The second story in the book is Flying Too High. Frankly, I wasn't as impressed by this one, as I was with the first one. It took me longer to read as well. It's actually not one case, but two that happen at the same time. They are connected by the use of a plane in them, but I think the bigger reason why they were put together was that they would just be too short on their own.
One is the kidnapping of a little girl, the other is the death of a rich man. As a side story, we meet more of Phryne's friends, and also see her moving into her new home.
The stories were a bit too simple. The kidnapping we already knew who had done it, it was just a matter of how they were going to get the girl back. About the death I had my suspicions, and I was proven right.
One thing that I noticed was that the stories suffer from the author not knowing when to stop. After all is said and done, we still get Phryne doing something, having a party, eating, etc. I skipped that. Hopefully the next story will be better, and this one just suffered from 2nd book problems.