The slightly larger ring is engraved with the name "Emma Brose". It weighs 24.2 grams, and the dimensions are 2" H x 1 3/4" in diameter. Marks inside appear to be those of Gorham Silver, Lion - Anchor-G plus the word Sterling and 1630.
The slightly smaller ring is engraved with the name Dr. L D Brose. It weighs 19.4 grams and the dimensions are 1 3/4" H x 1 3/8" diameter. Marks inside appear to be "670" over "A".