These 'popsicle stick'- like things are busks made of whalebone with scrimshaw designs. A busk is a part of a corset - it fits into a pocket down the middle of the front to lift and separate the breasts. These were made by sailors as gifts for their wives and sweethearts back home.
And these pretty ladies are whalers' wives, perhaps the very wives these busks were made for. (I wonder how many total yards of fabric are worn in that picture)
The busk on the left has a poem which seems to have been written by the sailor who carved it. Kind of an odd sentiment, not sure how I would feel if The COG presented me with such a thing upon returning from a trip:
"This bone once in a sperm whale's jaw did rest,
Now tis intended for a woman's breast.
This, my love, I do intend
For you to wear and not to lend."