Jack is the son of a Mr. Robert Ferguson. When he was a boy an accident left him permanently injured, meaning while he can walk, he is partially crippled. At fifteen years old, his father remained after his mothers death, to a Peruvian woman and has since had another child.
Consumed with envy towards his younger half brother, and the attention his father gave him, Jack attempted to murder him using a South American poisoned blow pipe, which belonged to his stepmother. His stepmother catching him, beat the boy and managed to suck the poison out of her infants neck.
However when she was caught doing this, she could not bring herself to tell her husband what his son had done, and instead retired to her room where she hid, she also soon became ill from the poison she had ingested. As such Robert Ferguson went to visit Sherlock Holmes. Holmes quickly realized what was going on, and by secretly watching Jack's actions around his brother realized what must have happened.
As such he broke the news to Mr. Ferguson, who was overcome with grief at the discovery. He was left to deal with Jack himself, with Holmes recommended sending the boy away for a year at sea, to straighten out his conflicted and envious mind.