Watches in the Merchant Service were of four hours duration. One blow is struck on the bell for each half hour, i.e. one blow for the first, two for the second, and so on, until the end of the four hours, which makes eight bells. The watches are then changed.
This song was well known in the 1800s, especially aboard British whalers. In Arctic whalers, the lookout position was inside barrel at the masthead, offering some protection from the elements. In the South Pacific, according to Stan Hugill,
...the barrel was not required. Mouth South Seas seamen had another set of crosstrees above the normal topmast crosstrees, part way up the t'gallant mast. Above these again, secured to the royal mast, were two hoops, in which the lookout stood with his feet on the t'gallant crosstrees.
Our protagonist, at least in Hugill's variant, is one of these whalermen "in the hoops".