The reader is forced into the role of a character that already has some developments. Walton's sister is a character that exists prior to the story; this can be seen by the way Walton treats his subject. Because the reader is the audience with her, the reader is pushed into that role, but not to become a part of the story, only to develop the relationship with Walton.
The purpose of this suddenly close relationship is to bring credibility to the narrative of Frankenstein and ultimately bring credibility to the narrative of the monster. This is done be enveloping Walton's letters around both these narratives. These layers sustain the relationship through the novel and allow the reader to be outside of the story, physically in another location as Walton's sister is, but to be close and credible.
This established relationship that the reader is now part of allows the emotions that Walton's sister may have felt to be recreated and obvious to the reader. "Be Assured I will not rashly encounter danger." Walton reassures his sister and it is made clear to the reader that she feels concern for him due to his tendencies. This emotion that she feels is recreated by his words of comfort to her. This pathos helps to build the relationship as do the other elements in combination with it.
In many circumstances, the letters also appeal to a more logical sense. Walton believes in his cause and believes that his sister (and reader) do not agree with this cause. Because of this temperament, Walton feels the need to justify his actions. So he justifies his actions with logical proof, these logical...