Establishing latitude and longitude involved calculating the positions of the sun, moon, planets and stars, then comparing them with those at known locations or times. Instruments such as the quadrant and sextant were used to measure the angles between celestial bodies or between a body and the horizon. Published tables gave information about these bodies at set places or times. Spherical trigonometry applied to this data gave the position of the ship.
The invention of the chronometer greatly improved the calculation of longitude. The chronometer was set to Greenwich time which, when compared to local time, gave the longitude. Matthew Flinders had a chronometer on the Norfolk voyage to Hervey Bay and several on Investigator. The chronometer was still in its infancy and Flinders verified its readings with the earlier methods for calculating longitude. It was not until 1803 that Thomas Earnshaw developed an affordable, accurate chronometer.