Holmes was observant, intelligent and rational, while Watson admired Holmes, yet he was sometimes irrational too. In chapter one, they were examining a walking stick, and made assumptions about the owner. The walking stick contained teeth marks, and carvings of the initial of C.C.H. Watson saw that, and predicted the owner was a member of a hunting club, as H stood for Hunt. After Holmes carefully observed it, he found most of them inaccurate. C.C. stood for Charing Cross, which was a name of a hospital. So he concluded that C.C.H. stood for Charing Cross Hospital, where the stick was given to the owner when he retired from the hospital. Also, in chapter 4, Sir Henry received a strange letter, in which the words inside were all cut out in newspaper.(p.35) Watson couldn 't see the significance of the sentence, while the observant Holmes made many good assumptions from the letter. He recognized that the words were come from the Times of the previous day observed from the kind of ink and paper. He could even conclude that the sender posed to be an uneducated man that the address was printed in rough characters, but Times were mostly read by educated man. Also in chapter 12 p.136, they discovered that Stapleton was the villain, and Watson was being irrational and asked Holmes why they didn 't seize him at once. But Holmes replied to Watson that they couldn 't prove that Stapleton did it, and they had to come up with a plan to capture Stapleton or else he might escape. From all the examples, it showed that Holmes was rational and careful in what he did.
Although Holmes was intelligent, he could be sarcastic and arrogant as well, but