How had Kit determined that Mr. Armthwaite was also one of the conspirators ?

When Mr. Armthwaite went to ring the bell, Kit realized that he was using it to signal Sir Phillip.

“You know,” she said. “Stand away from that bell. That’s better. Keep quite still. Pete, lock the door and put the key in your pocket. Don’t stand gaping! This man’s as bad as the rest of them. Why were you going to ring the bell?” she snapped at him, jabbing the air with her pistol.

“But not the letters we want written, or sent to the right people. It’s Sir Philip Morton you mean to warn— and goodness knows what you’d do with us, to keep us quiet.” She spoke to me then, without taking her eyes off the old gentleman. “We’ve been unlucky, Pete. We’ve picked on another of that crew. We’d better get out of here.”