The ship set sail in August of 1768 in anticipation of the transit that would occur the following June. Their destination was Tahiti, a tiny island of about 400 square miles that had become known to Europeans only one year earlier. It was a dangerous mission: "We ... took our leave of Europe for heaven alone knows how long, perhaps for Ever," wrote Joseph Banks, a young botanist on board the ship.
At the time, astronomers knew six of the planets in orbit around the sun (Mercury, Venus, Earth, Mars, Jupiter, and Saturn) and they knew, basically, the relative distances among them -- for example, that Jupiter was five times farther than the Earth from the sun. But absolute distances -- kilometers or miles -- were as yet unknown. A century earlier, Edmund Halley (of Halley's Comet fame) had developed a trigonometric method for getting the absolute distance, a formula that was simplified by French astronomer Joseph-Nicolas Delisle. The only catch was, they needed data from a transit, and there wasn't going to be one until 1761.
The transit of 1761 came and ... went. The data collected during the transit wasn't very good, due to weather, logistics, and observers' inexperience. Thankfully, they only needed to wait eight years until another transit, and this time they would be ready. They had to be, because the next one wasn't going to happen for another 105 years -- meaning, all of the astronomers alive in 1769 would go to their graves not knowing the answer to one of the biggest questions in their field.
And so they sailed; they sailed for eight months, making landfall in April of 1769, leaving them two months to set up their observatory. Other teams were making similar preparations in Philadelphia, St. Petersburg, the Hudson Bay, and Baja, California (two solid observation points were required for Halley and Delisle's formula). Cook's team had lost six of its 94 men en route, but, the rest had made it in time. "At this time we had but very few men upon the Sick list ... the Ships compney had in general been very healthy owing in a great measure to the Sour krout," Cook wrote.
For two months they waited, and then, finally, the day came. Cook described it in his journal:
This day prov'd as favourable to our purpose as we could wish, not a Clowd was to be seen the Whole day and the Air was perfectly clear, so that we had every advantage we could desire in Observing the whole of the passage of the Planet Venus over the Suns disk: we very distinctly saw an Atmosphere or dusky shade round the body of the Planet which very much disturbed the times of the contacts particularly the two internal ones.
But something was wrong. The different observers in Tahiti were looking at the same transit, but getting different measurements for the exact time that Venus "touched" the sun. "We differ'd from one another in observing the times of the contacts much more than could be expected," he wrote.