The language is by Yankievich in Russian called ‘На Островѣ Атуи’. The source for the words from this language (excluding the numerals) is the vocabulary by William Anderson which appears as “Appendix V”, p. 549-553 in Vol. III of Cook and King’s “Voyage to the Pacific Ocean” (first published in 1784). The title of the Appendix is “Vocabulary of the Language of Atooi, one of the Sandwich Islands, January, 1778.” (“Atooi” is the name which Cook et al. gave to the the island now known as “Kaua’i” in the Hawaiian Islands).
References:
Cook, James and James King. 1784. A Voyage to the Pacific Ocean, undertaken, by the command of His Majesty, for making discoveries in the northern hemisphere, . . . Performed under the direction of Captains Cook, Clerke and Gore, in His Majesty’s ships the Resolution and Discovery, in the years 1776, 1777, 1778, 1779 and 1780. In three volumes: Vol. I and II written by Captain James Cook, F.R.S., Vol. III by Captain James King, LL.D. and F.R.S. . . . Published by order of the Lords Commisioners of the Admiralty. London, Printed by W. and A. Strahan for G. Nicol and T. Cadell.