The lunar method for longitude amounts practically to this. The stars are fixed; the sun, moon, and planets move amongst them; the sun and planets with very slow rates of apparent motion, the moon with a very rapid one. If, then, it be predicted that at a certain instant of Greenwich time the moon will be a certain distance from a fixed star, and if the mariner at sea observes _when_ the moon has that exact distance, he will know the Greenwich time at the instant of his observation.[20] The moon thus becomes to him as the hand of a timepiece, whereof the stars are the hour and minute marks, the whole being, as it were, set to Greenwich time. Then if he knows (which he does by other observations easily obtained) the local time at his ship, he can take the difference between the Greenwich time and his time, which difference is in fact his longitude from Greenwich. The requisite predictions of the distance of the moon from several fixed stars near her are given to the utmost exactness for every three hours of every day and night (when the moon can possibly be seen) in the navigator’s _vade mecum_, the “Nautical Almanac,” and from these given distances the navigator can, by a simple process of differencing, obtain the distance, and hence the Greenwich time, for any intermediate instant at which he may chance to make his observation. Whenever he can see the moon he can obtain Greenwich time. Of course the whole value of this method depends upon the exactitude of the predicted distances corresponding to the given Greenwich times. These distances are obtained by tables of the moon’s motions, which must be found from observations. The motions in question are of an intricacy almost past comprehension, on account of the disturbing forces to which the moon is subjected by the sun and planets. The powers of the profoundest mathematicians, from Newton downwards, have been severely exercised in efforts to group them into a theory, and represent them by tables capable of furnishing the requisite exact predictions of lunar positions for nautical purposes. Accurate observations of the moon’s place night after night have, from the dawn of this lunar method for longitude, been in urgent request by mathematicians for the purposes specified, and it was solely to procure these observations that the Observatory at Greenwich was established, and mainly for their continued prosecution (and for the stellar observations necessary for their utilization) that it is sustained. For two centuries the moon has been unremittingly observed at Greenwich, and the tables at present used for making the “Nautical Almanac” (those formed by Prof. Hansen) depend upon the observations there obtained. The work still goes on, for even now the degree of exactitude is not what is desired, and astronomers are looking forward with some interest to new lunar tables which were left complete by the late M. Delaunay, formerly the head of astronomy in France, based upon a theory which he evolved.