The base of a bottle typically only has one primary function (besides helping hold the bottle together) and that is to provide a flat surface for the bottle to stand upright.Of course there are exceptions to that "rule", most notable being the rounded base mineral & soda water bottles whose purpose was to make sure the bottle did Bottle bottoms aren't flat because they need an arched structure to allow them to be stable on a flat surface.For additional information, click Dating Page to go to the pertinent section of that describes the differences between these bottles.
The bottom of a bottle is usually the thickest part, retaining more temperature throughout the production line.
Because the bottom is hotter, it is also more fluid and has a tendency to sag, forming a shape like a spinning top which makes it unstable on flat surfaces.
This commonly encountered symbol (at least in bottles found on Western historic sites) was intended either as a cryptic form of makers mark or simply an artistic flare of a specific mold cutter or engraver at the SF&PGW (or located in the Bay Area).
Although the marking cannot be irrefutably attributed to SF&PGW, it presence is still a datable feature as empirical evidence indicate that bottles with this marking (primarily liquor and food bottles) date between the mid-1870s and about 1890.
There is also large section on pontil marks or scars due to its size (hyperlink found several places below).
Short differentiating informational statements are provided below (in bold) to make an easy "break" between mouth-blown and machine-made bottles.
The best readily available source for classifying bottle base shapes/profiles is the "Bottle Base Profiles" illustration that was previously included in the IMACS (Intermountain Antiquities Computer System) guide.
That guide is no longer available online through its long time host (University of Utah) although a copy of the entire bottle section is now (2015) available via this website at the following URL: Guide1992The base illustration by itself is available at the following link: illustration was taken from Richard Fikes' excellent 1987 book (now again in print) on historic medicine bottles - The Bottle Book: A Guide to Historic Medicine Bottles.
Giving a bottle an arched shape at the bottom means that if it does sag, it can do so without touching the bottom.