What was the weighted rope called that was used to measure fathoms?

Well, the weight (made of lead) on the end of the line was/is a "sounding lead", so I guess the line could be a "sounding line", but I don't think the rope itself really has a name. By the way, the sounding leads come in different sizes/weights, to be used depending on the depth of water: hand lead, coasting lead, deep-sea lead. Answer I am a sailor and the name of the line to measure fathoms is called a lead line because of the lead at the end.

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Further to which, the lead was often made with a hollow end to sample the sea-floor to ascertain if an anchor would hold. The cavity held wax to which mud or sand would stick, but if it came up clean it indicated a rocky sea-bed.