Answering the demand of big-game hunters, Winchester set out to produce a heftier version of their already-popular Model 1873. Introduced to celebrate the American Centennial Exposition, the new Model 1876 quickly earned a reputation as an effective big-game hunting rifle.
Originally chambered for Winchester’s new .45-75 Winchester Centennial cartridge (mimicking .45-70 ballistics in a shorter case in order to accommodate the 76’s toggle-link action receiver), versions in .40-60 Winchester, .45-60 Winchester and .50-95 Winchester eventually became available. Our restored example sports the latter chambering, which was known to be popular among professional buffalo hunters of the day. https://www.turnbullrestoration.com/gun/restored-winchester-model-1876-50-95/

The .45-75 Winchester was designed for the Winchester Model 1876 Centennial lever-action rifle.
Lever-action rifles had a problem with .45-70 Gov't. ammo because some loads had longer bullets than others. The infantry used a longer 500 grain .45-70 bullet and the cavalry used a 400 grain bullet. The elevators on lever-action rifles need uniform cartridge and bullet lengths to keep from jamming, so Winchester made the .45-75, but it went nowhere and proved unpopular compared to other loads like the .44-40 Winchester Center Fire, .45 Colt, and .30-30 Winchester.

Rare to find a box of these babies.

Compare with the .44-40 Winchester (aka .44 WCF (Winchester Center Fire)) designed in 1873.

And that was an improvement over the early Civil War era .44 Henry Rimfire (11x23mmR) for the Henry 1860 lever-action rifle.

Here's some .44 Henry rounds under an 1860 Henry rifle, magazine open for loading, and a .44-40 WCF for comparison.

Here's an Italian Uberti reproduction of the 1860 US Henry Rifle in .44-40 or .45 Colt.

US Winchester Model 1892 Deluxe Takedown in .45 Colt by Turnbull Restoration.
Very nice work.

Forgotten Weapons has a series of videos on Winchester Lever Action Development: https://www.youtube.com/watch?v=ofGnRSE7lpI&list=PL9e3UCcU00TREsGA9nkvCqFp2e0Ht9u3e
Winchester Lever Action Development: 1860 Henry https://youtu.be/ofGnRSE7lpI
- US Winchester Model 1866 Deluxe with semi-relief engraving by Conrad F. Ulrich.