To move the seconds to the center, the 2nd wheel has a tall post that come up through the back plate. A sweep wheel mounts on that post.
The center wheel shaft is a hollow tube. Into that goes a long shaft that will have the second hand at one end and a pinion, engaging the sweep wheel, on the back.
The 4th wheel, which normally carries the second hand, of course does not stick thing the front as they usually do.
The watch is an Elgin grade 83, 16 size, 15 jewels. This fine example made about 1882, and it was a treat to work on it as these are quite rare - in any condition.
The rest of the watch as not nearly so bad in appearance inside. This mainspring barrel is a great example of why old watches that have not been serviced in decades, should be.
As an aside for a moment... These dials are typically held on by dial "feet" which are little posts that go into the bottom plate. Screws or pins go into the side of the feet to hold them. This watch has screws in the edge of the plate that tighten in against the feet and hold the dial. Or they would have. On this watch the dial feet have been neatly cut off.
Why? Elgin designed its dials with the feet in a certain arrangement such that the dial only goes one way. You can't put in on in a way such that the hole that a dial usually has for the seconds falls in line with the 4th wheel post where the second hand goes.
But there are two types of dials, one has the 12:00 opposite from the seconds for open-face movements (stem up at the 12:00, seconds at 6:00). And the other dial will place the seconds 90 degrees from the stem, the stem being at 3:00, for a hunter case.
This watch has had its dial feet cut off so that the dial can be rotated for the 12:00 "up" at the stem, for its open-face case. This watch has no sub-seconds dial at the 4th wheel, so it doesn't matter. This movement, and dial, were actually made for a hunter case!
Without the dial feet, this dial is held on by friction. A neat metal band has been attached around the edge of the dial. This makes a lip which snaps over the edge of the main plate perfectly. There is a tiny cutout for the setting lever. The cutout is blurry but visible in the image here, at the rear edge.
Was this done at the factory? I can't say, but it is extremely good work.