How did Holmes' digressions sometimes prove in the end to have a bearing on the matter on hand?
It is a queer thing about many detectives that they often deviate from the original question. It may seem surprising to anyone. Same was the case with Sherlock Holmes, when on a case visit, he seemed to digress from the objective. For example, he would ask a person to be interrogated about his plans, however he would ask him about his nationality and talk about his attire. Little the person would come to know what Holmes is progressing at. While he is solving the mystery in his mind. He would never run a background check on a person by directly asking him his whereabouts. He would pretend to know a person from the suspect's vicinity and call out his name to check if the person is honest about his background. However, the suspect would not realise and will fall to the bait by exclaiming how well he knows the person, while in reality the person does not even exist in reality. This way Holmes does his inspection of the matter and does not bring it to the suspect's notice as well.