at the depth of something—at a specified distance from the top down:
- At the depth of 180 feet, at what was called the third gallery, the width of ore was, as I have said, 45 feet.
in the depth of something—
1. in the deepest or most central part of smth.:
- In the depth of the valley, there is a lochan (the diminutive of loch) of superlative beauty.
2. in the middle of the winter or night (when the cold or darkness is most intense):
- In the depth of winter it is quite enough to fire up twice in the twenty-four hours.