This autographic version of the Vest Pocket Kodak was manufactured from 1915 to 1926 with a variety of lenses. This single meniscus lens was the cheapest option. Based on the finish and styling of this camera, I'd guess it was made rather early on in this period.
The lens suffers from excessive flare, so there's an aperture limiting ring in front of it, allowing only the center part of the lens to be used. Unscrewing this ring allows the aperture to open wider, but the flare will create ethereal, dreamlike images. Not a very bad thing, in my opinion.
The focal length of the lens seems to be about 75mm and widest aperture perhaps around f/11. I've modified the camera so that I can use it as an M42 mount lens on my DSLR. The camera by itself would use 127 film, which is no longer readily available.
For shots taken with or of this lens follow this tag.