The exposition sets up the problem for Holmes to unravel, understand and solve. In this story, it is brought to him by Miss Stoner who is newly engaged and deeply concerned about a recurrence of strange behavior at the home she shares with the stepfather, to whom her deceased mother left her daughters' share of wealth until the day they should be married. The rising action follows and includes the mad visit Roylott pays to Holmes and Watson, the inspection of the scene of the suspected crimes and Holmes' instructions to Miss Stoner. The falling action comes after the climax in which Holmes battles the snake and he and Watson hear Roylott's piercing screams. It includes entering the adjoining room occupied by Roylott and finding him dead from the adder attack. The resolution is how Holmes ends the case by capturing the snake and locking it back in the safe. The resolution is followed by an epilogue, or "afterward," in which Holmes and Watson ruminate on the case.
As [Holmes] spoke he drew the dog-whip swiftly from the dead man’s lap, and throwing the noose round the reptile’s neck he drew it from its horrid perch and, carrying it at arm’s length, threw it into the iron safe, which he closed upon it.
The Rising Action
The rising action comes when Holmes and Watson begin investigating the strange and alarming story Miss Stoner tells about her present concerns and and about the death of her newly engaged twin sister two years earlier. Her present situation bears so much resemblance to her late sister's situation, including metallic and whistling sounds and sudden abrupt building repair projects, that she turns for help to Holmes. The first step in the rising action is the threatening visit of her stepfather, Dr. Grimesby Roylott of Stoke Moran. He stands darkly in the doorway, an imposing figure, and demands in a loud voice that Holmes refrain from any interference with his family affairs. To prove his point that he is a dangerous man, he invades the room and bends a fire poker with his bare hands.
"Don’t you dare to meddle with my affairs. I know that Miss Stoner has been here. I traced her! I am a dangerous man to fall foul of! See here." He stepped swiftly forward, seized the poker, and bent it into a curve with his huge brown hands.
The rising action continues as Holmes and Watson take a train trip to and make an inspection of Stoke Moran to investigate the premises wherein Miss Stoner and Roylott live, where they are alone as no servants will stay. In the rising action at Stoke Moran, Holmes sees that the sudden structural repairs to the building are undertaken without need; that Miss Stoner's bedroom--the one Roylott has forced her into by his building construction--window cannot be breached from the outside; and that there are several disturbing features of the interior of that room, namely, a bed that can't be moved, a bell cord that rings no bell, an air vent that provides no ventilation. He also notices a saucer of milk in the room adjoining hers, although they keep no cat.
Further suspenseful rising action occurs when Holmes directs Miss Stoner to pretend she has a headache that night and retire to bed as early as she can; to signal him with a lamp in her window that she is there and alone; to gather what she needs for the night and return to her original room (despite its disheveled condition) further down the corridor.
The falling action comes after the adventure draws to a climactic close having been safely concluded, with nefarious plans thwarted, threatened people saved and the guilty disposed of (in one way or another). In this case, Holmes, sitting in a deeply dark room, listening intently, has climactically stopped the speckled band snake ("Indian swamp adder") from progressing on its murderous mission and has beaten it, turning it back upon Roylott--who had sent it through the vent from the adjoining room--where it attacks and kills Roylott.
The falling action begins when Watson gasps, "What can it mean?" and Holmes replies, "It means that it is all over." The falling action continues for a short space, while Holmes says the ending may "be for the best" and asks Watson to take his "pistol" in hand as they "enter Dr. Roylott’s room." They go down the hall, knock fruitlessly at the door, enter and are met with the chilling site of Roylott's still body, with the speckled band snake round his head.
"It is a swamp adder!” cried Holmes; “the deadliest snake in India. He has died within ten seconds of being bitten. Violence does, in truth, recoil upon the violent, and the schemer falls into the pit which he digs for another."
Resolution and Epilogue
The resolution occurs immediately after the falling action and is when Holmes lassos and throws the still living snake back into the iron safe it was kept in. An epilogue follows the short, effective resolution. An epilogue is distinguished from the resolution in that one, the latter, concludes the mystery while the other, the epilogue, leisurely sums up what transpires afterward.
In the epilogue, on the train trip back to London, Holmes explains all things to Watson, including that he had at first been on the wrong track but had seen the problem clearly once he saw the pointless bell pull at the corner of the bed below the vent. Everything had hinged upon the will of Miss Stoner's and Lucy's mother, which left Roylott control of the wealth that would go to her daughters on the event of their marriages. Roylott was too well pleased with the life he'd constructed on that money--still in his control as long as Lucy and Miss Stoner were unwed--to allow it to depart from him. The young ladies must be prevented from marrying at all costs. His collection of animals from India provided the perfect solution in the Indian swamp adder.
Holmes explains that the odd room arrangements, the stationary bed, the useless bell pull, the ventilator that didn't ventilate, "dummy bell-ropes, and ventilators which do not ventilate," were integral to Roylott's plan of murder. The interior changes and restrictions to bedroom use kept first one sister, then the other sleeping in one carefully measured location, while the external changes constrained the bothersomely engaged sister to sleep in the murder room:
"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."
Holmes explains that some of the "blows" he gave the adder in the matchlight "hit home," enraging the snake which then lashed out at the first victim it encounter after dashing in retreat back up the bell pull: Roylott. Holmes admits that in an indirect way, he is responsible for Roylott's death:
"Some of the blows of my cane came home and roused its snakish temper, so that it flew upon the first person it saw. In this way I am no doubt indirectly responsible for Dr. Grimesby Roylott’s death, and I cannot say that it is likely to weigh very heavily upon my conscience.”
In my opinion, the climax of this story is the point at which Holmes strikes the snake with his cane. When he does this, the snake is driven back through the hole where, we later learn, it kills Roylott.
If that is the climax, then what comes before is the rising action. The rising action has to do with the explanation of the situation and with Holmes's and Watson's preparations for the climactic night in Helen's room.
The falling action comes after the climax as Holmes explains how he knew what was going on.