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From: http://www.captcook-ne.co.uk/ccne/gallery/gallery4.htm

Vaitepiha Bay, Tahiti
18 – 23 August 1773

Matavia Bay, Tahiti
26-31 August 1773

Huahine
2-7 September 1773
(Called again 15-22 May 1774)

Raiatea
9-18 September 1773
(Called again 25 May- 4 June 1774)

It may be the Antoine has the correct lat and long for 7 Sept, and Cook does not get to Raiatea until the 9th.

And from: http://www.mostlymaps.com/reference/The-Voyages-of-Captain-Cook/2nd-voyage.php

Entertainments were provided for the visitors but provisions were in short supply and so on 1st.September the two ships sailed to Huahine and the other Society Islands. On reaching Huahine the next day Cook was welcolmed by the island chief Ori and gifts were exchanged. Here, supplies were plentiful but unfortunately the naturalist Anders Sparman while inland, was robbed and stripped which resulted in a tense atmosphere but the matter was resolved peaceably and on 7th September the ships set sail with the addition of a passenger, Mai, on board the Adventure who was later to gain fame in London. They sailed across to Raiatea and headed for the anchorage at Rautoanui making and ammending charts as they went. They again received a warm welcolme from the chief, Orio who laid on dancing and musical entertainments every day of their visit. Provisions were obtained and the ships left on 17th September but instead of returning straight to New Zealand as Cook had originally intended they decided instead to make for the Tongan Islands which Tasman had visited in 1643. Relations with the...

And:http://pages.quicksilver.net.nz/jcr/~cookbio3.html

The ships sailed on September 1st for Huahine and the other Leeward Islands of the Society Islands.

Huahine was reached the next day and Cook sailed the Resolution through Passe Avapeihi to anchor near Fare. He had to send his boats though to assist the Adventure, which nearly hit the reef. Ori, who was still Chief on Huahine, greeted Cook warmly and gifts and compliments were exchanged. Unlike Tahiti provisions were in good supply and trade was brisk. Sparrman went inland where he was robbed and stripped, which led to a tense situation. Ori offered himself as hostage but the matter was quickly sorted out and, since the ships were ready, Cook determined to leave. On September 7th they sailed with an extra passenger on the Adventure. This was Mai (later known as Omai) who would gain fame in London.

They sailed across to Raiatea and rounded the south end of the island. Cook modified his charts as he sailed past, fixing the islands of Haaio and Nao Nao and Vaihuti Bay, before reaching the anchorage at Passe Rautoanui. Orio, the Chief welcomed Cook lavishly with entertainments, dancing, theatre and music every day of the visit. Pickersgill was charged with obtaining fresh supplies and even went north to Tahaa for fresh pigs. The ships left Raiatea on September 17th and Cook, having changed his mind about returning straight to New Zealand, headed instead for some islands, the Tonga Group, that Tasman had visited in 1643.
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