We took a closer look at the old picture of old Joe Lynch, and we saw that there was a code on the sign above the ring:
Ring the ring once if there was a fire in the Bay section, two rings for fires in the middle of the Village, and three rings for a fire in the Ocean. It also warned that "Fires on Grounds and Beaches within the Limits of the Village of Saltaire are Prohibited Under Penalty of Law -- Board of Trustees."
Picture courtesy Larry Lynch. Click images to enlarge
(It is amazing what you can discover with Photoshop.)