This is a very persuasive letter that includes the triangle of rhetorics: pathos, ethos and legos. The author clearly states his purpose at the start and reinforces it at the end of the letter so as to bring the reader back to the original focus. I will now break this letter into parts to observe the different technique used in each of them.
The first paragraph consist of pathos. The author constantly boot-licked the reader by complimenting his status and career. He also states the purpose of this letter (request).
The second paragraph consist of legos. Dead facts were thrown into this paragraph to prove his point "the problem with guns is that they make it easy to kill or injure a person".
The next three paragraph has both pathos and legos. As author tries to convince the reader with even more facts and surveys proving that easy possession a handguns nowadays makes the community more endangered and that it does not live up to its job as a self-defence, he throws a rhetorical question at him. This method of persuasion is very effective as it makes the reader think about what the author just said.
The next paragraph consist of ethos and pathos. The author brings in his situation as a real-life example, raising credibility of the letter, and finally throws a conscience pricking rhetorical question.
The last paragraph consist of pathos. The author turns back to the original focus (request) and begs him to accede to it at the end.