A string of seven optical detectors deployed from a ship was used to detect the Cherenkov light from muons at ocean depths ranging from 2000 to 4000 m in intervals of {similar to}500 m. The flux and angular distributions of cosmic-ray muons were measured. An effective area for fivefold coincidences of 420 m{sup 2} for downward-going muons was achieved. The results are consistent with those derived from underground observations and theoretical calculations. The measured vertical intensity ranges from (9.84{plus minus}6.5){times}10{sup {minus}8} cm{sup {minus}2} s{sup {minus}1} sr{sup {minus}1} at 2090 m of water equivalent (mwe) to (4.57{plus minus}1.37){times}10{sup {minus}9} cm{sup {minus}2} s{sup {minus}1} sr{sup {minus}1} at 4157 mwe.