They get an assignment, visit a sanitarium, and then descend into the bowels of the earth to discover... well, the Harrowmoor Dogs, if that's not too much of a spoiler. The story is brief, tense, vivid, and leaves a lot of threads hanging for more stories.
Running through the story is the Victorian-era view of homosexuality. I'm not sure it fits in smoothly -- there's a story frame whose only purpose seems to be to give baby Alan Turing a cameo. But again, this may make more sense in the context of more Balfour and Meriwether stories.
(Upon searching, there are two earlier ones and the author hasn't decided whether to write more.)