accurately measuring the angular distance between the centres of the moon and of the sun, or of the moon and some star.
The motion of the moon is so rapid that this angular distance changes from second to second, and thereby, by previous astronomical calculation, the time at Greenwich at which its distance from any body is a certain number of degrees can be ascertained and recorded.
By well-known calculations the local time at any spot can be obtained, and when this is ascertained, at the precise moment that the angular distance of sun and moon is observed, the difference gives the longitude.
This seems simple enough, but there is a good deal of calculation to go through before the result is reached, and neither the observation nor the calculation is easy, especially with the astronomical tables of those days, and there were very few sailors who were capable of, or patient enough to make them, nor was the result, as a rule, very accurate. For one thing, the motions of the moon, which are extremely complicated, were not enough known to allow her calculated position in the heavens to be very accurate, and a very small error in this position considerably affects the time, and therefore the longitude.
Luckily for Cook, the Nautical Almanac had just been started, and contained tables of the moon which had not previously been available, and which much lightened the calculations.
The great invention of the chronometer, that is, a watch that can be trusted to keep a steady rate for long periods, was at this time completed by Harrison; but very few had been manufactured, and astronomers and sailors were slow to believe in the efficacy of this method of carrying time about with a ship. Thus Cook had no chronometer supplied to him.
Green had accompanied Mr. Maskelyne, afterwards Astronomer Royal, to Barbados in 1763 in H.M.S. Princess Louisa, in order to test Harrison's timekeeper, and also a complicated chair, from which it was supposed observations of Jupiter's satellites could be observed on board ship; and as this trial afforded the final triumph of the new method, one would have thought that on a voyage of circumnavigation he would have made every effort to get one of these watches.
Be this as it may, the Endeavour had no chronometer, and lunars were the mainstay of the expedition.
In these observations Green was indefatigable. Cook, an excellent observer himself, frequently took part in them; but it was Green's especial business, and no doubt to him is due the major part of the determinations of accurate longitude, which is one of the very remarkable points of this voyage.
