James T. Kirk told Sheme about Bredell's plot to destroy the Federation by means of his Big Bang Weapon - a plan that, if it were successful, would lead to the deaths of many billions of innocents. Kirk told to Sheme that Earth was the first target Bredell intended to destroy with this weapon and he convinced Sheme to turn on Bredell and help prevent these catastrophes. Kirk's exact words were:
"Do you want to see a hundred billion people die? Do you want to see the survivors of the Federation destroy Vardaine?"
The quote is interesting because it can be interpreted to suggest that in 2269, the total population of the United Federation of Planets, may have been approximately 100 billion people.
In their discussion, Menao Sheme mentioned to Captain Kirk that Ies Bredell had a son who had visited Espoir station some months before, whose name was Vas Bredell. On this occasion, Sheme told Kirk, the elder Bredell had become drunk and Sheme heard him boast to his son about the power of the Big Bang Weapon. There is no indication of whether Kirk had already known of Vas Bredell.
Kirk was able to secure Sheme's cooperation by relating the good memories he had of his father, that the man had a sense of compassion and honor that were not shared by Vardaine society in general.