John Watson meets Sherlock Holmes for the first time in a medical laboratory. The setting is described as follows:
This was a lofty chamber, lined and littered with countless bottles. Broad, low tables were scattered about, which bristled with retorts, test-tubes, and little Bunsen lamps, with their blue flickering flames.
Holmes is energetically enthusiastic when he meets Watson for the first time, because he has successfully concluded an experiment that will offer "an infallible test for blood stains."
This setting is particularly appropriate for a first encounter with Holmes because it characterizes him as a man of science. Logic, empiricism, and the scientific method are all essential to how Holmes solves crimes. Showing him in a lab setting, enthusiastically experimenting, introduces us to the core of who he is. We see in this setting that he is not only science based but hardworking and dedicated to his vocation.
The rooms the two men look at on Baker Street and decide to rent together help characterize their relationship. While Holmes will always be the senior partner when it comes to detecting, the equality of the flat, with two bedrooms and a central living area, is fitting for the men who will become friends and in many ways function as equals in the ordinary aspects of life:
A couple of comfortable bed-rooms and a single large airy sitting-room, cheerfully furnished, and illuminated by two broad windows. So desirable in every way were the apartments, and so moderate did the terms seem when divided between us, that the bargain was concluded upon the spot, and we at once entered into possession.
The setting of the first encounter with Lucy Ferrier, in the far West, at this point a child, associates her with innocence and as "a wisp of pink" when she is spied in a "crag":
From its summit there fluttered a little wisp of pink.
This setting, where she is an orphan with only one other person beside her, emphasizes her apartness, especially from the Mormons.
Later, the setting of her upbringing in the American West will be tied to the beautiful person she becomes:
Lucy Ferrier grew up within the log-house, and assisted her adopted father in all his undertakings. The keen air of the mountains and the balsamic odour of the pine trees took the place of nurse and mother to the young girl. As year succeeded to year she grew taller and stronger, her cheek more rudy, and her step more elastic. ... As fair a specimen of American girlhood as could be found in the whole Pacific slope.
Here, as is often the case with Holmes, a threat to the stability of English life comes from an exotic place far different from England, be it India or the American West.