ON A DYNAMICAL TOP. 249 



The top which I have the honour to spin before the Society, differs from 

 that of Mr Elliot in having more adjustments, and in being designed to exhibit 

 far more complicated phenomena. 



The arrangement of these adjustments, so as to produce the desired effects, 

 depends on the mathematical theory of rotation. The method of exhibiting the 

 motion of the axis of rotation, by means of a coloured disc, is essential to the 

 success of these adjustments. This optical contrivance for rendering visible the 

 nature of the rapid motion of the top, and the practical methods of applying 

 the theory of rotation to such an instrument as the one before us, are the 

 grounds on which I bring my instrument and experiments before the Society 

 as my own. 



I propose, therefore, in the first place, to give a brief- outline of such parts 

 of the theory of rotation as are necessary for the explanation of the phenomena 

 of the top. 



I shall then describe the instrument with its adjustments, and the effect of 

 each, the mode of observing of the coloured disc when the top is in motion, and 

 the use of the top in illustrating the mathematical theory, with the method of 

 making the different experiments. 



Lastly, I shall attempt to explain the nature of a possible variation in the 

 earth's axis due to its figure. This variation, if it exists, must cause a periodic 

 inequality in the latitude of every place on the earth's surface, going through its 

 period in about eleven months. The amount of variation must be very small, 

 but its character gives it importance, and the necessary observations are already 

 made, and only require reduction. 



On the Theory of Rotation. 



The theory of the rotation of a rigid system is strictly deduced from the 

 elementary laws of motion, but the complexity of the motion of the particles of 

 a body freely rotating renders the subject so intricate, that it has never been 

 thoroughly understood by any but the most expert mathematicians. Many who 

 have mastered the lunar theory have come to erroneous conclusions on this sub- 

 ject ; and even Newton has chosen to deduce the disturbance of the earth's axis 

 from his theory of the motion of the nodes of a free orbit, rather than attack 

 the problem of the rotation of a solid body. 



VOL. I. 32 



