Stevenson will have his characters walk in silence as they compose their thoughts, such as in the following passage where Utterson tries to absorb Mr. Enfield's telling him that the man who ran over the child was Mr. Hyde:
Mr. Utterson again walked some way in silence and obviously under a weight of consideration.
Another instance comes when both Mr. Utterson and Mr. Enfield see something in the window at Dr. Jekyll's that leaves them speechless:
In silence, too, they traversed the by-street; and it was not until they had come into a neighbouring thoroughfare, where even upon a Sunday there were still some stirrings of life, that Mr. Utterson at last turned and looked at his companion.
We as readers don't know what they saw, but clearly it is something they don't want to talk about, even to each other.
Not long afterwards, Dr. Jekyll's butler Mr. Poole comes to visit Mr. Utterson and silence is implied. This silence, showing an unwillingness to speak, is conveyed through Mr. Poole's behavior. The butler has come because of something he can't "bear" anymore:
Even now, he sat with the glass of wine untasted on his knee, and his eyes directed to a corner of the floor.
Stevenson also uses ellipses (...) to suggest a silence that means a character is hesitant to speak. For example, when Mr. Enfield is trying to describe to Mr. Utterson the strange, small man he has seen around Dr. Jekyll's house, he is surprised into silence by Mr. Utterson's question as to whether the man let himself in with a key. It is clear that Enfield does not want to answer:
"My dear sir…" began Enfield, surprised out of himself.
Mr. Enfield's silence is the answer, however, that Utterson needs; he now knows that the strange man did use a key.
Ellipses are used again when Poole does not want to speak:
If it was my master, why did he cry out like a rat, and run from me? I have served him long enough. And then…" The man paused and passed his hand over his face.
Whatever Poole is thinking, he pauses and runs a hand over his face before he speaks. This prepares us for a startling or unsettling revelation.