This is very very similar to the Arthur Hale (No.1) in Ted Saucier’s Bottoms Up (1951).

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.