This is one of those older pencils, or perhaps style of pencils, that yielded many iterations and variations. This pencil, from the early 1900s, closely resembles what was to be called the Pony Clip pencil by Eberhard Faber:
It’s of the pocket pencil variety, and it consists of a hollow metal sleeve that screws to a hollow wooden body (perhaps the pencil equivalent of a full metal jacket). The cone has slits which are compressed to hold the lead when the two parts are joined (I mistakenly left off the accommodation clip when I took the photos):
So to lengthen the lead you just need to slightly unscrew the cap, pull the lead forward, then re-tighten the cap. The lead I have in there is the modern-day 2.0 mm variety, which fits nicely. Eberhard Faber marketed lead refills specifically designed for the Pony Clip (No. 3002).
There are several patents with similar mechanisms, but this is the one that corresponds to the date embossed on the barrel:
There was a tremendous advertising push in the early 1900s for this pencil, sometimes offered as a premium:
The Pony Clip pencil is actually a little larger than the one in the photos, and I’m not certain of the name or number of the smaller one. But they were all designed to be serviceable and handy, and next to a pocket mechanical pencil, they are incredibly durable.