But the small motion we have discovered is neither cumulative nor continuous in one direction. It is what we call a periodic motion, the pole swinging now to one side, and now to the other, of its mean or average position. Thus this new discovery cannot be said to unravel the mysterious puzzle of the geologists. Yet it is not without the keenest interest, even from their point of view; for the proof of any form of motion in a pole previously supposed to be absolutely at rest may mean everything. No man can say what results will be revealed by the further observations now being continued with great diligence. In the first place, it is important to explain that any such motions as we have under consideration will show themselves to ordinary observational processes principally in the form of changes of terrestrial latitudes. Let us imagine a pair of straight lines passing through the centre of the earth and terminating, one at the observer's station on the earth's surface, and the other at that point of the equator which is nearest the observer. Then, according to the ordinary definition of latitude, the angle between these two imaginary lines is called the latitude of the point of observation. Now we know, of course, that the equator is everywhere just 90 degrees from the pole. Consequently, if the pole is subject to any motion at all, the equator must also partake of the motion. Thus the angle between our two imaginary lines will be affected directly by polar movement, and the latitude obtained by astronomical observation will be subject to quite similar changes. To clear up the whole question, so far as this can be done by the gathering of observational evidence, it is only necessary to keep up a continual series of latitude determinations at several observatories. These determinations should show small variations similar in magnitude to the wabblings of the pole. Let us now consider for a moment what is meant by the axis of the earth. It has long been known that the planet has in general the shape of a ball or sphere. That this is so can be seen at once from the way ships at sea disappear at the horizon. As they go farther and farther from us, we first lose sight of the hull, and then slowly and gradually the spars and sails seem to sink down into the ocean. This proves that the earth's surface is curved. That it is more or less like a sphere is evident from the fact that it always casts a round shadow in eclipses. Sometimes the earth passes between the sun and eclipsed moon. Then we see the earth's black shadow projected on the moon, which would otherwise be quite bright. This shadow has been observed in a very large number of such eclipses, and it has always been found to have a circular edge.