So Byron crossed the Pacific tracking along the usual northwesterly route between the Tropic of Capricorn and the Equator, which was more or less the course proposed for Anson's proposal back in 1749. That reversion to the 1749 plan may account for the lack of formal censure for a clear breach of his written orders. In Byron's version of events, he hoped to locate islands, specifically the long-sought Solomon Islands, first discovered in the sixteenth century but subsequently lost, along this track.
In his own words, he decided to ‘make a NW Course til we get the true Trade wind, and then to shape a Course to Wtward in hopes of falling in with Solomons Islands if there are such, or else to make some new Discovery’.
Still, that track took him too far to the north to run among the great atoll clusters of the central Pacific, so he crossed the Pacific without making significant discoveries. Several small islands in the Tuamotus, where he was unable to anchor, appear on his charts as the Islands of Disappointment, and he narrowly missed sighting Tahiti but claimed to have seen signs indicating the proximity of a southern continent:
Sunday, June 16*. Wind East with a mountainous Swell from the S°ward. For a day or two before we made the Islands of Disappointment till this day we had entirely lost that great Swell & for some time before we first made the Land we saw vast Flocks of Birds which we observed towards Evening always flew away to the S°ward. This is a convincing proof to me that there is Land that way, & had not the Winds failed me in the higher Latitudes
as mentioned before, I make no doubt but I should have fell in with it, & in all probability made the discovery of the S" Continent; Indeed if it had not been for the Sickness in both Ships, I would still have attempted it by hauling away to the S°ward immediately from those Islands. I remarked before that all the Islands we have seen are well peopled; Now if there are not a Chain of Islands reaching to the Continent how can we account for these Peoples being here, situated we may say in the middle of this vast Southern Ocean. (Byron's Journal, pp. 104-105)