The first piece of evidence for poison is the one which gives the story its name. Ferguson suspected his wife of being a vampire because he saw her beside his son's cot with blood on her lips. Holmes realized that this could indicate not that she had bitten the child but that she had sucked poison from a wound to save him.
Holmes then saw the South American weapons fixed on the wall, including a quiver from which the arrows had been taken. He therefore surmised that the child had been pricked with an arrow dipped in curare or some similar venom.
Finally, Ferguson's dog has been ill, with an obscure sickness that puzzles the veterinarian. Holmes realized that the poisoner would want to ascertain that the poison worked properly and would therefore be likely to test it on an animal, such as the dog.
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