This is a variation of the 1952 Adorable. 17 Jewels, white gold, wind-up, and in perfect working condition. It has two diamonds in the top and bottom engravings and 4 smaller diamonds along each side of the face.
To narrow it down a bit more... you need to take out the movement from the case. If you've taken the watch down to having the back of the case off the front (your picture of the dial by the dime) all you have to do now is gently lift the movement itself out of the back of the case. Then show us a picture of the back of the movement. It should have a date code that we can help date your watch with. It's the thing that shows all the guts and gears of the watch.
Then it should be a bit better for us to guesstimate the model name. Though realize some of the fancier woman's watches... which your grandmother/greatgrandmothers watch seems to be very intricate might not be listed.
In reply to To narrow it down a bit by plainsmen