Mystery Off Pirate's Point, by L. A. Wadsworth (epub/Kindle/pdf)

The Lawrence twins, Steve and Tony, found this summer at Pirate's Point quite different from the usual even dullness. First they had new neighbors -- Professor Hillyard and his daughter, Pat. Then motorboats sped into the Cove mysteriously at night, without running lights. And Steve broke his leg, so Tony had to print his brother's weekly newspaper, though he had little interest in it.

The annual calm is broken by a burglary, a theft, a series of perculiar advertisements and an adventure on the high seas, in all of which Pat Hillyard and Tony are tangled.