Page:Popular Science Monthly Volume 75.djvu/424

Fig. 2. The upper figures denote the number of stars observed, the lower figures, the number of days on which observations were made.

explained through the assumption of a revolution of the axis of rotation about the shortest axis of the earth, or the axis of figure as it is called.^[1] In Fig. 3 let PP₁ be the axis of figure and P′P₁′ the position of the axis of rotation at a time when P and P′ lie in the meridian of the place of observation O, and let E′E₁′ be the line in which the plane of the equator cuts the meridian plane of this place. If now the axis of rotation is given a motion of revolution about the axis of figure, then when one half a revolution has been completed the axis of rotation will be in the position P″P₁″, the equator line will have shifted to E″E₁″, and the latitude of the place O will have changed from E′O to E″O, the whole change in the latitude, E′E″ being 2i, or twice the angle between the axis of figure and the axis of rotation. After a complete revolution of the axis has been accomplished the latitude of the place O will again be E″O and it will oscillate between the maximum value E′O and the minimum value E″O. The reader should bear in mind that the figure is grossly exaggerated, the actual value of the angle i being less than one half of a second of arc. If the angle i remains constant and the axis of rotation revolves about the axis of figure with a uniform speed then the place of observation will apparently swing back and forth in its meridian through an arc equal to 2i. If the

1. The usual statement of the problem is the converse of that just given, that is, that the axis of figure revolves about the axis of rotation, but the effect is the same, provided the distance from O to the end of the shortest axis remains constant, and for purposes of illustration the above statement of the problem seems simpler. The direction of the axis in space remains nearly fixed, but its position within the earth is not fixed.