Here is a picture of a smaller mine hoist to show what's going on with that huge conical hoist drum:

https://c8.alamy.com/comp/J3BRD8/dickson-hoisting-engine-new-catechism-o...

There are two elevator cars, one going up while the other is going down, balancing each other. The idea of the spiral cable drums is to compensate for the substantial weight of the hoist cable, probably more than the weight of the cars. When the cable is coming off the small end of the spiral, it has a mechanical advantage over the other cable at the big end of the other drum, compensating for the weight of the hoist cable down the mine shaft. The drum diameter is very large, since it needs to hold the entire length of the cable in a single wrap.

A side effect is that the elevator cars would crawl at the bottom, but be screaming fast when they reached the top.

The 4 cylinder Corliss engine is a masterpiece of the machinist's art. Terminology on this setup is odd. Although the engine is split at opposite ends of the drum, all four cylinders operate as a single engine. So it could be described as one engine, two engines or four engines. From the camera angle, it's unclear whether the engine is simple or compound; given the era, it's probably compound. The hoist drum is controlled by a similarly huge steam operated clasp brake.

One wonders how much that monster cost, and how long it took to amortize it, given the high value of the copper it pulled up.

This looks to be the sort of thing that would have set Charles Sheeler's heart aflutter. Very lovely, I must say.