Waterhouse spends much of the next week commuting to London for meetings at the Broadway Buildings. Whenever civilian authorities are going to be present at a meeting—especially civilians with expensive sounding accents—Colonel Chattan always shows up, and before the meeting starts, always finds some frightfully cheerful and oblique way to tell Waterhouse to keep his trap shut unless someone asks a math question. Waterhouse is not offended. He prefers it, actually, because it leaves his mind free to work on important things. During their last meeting at the Broadway Buildings, Waterhouse proved a theorem.