Probably shouldn't... but can't help myself >.>
Crossent saws are the large two-man crosscut saw used for felling trees (Oregonian here, we know our logging history).
The band of Lime (and the 25# White Lime) could have had any number of purposes aboard the Albatross, realistically. The "band" was probably a semi-formed strip of hydraulic lime, which would have more than likely been used as a sealant for seams below the waterline (hydraulic limes were great for this, as they could set nearly as hard as cement, and *required* water in order to set).
The unspecified white lime could have had any number of applications, but given the rather paltry amount, it was probably quick lime, which would have been used in the process of cleaning the funnel. If not quick lime, than it was probably a combination of calcium hydroxide and calcium carbonate, to be used as a whitewash, which would have kept the ship's white hull rather tidy, and would have had the added benefit of protecting the timber from the elements. I'm not terribly inclined to believe this to be true, except in touch-up situations, because whitewash takes a bit of time to dry properly and isn't exactly waterproof.
Depending on the year, there's also the option that it could have been an experimental silicate mineral paint, which would have been pretty great aboard a 19th century warship.