This appears earlier than the 1934 edition. The 1908 ‘Latest Edition’ version (there are two 1908 editions on EUVS) has a section after the end of the previous edition named ‘Some new-up-to-now seductive American cocktails’; the Ocean Shore Cocktail appears there. That recipe has raspberry syrup as an alternative sweetener to orgeat.
I noticed this on a few entries including some my own that I’ve added. It occurs where ‘to top’ is used for, eg, soda. If you specify an actual amount then a unit count is provided.
This is pretty similar to the Liberal Cocktail in Jacques Straub’s Manual of Mixed Drinks (1913), albeit that is made with rye whiskey rather than rum.