The bowls most probably originated from Cambay on the west coast of India, which was an important port in the 17th Century and also the centre of the Indian hardstone industry, as it still is today.
There were many cornelian and agate pieces in the large bequest from Elizabeth, Countess of Devonshire (1619-1689), to her daughter, Anne, Countess of Exeter (1649-1703).
The bequest, which comprised the entire contents of her suite of private apartments at Chatsworth, was listed in an inventory known as the 1690 Devonshire Schedule, or Deed of Gift.
The bowls in question are those to the right and left of the first image and the one to the right of the second image.
