168 AN EMPIRICAL STUDY OF GYRATING BODIES. 



the weight which causes them to tilt— and which, for 

 convenience, may be called the tilting force, acts upon a 

 point in the axis, or axis produced, and it may be thought 

 by some who have not reflected upon the matter, that a 

 force applied elsewhere might not produce the same ef- 

 fect. To make the case as different as possible, we will 

 suppose the second force to be parallel to the axis, and 

 applied at the equator, but in such a way as to allow per- 

 fect freedom of rotation — a thing easily imagined but not 

 easily attained with laboratory appliances. Furthermore, 

 because it suits my purpose better, we will suppose the 

 gyrating body to be a sphere. If we imagine this force 

 to pull upon an inextensible cord running to the pole, 

 and moving without friction over the surface as the body 

 revolves, we shall have the same amount of force tangent 

 at the pole, acting in the same plane, and tilting the body 

 in the same sense. Hence, so far as tilting is concerned, 

 we may indifferently speak of a force perpendicular to 

 the equator, or to the axis at the pole, provided the 

 plane in which it lies is the same. 



It is hardly necessary to remark that the size of the 

 gyrating body is a matter of indifference ; whether, for 

 example, it be one inch in diameter, or eight thousand 

 miles, since all bodies are equally obedient to the laws 

 of motion. We may, therefore, apply gyroscopic laws 

 to the movements of our earth as if it were no larger 

 than our gyroscopes and Bohnenberghers. 



If our earth were a perfect sphere, it would revolve 

 upon its axis and travel on its journey around the sun, 

 as now. The moon would accompany it, and would wax 

 and wane as now, and to all, save to astronomers, there 

 would be no difference between what would then appear, 

 and what we now see. In such a case, the attraction of 

 other bodies would have no tendency to change the 

 direction of the earth's axis, since the influence upon one 



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