said person countless cigarettes in the past. Said person may allow said friend to smoke the last 1/9th of of said persons cigarette seeing as said person would rather not take that drag anyway.
"Who wants the logan-drag"
"I gave him the logan-drag"
"Can I take the logan-drag"
-Can I have a stogey bro?"
~No Logan, I am sick of bumming you cigarettes but you can have the logan drag"