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. Pornsor 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 Monee, 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 Pornsor 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. Haywanrp, 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.” (Z'vrans. 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. 
