He also showed how the tidal waves reached different stations in successive regular order each day; and how some places might be fed with tide by two distinct channels; and that if the time of these channels happened to differ by six hours, a high tide might be arriving by one channel and a low tide by the other, so that the place would only feel the difference, and so have a very small observed rise and fall; instancing a port in China (in the Gulf of Tonquin) where that approximately occurs. In fact, although his theory was not, as we now know, complete or final, yet it satisfactorily explained a mass of intricate detail as well as the main features of the tides. No. 16. The sun's mass being known, he calculated the height of the solar tide. No. 17. From the observed heights of spring and neap tides he determined the lunar tide, and thence made an estimate of the mass of the moon. Knowing the sun's mass and distance, it was not difficult for Newton to calculate the height of the protuberance caused by it in a pasty ocean covering the whole earth. I say pasty, because, if there was any tendency for impulses to accumulate, as timely pushes given to a pendulum accumulate, the amount of disturbance might become excessive, and its calculation would involve a multitude of data. The Newtonian tide ignored this, thus practically treating the motion as either dead-beat, or else the impulses as very inadequately timed. With this reservation the mid-ocean tide due to the action of the sun alone comes out about one foot, or let us say one foot for simplicity. Now the actual tide observed in mid-Atlantic is at the springs about four feet, at the neaps about two. The spring tide is lunar plus solar; the neap tide is lunar minus solar. Hence it appears that the tide caused by the moon alone must be about three feet, when unaffected by momentum. From this datum Newton made the first attempt to approximately estimate the mass of the moon. I said that the masses of satellites must be estimated, if at all, by the perturbation they are able to cause. The lunar tide is a perturbation in the diurnal motion of the sea, and its amount is therefore a legitimate mode of calculating the moon's mass. The available data were not at all good, however; nor are they even now very perfect; and so the estimate was a good way out. It is now considered that the mass of the moon is about one-eightieth that of the earth. * * * * * Such are some of the gems extracted from their setting in the _Principia_, and presented as clearly as I am able before you.