The mood throughout How the Other Half Lives is consistently a serious and somber one—justifiably so, given the subject matter Riis took upon himself to discuss. In particular, the passages detailing specific instances of death, disease, or other suffering maintain this somber mood. As a persuasive piece, this is fitting. It would not do, after all, for Riis to treat such suffering with anything less than the consideration and solemnity it requires.
The solemnity of the mood in How the Other Half Lives can also be attributed to genre: as an informative, journalistic piece of writing, it must maintain its integrity to incite readers to action. Any irreverent mood or lack of seriousness would not only be inappropriate; it would demolish Riis's credibility with his audience. Riis wants his readership to take this book seriously and take actionable steps towards abolishing the tenement system. It is in his best interest, both as a social reformer and a journalist, to maintain a respectfully somber mood discussing the subject at hand.
Even if Riis had not worked hard to maintain a serious mood throughout the book, the mood would have remained serious regardless, given the content and its tragic reality. Readers should generate this solemnity of their own accord, pondering the true sufferings of their fellow citizens.