According to Waits, this dates to around 1920.
When doing some online research on the other Penn adjustable, I found out that there was one with a twist knob adjuster.
Its a one piece Singe Edge razor that and has a twist knob that does the adjusting. It is "Continously" adjustable although the adjustment range is pretty small.
This one is the complete kit, including the case, the razor itself, the blade bank with some blades, a strop and a handle to hold the blade to strop it.(see middle picture of the second row)

It takes a proprietary blade, but guys use the non-adjustable ones with normal Injector blades. That doesn't work in the adjustable because the adjuster mechanism just pushes the blade against the top cap, which in turn pushes the top cap upwards and increases the blade gap. The width of the injector blades are too thin for this to happen.

I found two patents for this, both granted to Harry W. Greenbrier.
    The first is a US patent dated Jan, 22, 1918 and the number is US1254037 (Click to open in a new window)
    The second is a British patent dated Apr, 7, 1922 and the number on that is GB156704 (Click to open in a new window)

How does it shave? I don't know as I haven't figured out a blade solution yet. I'm not too comfortable with just the tension of the top cap holding the blade in place. I've made two spacers, the first one out of this stainless steel and the second out of thin plastic but neither will hold the blade in place when its on its open setting. WATCH THIS SPACE.