On the Half Moon, we traditionally use a Secchi disk to measure turbidity, although this device would have been an anachronism in 1609. Hudson's voyages predate the invention of the Secchi disk by more than two centuries; in the 17th century, sailors would simply keep an eye on objects floating beneath the water's surface — an inexact, "rule of thumb" approach.
A Secchi disk works like a lead line, except that instead of flinging a lead line overboard, its user simply lowers the disk into the water.