560 PROFESSOR MAXWELL ON A DYNAMICAL TOP. 



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. 



The method by which M. Poinsot has rendered the theory more manageable, 

 is by the liberal introduction of " appropriate ideas," chiefly of a geometrical 

 character, most of which had been rendered familiar to mathematicians by the 

 writings of Monge, but which then first became illustrations of this branch of 

 dynamics. If any further progress is to be made in simplifying and arranging 

 the theory, it must be by the method which Poinsot has repeatedly pointed out 

 as the only one which can lead to a true knowledge of the subject, — that of pro- 

 ceeding from one distinct idea to another, instead of trusting to symbols and 

 equations. 



An important contribution to our stock of appropriate ideas and methods has 

 lately been made by Mr R. B. Hayward, in a paper, " On a Direct Method of esti- 

 mating Velocities, Accelerations/ and all similar quantities, with respect to axes, 

 moveable in any manner in Space." {Trans. Cambridge Phil. Soc. vol. x. part i.) 



* In this communication I intend to confine myself to that part of the subject 

 which the top is intended to illustrate, namely, the alteration of the position of 

 the axis in a body rotating freely about its centre of gravity. I shall, therefore, 

 deduce the theory as briefly as possible, from two considerations only, — the per- 



* 7th May 1857. — The paragraphs marked thus have been rewritten since the paper was read. 



