The lead line was a traditional way of testing the depth of water and the nature of the seabed. It was a line with regular lengths marked off, ending in a weight made of lead or another heavy substance. The weight was tipped with tallow during this period to bring up samples from the seafloor. The lead line would be cast or swung out from the ship by a leadsman - as can be seen in this much later drawing  - who would also call out the depth reading. Heavier lines were run through blocks, like this one  at the National Maritime Museum which was recovered from the 1782 wreck of the HMS Royal George . The use of the lead line was later called sounding or depth sounding, and the resulting information was recorded in log books and later added to hydrographic charts in units such as fathoms. Knowledge of the water depth and of the type of sediment on the seafloor assisted navigation including deciding where to anchor and avoiding dangerous shallows and rocks.
The lead line was vital to navigation until the twentieth-century invention of echo sounding, which employs sound pulses to find the sea depth. It was therefore used on all of the expeditions in which the Board of Longitude was involved, whether or not specific archival records such as log books mention it. It could also be used to make experiments aboard ship, as was recorded [RGO 14/57:9] by the astronomer William Bayly off of Madeira in 1772: ‘This day the Weather being very fine with little wind, I got the use of the Resolutions boat to try the heat of the water at difference depths – I suspended the Thermometer in an wood case [...] made fast to the Dipsea Lead, or the lead they sound with on board Ships, & let run down into the Sea, & let remain there 15’ or 20’ Minutes or untill [sic] it has required the same degree of heat with the water which surrounds it, & then drawn up as quick as possible & examined & the height of the Mercury noted'.
There are other records and letters in the archives about improved buoys and nippers to keep the lead lines vertical in the water as well, and suggestions for improved depth-sounding technologies called sounding machines. A number of such letters are in RGO 14/31 [RGO 14/31:1], which was originally labelled 'Sounding Machines and Ships Logs &c'. For example, the volume includes communications from Peter Burt, who asked [RGO 14/31:190] for the Astronomer Royal John Pond to return the papers about his buoy and nipper which he had submitted to the Board. This was when Burt was preparing to send a petition to the House of Commons in 1817 because he was unhappy with the Commissioners' decisions. His design was ultimately used by the Admiralty, as were similar designs by other projectors including Edward Massey. You can see one of Massey's sound machines  in the National Maritime Museum collection.
History and Philosophy of Science
University of Cambridge