History of the study of of Polynesian languages

Polynesia is a section of Oceania, consisting of over 1,000 islands, forming a triangle stretching from New Zealand to Hawaii to Rapa Nui (Easter Island), known to be colonised by humans for hundreds of years. Since their discovery to the western world, the question was posed how they arrived there. Early hypotheses suggested a migration from South America, and while some modern genetic evidence suggests limited peopling of Rapa Nui by Native Americans \cite{Thorsby_2016}, it's clear today that Polynesian migration started from the west. Historically it was the naturalist Joseph Banks who began to discover the real origin to their Polynesian migration. He recorded vocabulary used by the Tahitians, Maori, and other cultures not just from Polynesia, but from Micronesia and South East Asia \cite{banks1790}. He was able to draw a linguistic relationship by directly comparing Polynesian languages, which showed no clear difference, and then applying this comparative method to the examination of Polynesian and Micronesian languages, and follow the relationship back to South East Asia. This relationship was discovered to have spread to Madagascar, forming what we now know as the Austronesian language family. Given the discovery of the widest spread language family of all time, linguists tried to extrapolate the migration of these people using known data. 
One of the earliest attempts at this was by William Churchill, who compared Melanesian and Polynesian languages to test the two prevailing theories of Polynesian origin at the time, and to attempt to plot migratory routes through East Asia \cite{Churchill1911}. The sieve theory posited that the islands of Melanesia and west Polynesia acted like meshes in a sieve, catching seafarers originating from central Polynesia who were blown westwards by the strong prevailing winds (known today as the "roaring forties"). This theory also posited that the initial peopling of central Polynesia occurred by seafarers from East Malaysia, who travelled with the current north of New Guinea, through the Marshall Islands to Samoa and Fiji. The migration theory on the other hand suggested that the migration began in India, and they journeyed eastwards through the Malay Archipelago, travelling slowly (and suggests of many generations between migrations), they eventually reached Fiji, and settled there for generations before voyaging again. Churchill tested these theories using what we would now describe as a comparative method: By comparing cognate lists of 18 languages, and comparing word differences and language differences, he discovered that the linguistic features of Melanesian islands share many deep commonalities with the Polynesian languages, while Marshallese (which according to the sieve theory will have been one of the oldest Polynesian languages) lacks many of these features, and has many more unique features. This was the first major linguistic work showing the migration of Polynesia occurred through Melanesia, not Micronesia. He also suggested the migration occurred in two "swarms", the first travelled north of Papa New Guinea, between the Bismarck Archipelago and Solomon Islands until settling in Samoa; while the second "swarm" travelled south of New Guinea, through the Torres Straits and settled in Fiji. His work however, even by the standards of the time was very flawed, as pointed out in a review of his book in Nature: Churchill compared languages with vastly different lengths of word lists (of varying quality), leading to false conclusions \cite{Ray1911}. Later linguists took issue with Churchill's work as no attempt was at proto-language reconstructions, Churchill was notoriously poor at identifying cognates and was often fooled by  analogous terminology and performed no phoneme-grapheme correspondences (letter-sound correspondences)  \cite{Elbert_1953}. All that being said, Churchill's work was an enormous step forward for linguistic based migratory study into Polynesia.