It is typical of Arthur Conan Doyle's Sherlock Holmes stories that the great detective explains his whole line of reasoning--almost invariably to his friend and biographer Dr. Watson--near the very end of the story. This is understandable, since the usual pattern of these stories is to describe what Holmes says and does through the eyes and ears of Watson, but not to tell what Holmes might be thinking. Watson himself usually sees the same things as Holmes, since they are both together at the scene, but Watson is not capable of making the same kinds of deductions as his friend. Since the reader is getting the whole narrative from Watson, the reader is challenged to make his own deductions from the evidence. These deductions may be correct or incorrect, or partially correct and partially incorrect, but the reader cannot be sure about his suspicions or conclusions until he reaches the end of the story. In "The Adventure of the Speckled Band," Sherlock Holmes explains all of his observations and deductions in detail as follows:
"The presence of the gipsies, and the use of the word ‘band,’ which was used by the poor girl, no doubt, to explain the appearance which she had caught a hurried glimpse of by the light of her match, were sufficient to put me upon an entirely wrong scent. I can only claim the merit that I instantly reconsidered my position when, however, it became clear to me that whatever danger threatened an occupant of the room could not come either from the window or the door. My attention was speedily drawn, as I have already remarked to you, to this ventilator, and to the bell-rope which hung down to the bed. The discovery that this was a dummy, and that the bed was clamped to the floor, instantly gave rise to the suspicion that the rope was there as a bridge for something passing through the hole and coming to the bed. The idea of a snake instantly occurred to me, and when I coupled it with my knowledge that the doctor was furnished with a supply of creatures from India, I felt that I was probably on the right track. The idea of using a form of poison which could not possibly be discovered by any chemical test was just such a one as would occur to a clever and ruthless man who had had an Eastern training....It would be a sharp-eyed coroner, indeed, who could distinguish the two little dark punctures which would show where the poison fangs had done their work. Then I thought of the whistle. Of course he must recall the snake before the morning light revealed it to the victim. He had trained it, probably by the use of the milk which we saw, to return to him when summoned. He would put it through this ventilator at the hour that he thought best, with the certainty that it would crawl down the rope and land on the bed. It might or might not bite the occupant, perhaps she might escape every night for a week, but sooner or later she must fall a victim.
"An inspection of his chair showed me that he had been in the habit of standing on it, which of course would be necessary in order that he should reach the ventilator. The sight of the safe, the saucer of milk, and the loop of whipcord were enough to finally dispel any doubts which may have remained. The metallic clang heard by Miss Stoner was obviously caused by her stepfather hastily closing the door of his safe upon its terrible occupant.
The presence of the gipsies was intended to put the reader as well as Sherlock Holmes "upon an entirely wrong scent." It was only too obvious from the beginning that the terrible Dr. Roylott must be the villain in the piece. The gipsies make it just vaguely possible that someone other than Roylott was responsible for Julia's death and is planning to murder her sister Helen. But even if the gipsies are directly responsible for killing Julia, that still doesn't exonerate Dr. Roylott. He is on exceptionally friendly terms with this "band" of gipsies who camp on his estate. He could have paid them to kill Julia, and he could be paying them to kill Helen.
It is only when Sherlock Holmes, accompanied by his faithful friend Dr. Watson, inspects the room in which Helen is now sleeping, along with the room directly next door which is occupied by her stepfather, that he is able to put the pieces of the puzzle together. In Helen's room he first notices the ventilator and the bell-rope. He quickly discovers that the bell-rope is a dummy, which suggests that it is there for some sinister purpose. Then when he finds that the bed has been bolted to the floor so that it cannot be moved to any other part of the room, the idea of a snake, as he says, occurs to him instantly. Holmes is expecting to find evidence of the existence of a poisonous snake even before he enters Dr. Roylott's room. A man with Roylott's scientific background and knowledge of Indian animals could possess a snake whose venom would not be detected upon autopsy.
Then Holmes and Watson go into Dr. Roylott's room. There the detective finds clues that convince him he has solved the mystery. The four most important clues in the room are the chair, the safe, the saucer of milk, and the whipcord with a loop on the end. Holmes could see that Roylott had been standing on the chair in order to put the snake through the ventilator. Holmes assumes that Roylott keeps the snake in the safe and that the snake must be there inside it right now. The milk must have been used to train the snake to return through the ventilator, and the whipcord must have been used to handle the dangerous swamp adder.
Holmes already knew before coming down to Stoke Moran that Dr. Roylott was having financial troubles and that he was legally bound to pay either stepdaughter one-third of the income from the girls' mother's estate when either of them got married. That would have meant financial ruin for Roylott. Julia died shortly before she was to be married. Helen was not in danger for two full years--but then she became engaged to be married within a month or six weeks. It was right after Roylott learned of Helen's engagement that he found an excuse to move her into the room next to his, and she had only been occupying the room for two nights when she first heard the whistle which, as she tells Holmes, had been the herald of her sister's death.