Why does Holmes make the following statement in The Adventure of the Speckled Band?

Dr. Roylott is poisoned by the snake he used to kill Julia. Holmes, in this question, refers to the fictional character Sherlock Holmes. This question relates to the Adventure of the Speckled Band, which is a short story by Arthur Conan Doyle.

This particular short story appears in The Adventures of Sherlock Holmes, which is a collection of twelve short stories. The Adventure of the Speckled Band is the eight to appear in the collection, and it is defined as a locked room mystery. In a later interview, Doyle stated that he believed this was his best story about Sherlock Holmes.