How did Holmes establish Stapleton's motive for the committed and intended crime? chapter 13

In Chapter 13, Holmes begins to lay out a plan, but his attention is struck by the line of portraits on the opposite wall. He observes that Hugo Baskerville looks quite meek in his portrait, and Sir Henry adds that the canvas is dated 1647. After dinner, Holmes brings Watson to the portrait and leads the latter to recognize that the picture resembles Stapleton, if one ignores the hair and focuses solely on the facial shape. They have finally discovered the missing link of their mystery: Stapleton is a Baskerville!