This bulb is called a HYLO bulb. It has two carbon filaments
that can be switched on and off with a string that is integrated into the base, which moves a switch inside. The small filament is a one loop, 1 candlepower filament, while the large one is a 3 loop, 16 candlepower filament. This was a novel idea at the time: You could use the large filament for regular lighting, and you could use the smaller filament as a night light for example, all at the flick of a switch. These were also advertised for their power-saving benefits. It seems that my bulb was almost always operated with the smaller filament, because the large filament is intact and shiny and the little one is black and broken. Also, more than half of the string is gone. There used to be another ball like the white one shown, but it was black in color, and came out of the opposite side of the base.
In the beginning, these "power saving" bulbs had no strings
. The switch was a simple metal plate that would connect the other filament by screwing or unscrewing the bulb a bit. This was inconvenient because a person had to physically touch the glass part of the bulb to unscrew it, and as you might guess, by then it was probably already very hot. Bulbs with that kind of mechanism are extremely hard to find. I was very fortunate to get one with BOTH filaments intact. This mechanism was replaced by the string type.
There is a very similar bulb called the "Economical" lightbulb, which was made by the same company (Economical Electric Lamp Works, N.Y.). The difference between the HYLO and the Economical is that the Economical bulbs with strings had an external switch, while HYLOs with strings had an internal switch. It appears that Economical lightbulbs were renamed as "HYLO" bulbs when the Economical Electric Lamp company was bought by the bulb supergiant, the General Electric Company. It became a division of the latter, as can be seen at the bottom of this
This is the Carbon HYLO bulb, but cage filament
and even coiled tungsten filament
HYLO bulbs were also made. At the time of this writing I still don't have a coiled tungsten filament HYLO bulb. I've been browsing eBay for about 3 years and I have only seen 2 or 3 auctions with them.