420 



THE POPULAR SCIENCE MONTHLY 



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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. 2 

 In Fig. 3 let PP r be the axis of figure and P'P^ the position of the 

 axis of rotation at a time when P and P' lie in the meridian of the 

 place of observation 0, and let E'E{ 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"P", the equator line will have shifted to E"E", 

 and the latitude of the place will have changed from E'O to E"0, 

 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 

 will again be E'O and it will oscillate between the maximum value 

 E'O and the minimum value E"0. The reader should bear in mind 

 that the figure is grossly exaggerated, the actual value of the angle % 

 being less than one half of a second of arc. If the angle % 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 



2 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 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. 



