"If I have set it down it is because that which is clearly known hath less terror than that which is but hinted at and guessed at."
This quotation is from the 1742 manuscript that details the legend of the hound, and it gives the document an air of authority. The manuscript seems to provide the best explanation for the mysterious events which occur in the novel - if one allows a religious world view. Though it does provide a basis to explain Sir Charles's death, it is important to remember that the manuscript is 150 years old, even at the time of the novel's events. It reflects an attitude that accepts superstition as fact. For Holmes, the fact that the legend is "written down" does not at all make it "clearly known." Instead, this professed authority is just an example of the type of assumption that hinders true investigation. The contrast between the manuscript's professed authority and the actual explanation shows how knowledge had changed in the 18th century. It also reveals the human tendency to accept occult explanations when others do not easily present themselves.
"I knew that seclusion and solitude were very necessary for my friend in those hours of intense mental concentration during which he weighed every particle of evidence, constructed alternative theories, balanced one against the other, and made up his mind as to which points were essential and which immaterial."
Here, Watson provides one of his clearest understandings of Holmes's method. Though he is the detective's partner, Watson is often left out of the man's problem-solving. Here, Watson implicitly defends Holmes's distance, suggesting that genius needs solitude. By suggesting that Holmes uses a method that Watson cannot replicate, Watson paints Holmes as not only a genius but as a hero. It also reflects the self-sufficiency that Holmes employs throughout the mystery, using others only when he needs them. Amusingly, one can claim that Watson is essential towards allowing Holmes the illusion of self-sufficiency (in other words, Holmes without Watson could not get as far), but the quote in any case gives some indication into how Watson - and Doyle - understand genius.
"The world is full of obvious things which nobody by any chance ever observes. Where do you think that I have been?"
When Holmes addresses Watson this way after Watson returns from his club, the detective gives some great insight into his method. In short, he is capable of observing and managing many details at once, so that he can often do his best work from the comfort of his armchair. And yet that observation is only the first step - what he can do afterwards is construct many possible interpretations for each observation at once. His true gift is for imaginative recreation. Therefore, what he suggests here is that can 'travel' to many myriad places simply in the confines of his imagination.
"Of course, if Dr. Mortimer's surmise should be correct, and we are dealing with forces outside the ordinary laws of Nature, there is an end of our investigation. But we are bound to exhaust all other hypotheses before falling back upon this one."
Though somewhat disingenuous here - Holmes would likely never accept an occult explanation for anything - he does illustrate what fascinates him most: cases which seem to have no explanation. This is because such cases allow Holmes the opportunity to employ his method, of observing the tiniest details and then constructing an explanation from them. When nobody else can see clues in a situation, then Holmes enjoys himself most of all, both because it allows him to display his genius and because it poses the challenge of exploring several different "hypotheses."
"But we hold several threads in our hands, and the odds are that one or other of them guides us to the truth. We may waste time in following the wrong one, but sooner or later we must come upon the right."
After Holmes and Watson encounter several dead ends in their investigation, it is notable that Holmes does not panic. Instead, he seems almost enthralled by the multitude of "threads." His faith that one of these threads will lead to the solution is built upon his basic belief that humans always leave a trail. He knows he will eventually find the right clues, and so seems to enjoy when that proves difficult. Finally, his confidence is not only in himself, but in the power of the intellect. Because he can eschew the possibility of occult explanations, he knows a rational solution will eventually be found.
"Just tell me what it all means, Watson, and I'll owe you more than ever I can hope to pay."
When Sir Henry addresses Watson this way, asking why Stapleton would so vehemently oppose the man's union with Miss Stapleton, it provides the latter the rare opportunity to play the primary detective, both for his charge and for us as readers. Typically in Holmes stories, Watson asks Holmes the explain the situation; here, Watson is the one being asked that question. This alternate situation describes the whole middle of the novel, when Watson is (seemingly) alone with Sir Henry out on the moor. Watson's means of attempting to answer questions like this provide a wonderful foil to Holmes's method, which usually drives the stories and which certainly drives the latter section of this novel. Finally, this moment employs situational irony, since Sir Henry is actually asking the question that could unravel the whole mystery, even though he believes he is only asking a question about romance.
"A spectral hound which leaves material footmarks and fills the air with its howling is surely not to be thought of. Stapleton may fall in with such a superstition, and Mortimer also; but if I have one quality upon earth it is common sense, and nothing will persuade me to believe in such a thing."
When Watson records this passage in his diary, he has been away from Holmes for some time. What this passage reflects is the human tendency to turn to occult or supernatural explanations when no rational evidence presents itself. Even Watson - who vehemently insists that he will consider no occult explanations - exhibits that tendency here. By having Watson battle this tendency, Doyle explores the conflict between the rational and supernatural, and provides an extra hurdle that Holmes has to conquer. Watson speaks as though he must fight his instincts in order to pursue a rational course; it is often easier to settle for an occult explanation, which is why it is all the more important that we insist to ourselves that such explanations are impossible.
"Always there was this feeling of an unseen force, a fine net drawn round us with infinite skill and delicacy, holding us so lightly that it was only at some supreme moment that one realized that one was indeed entangled in its meshes."
Here, Watson describes his feelings as he approaches the hut where the mysterious figure seems to be living. Of course, he soon discovers that it is Holmes himself who has drawn this "net" around him. The net is an important image in the novel, symbolizing the way knowledge is used to manipulate others like puppets or toys. Those who possess knowledge control those who do not have it. For example, Stapleton orchestrates Sir Charles's death and creates an aura of superstition because he knows much that others on the moor do not. Similarly, Holmes must hoard his own knowledge throughout the case, so that Stapleton does not realize that they are on his trail. Only when knowledge is kept secret or private can it become a "net," a means of control.
"I shall soon be in the position of being able to put into a single connected narrative one of the most singular and sensational crimes of modern times."
Holmes confidently announces this prediction even before he has entirely solved the crime. In fact, he must have Stapleton re-enact a version of the original crime in order to catch the culprit red-handed. Holmes's confidence in those circumstances reveals his belief that any trail will eventually lead to its end; he does not need to have the answer, but only needs to know he has chosen the right path out of all the possible paths. Then, trusting his power of observation, he knows that the markers humans leave behind will eventually reveal the final solution. The quote also reminds us that Holmes likes difficult cases most of all; "singularity" is an essential quality in a case that interests Holmes. In nearly every one of his cases, he remarks on the uniqueness of its clues.
"One of Sherlock Holmes' defects--if indeed, one may call it a defect--was that he was exceedingly loath to communicate his full plans to any other person until the instant of their fulfillment. Partly it came no doubt from his own masterful nature, which loved to dominate and surprise those who were around him. Partly also from his professional caution, which urged him never to take any chances. The result, however, was very trying for those who were acting as his agents and assistants."
Watson writes this right before he reveals everything that Holmes told him about the case. The passage tells a lot about Holmes's personal character: the man is often uncommunicative, distant, and "trying" (or annoying). Of course, Watson suggests that there are contradictory reasons for his silence. On the one hand, he is extremely self-sufficient, and likes to maintain control of a situation. This is likely the "trying" aspect, since it is solely about Holmes's ego. On the other hand, Watson does recognize value in secrecy, since its allows Holmes to manipulate situations, to avoid "chances" that indiscriminate sharing might produce. Ultimately, Watson's feelings about Holmes are ones we likely feel as well. The Hound of the Baskervilles leaves out much of Holmes's thought process, so that we often lack even the information with which Holmes constructs his theories. Like Watson, we must simply wait to learn the fruits of that method when Holmes is ready to share.