C. B. WARRING. 153 



of an inch in diameter. In one case, the curves began, 

 say, three-eighths of an inch in diameter, gradually grew 

 a little smaller, and then as gradually grew larger. In 

 another case the spiral was decidedly smaller at the 

 beginning than at the end. 



When the point is not properly centered, each line will 

 seem strung with dew-drops placed with the utmost 

 regularity, each corresponding to a revolution of the top 

 on its axis. 



It may help us to see the reason for the varying size 

 of these spirals, if we reflect that the less the friction of 

 the "point'' the greater the distance from o, fig. 30, the 

 center of the gyrations, to d, the point of contact, and 

 consequently the greater the radius of the curve de- 

 scribed. The rolling of the ''point" always tends to in- 

 crease the rate of gyration ; but its influence varies 

 directly as its size (diameter), and inversely as its dis- 

 tance from the center of the spiral, and also directly as 

 the rotation of the top. 



As the top rises, g, the projection of the center of 

 gravity (fig. 30), moves nearer to d, and consequently 

 the distance from o, the centre of gyration, to d, grows 

 less, and therefore the spirals also grow smaller, at last 

 becoming only a point. 



The abnormal forms which sometimes occur are due to 

 changes of condition which it is not always easy to trace, 

 but which are reducible to the same principles. 



THE GYROSTAT. 



This instrument was invented by Sir William Thom- 

 son. It is described in Thomson & Tait's Natural PJii- 

 losophy, page 397, also in Nature, Yol. xv., page 297. 

 In both of these tliere is a drawing of it. As there repre- 

 sented, it is rather an expensive and formidable instru- 

 ment ; but, at a very trifling expense, any gyroscope 

 can be turned into an excellent gyrostat. 



137 



