564 SCIENCE PROGRESS 



and with rigid accuracy by Professor Greenhill in his articles 

 in the Encyclopedia Britannica. It is sufficient here to state 

 shortly the facts. Take the case of the spinning-top. This, 

 if not spinning, would fall over, the toppling-over effect of 

 gravity being greater as the inclination is greater. When 

 the top is spinning the forces due to gravity are the same as 

 before, tending to drag the axis of spin over and downwards, 

 but in consequence of the spin it has a different effect : the 

 axis does not move downwards but sideways, always at right 

 angles to the direction in which it is urged, and so the top 

 gyrates. Further, the rate of moving sideways is greater as 

 the rate of spin is less. If the point on which the top spins 

 is adjustable so that it may be made to project more or less, 

 or may be withdrawn until it is above the centre of gravity, 

 then as it is fixed nearer to the centre of gravity the toppling 

 effect of gravity will be less and the top will gyrate more slowly. 

 When the point on which it spins is at the centre of gravity the 

 toppling effect of gravity is destroyed, and so it ceases to gyrate, 

 and when the point is raised higher still gravity tends to topple 

 no more, but to set it upright : it then gyrates the other way. 

 When gravity acts so as to make it fall it gyrates in the same 

 direction as it spins ; when gravity acts so as to set it upright 

 it gyrates in the opposite direction. An example of a slow 

 gyration of this sort is presented by the earth, which would, 

 if it were spherical, maintain the direction of its axis of rotation 

 indefinitely. Any star in the line of this axis would be for 

 all time the pole star. Both the sun and moon in their attraction 

 upon the " equatorial protuberance," or excess of matter outside 

 the sphere, act in such a manner as to drag it towards the plane 

 of the ecliptic, or the earth's orbit round the sun. If this is 

 looked upon as a level, then the sun and moon act together so 

 as to set the top upright. The gyrations then are in the 

 opposite direction to the spin, which is also the direction 

 of revolution round the sun, and so the " equinoxes precess." 

 The pole of the earth describes a circle round the pole of the 

 ecliptic once in about twenty-six thousand years. 



When a spinning body of other shape than a ball is projected 

 through the air, the effects of the air upon the direction of the 

 axis of spin, and hence on the motion of the body, give rise to 

 numerous interesting problems. For instance, a disc spun and 

 thrown by the right hand edgeways turns so that the right side 



