1. The Strange Whistle: Holmes notices a peculiar whistling sound coming from the room next to Helen Stoner's bedroom. This leads him to suspect a connection between the whistle and the death of Helen's sister.
2. The Discoloration on the Wall: Holmes observes a dark discoloration on the wall near the ventilation shaft. He theorizes that this discoloration is caused by some sort of corrosive substance, possibly a poisonous gas.
3. The Ventilation Shaft: Holmes discovers a peculiar ventilation shaft leading from Helen's bedroom to the room next door. This becomes a key point of interest, as it provides a potential means for something to be introduced into Helen's room.
4. The Indian Snake: Holmes learns that the previous tenant of the room next door was a native Indian, who owned a collection of venomous Indian snakes. This knowledge, combined with Helen's fear of snakes, leads him to suspect that the snake is the weapon used in both murders.
5. The Escape Route: Holmes meticulously examines the room next door, discovering a hidden door leading to the outside. He theorizes that this door was used as an escape route for the snake after it had done its deadly work.
6. The Time of Death: Holmes studies the time of death of both sisters, noting that the attacks occur at night, shortly after Helen and her sister went to sleep. This helps him to narrow down the timeframe of the killer's actions.
7. The Yellow Eyes: During his observation of the room next door, Holmes sees a pair of yellow eyes peering from the ventilation shaft. This confirms his suspicion that a snake is present.
8. The Speckled Band: The final piece of the puzzle is the "speckled band" itself. Holmes carefully examines the victim's room and finds a small, speckled, poisonous snake lurking behind the furniture. This snake, along with the evidence he has gathered, allows him to definitively identify the killer and the weapon used.
9. The Murderer's Identity: Through the combination of these clues, Holmes is able to deduce that the killer is Dr. Roylott, Helen's stepfather, and the weapon is the poisonous Indian snake that he uses to attack the women through the ventilation shaft.
10. The Motives: Holmes also determines that Dr. Roylott's motives are financial. He stands to inherit a significant sum of money upon the deaths of both Helen and her sister.
By carefully observing, analyzing, and interpreting these clues, Sherlock Holmes unravels the mystery of the Speckled Band, bringing justice for the victims and exposing the true nature of the killer.