I believe this is your Charles Hedden, of Hedden & Eberhardt, New York, NY, makers of perfumes, toilet waters, sachets and powders. This is a 1915 patent reference.
Also, here is a link to a 1910 announcement of the company incorporating.
The American Perfumer and Essential Oil Review (1906) -...
Here's an 1898 listing for them at the Division and Hester St in NY:
Trow's (formerly Wilson's) Business Directory of the Boroughs of Manhattan ... - Google Books
There is also a Suffolk St in NYC, the Lower East Side, but I couldn't figure out what BET is or find any link to the company at...
I picked up this stoneware jar at a thrift store tonight for .99 cents - for that price I couldn't say no. It's 6" tall, and the only markings on it are S S Co with a star stamped into the base. Any help in ID'ing the mark, age and origin would be appreciated. Thanks in advance!
That's a very nice local pharmacy bottle, I love that it has the name in script, the embossed cross and the graduation marks on the sides. It checks all the boxes!
Here's a link to a 1912 ad for the company, on the bottom right corner of the page:
Alton, Illinois - Google Books
That Burrington's Ink is amazing, what a great find as a family heirloom. I assume you probably already have one, but there is also a Burrington's Vegetable Croup Syrup bottle from Providence as well? It must be the same Burrington, RI isn't a very big place.
PROVIDENCE RI RHODE ISLAND...
I agree on the European, probably Germany. It's very similar to these "Providentiae Memor bottle. Providentiae Memor is Latin for Providence Remember, and is the motto is the Kingdom of Saxony, now part of modern Germany.
Kingdom of Saxony - Wikipedia
I can't help with the age of this bottle...
I was thinking alcohol too, but could it be a med? Here's a long shot possibility for you. I found this in an 1898 medical journal, PIX Cresol Solution, sold in one pint bottles.
Medical Arena - Google Books
Here's a link to an old auction where a blue one sold for $240.00 in 2013. There's alots of search results for the cobalt blue but I couldn't find any aqua green examples like yours. Maybe it's a harder one to find? Either way, it's a great bottle...