Okay, I believe I got it. It was for salad dressing. In the first quarter of the 20th century that probably meant a mayo. The JF Howard has an Owens boxed O on the base to boot.
Maybe but a little hard to tell from the original pic. I hesitate to call that a widemouth. Perhaps a horseradish if not a mayo. I'm thinking a bottle that a spreader knife can be easily inserted into and the bottle is small enough to have its contents used up before it spoiled.
If that is a 'cap-seat' inside the rim it could be a non-milk dairy bottle. I can't tell from the pic. It might have been used for heavy cream or sour cream. Those bottles had wider mouths and were smaller.