These object is part of a swivel-loop suspender that have been
documented at numerous western United States sites of similar age:
Trapper Wilson's Cabin at Silcott Washington; Lynn Furnis (Rogers)
correctly identified them from a lumber work camp in the Sierras; and I
have found them at Alabama Gates work camp.  Sears 1908:972 carries
similar models for those of you who would like to see how they work.
The cord that runs through the 3 loops and other 1 looped fasteners
allows for the suspenders to (technically they are braces since these
are buttoned onto a garment) adjust to the different movements of the
wearer.  One Sear's 1908 description said they were "deservedly
popular."  The patent dates makes a nice addition.  If you look at the
1902 Sear's catalog (sorry mine is at work) you will see the earlier
models tried other contraptions for the back part.

Sunshine Psota