320 James Elliot on certain 



point also back to b' ; and this process, being continued, will 

 produce the retrograde conical motion exactly as experiment 

 shows it. In this case we are not required to prove that the 

 top will not fall, since it will not do so when at rest. The 

 only effect of the production of the conical movement will be 

 to retard the tendency towards a vertical position. 



When the centre of gravity coincides with the centre of 

 motion, there will be no tendency either to fall or to rise ; 

 consequently, no conical revolution ; and the top will con- 

 tinue to revolve in any position in which it may be placed, 

 without any change either in the direction or in the inclina- 

 tion of the axis.* 



The theory I have thus attempted to establish is borne 

 out, in its main points at least, by experiment, as we have seen 

 in the different movements of the revolving sphere already de- 

 scribed. An additional instance is, that our theory leads ob- 

 viously to the conclusion that, with any given position of the 

 centre of gravity, the more rapid the rotation the slower will 

 be the conical revolution, and that this is at once confirmed 

 by trial with the same apparatus. 



The conical revolution of the axis, in the model, not only 

 illustrates that of the earth, but appears to me to depend on 

 the same or a similar cause. There are, however, some ob- 

 jections to this idea, in limine, which it may be as well to 

 dispose of first. I have already stated that this motion of 

 the top depends on the relative positions of the two centres. 

 Where, then, it will be asked, are those centres in the case of 

 the earth itself ? Before I can answer this I must come into 

 collision with one of our most common, and, I must admit, 

 most useful ideas in physics, — that of a centre of gravity. 

 It is one of those hypotheses or theories which we meet with 

 every day, answering very well all ordinary purposes, and 



* There is another movement of the top, to which in this place I can only 

 briefly allude. It may be called its erratic motion. When the pivot is not 

 confined to a point, but running upon a smooth and level surface, with the 

 axis inclined, the top describes a circular orbit, by no means capriciously, 

 but subject to given laws. Its periodic time is the same as that of one revo- 

 lution of the equinoxes, and its diameter is a fourth proportional to the time 

 of one rotation on the axis, the time of one revolution of the equinoxes, and 

 the diameter of the point of the peg where it rolls on the table. 



