Mechanical Illustrations of the Planetary Motions. 315 



A, would necessarily rise. But the point B, in beginning to 

 fall, is, at the same time, carried forward from B to 6, con- 

 veying the tendency to fall with it, so that the actual fall 

 would take place at a point, 5, immediately in advance of the 

 lowest ; at the same time, the highest point, A, beginning to 

 rise, carries that rise forward to a point, a, immediately in 

 advance of the highest.* Now let us observe the effect 

 which this has produced upon the top : the point a, in advance 

 of the highest, is raised, and the point b, in advance of the 

 lowest, is depressed : this change tilts the top over, if I may 

 so express it, aside from its former inclination, bringing the 

 higher extremity of the axis from C to c, and making it now 

 lean towards the side immediately in advance of its former po- 

 sition, and, if continued, produces the slow conical revolution 

 of the axis which I have pointed out before, and an accom- 

 panying revolution of the lowest and highest point in the 

 circumference, both in the same direction as that of the ro- 

 tation. Into that conical movement, then, the tendency to 

 fall is converted.] 



* No doubt, ever}' point in the semicircumference next B, has a tendency to 

 fall, and every point in the opposite semicircumference A, to rise. But the 

 greatest rise and the greatest fall would take place at A and B, and the united 

 effects of the tendencies of all the points in each semicircumference is the same 

 as if the whole were accumulated at one point. 



t This explanation of the standing of a top is not so new as I supposed. 

 When the communication was read to the Society, and subsequently, it was 

 pointed out to me that the same thing might be found in Euler's work entitled 

 " Theoria Motus Corporum Solidorum seu Rigidorum," and also in the works 

 of Poisson and Whewell. I admit it to a certain extent, although I was pre- 

 viously ignorant of the coincidence. With regard to Euler, however, his in- 

 vestigation is altogether so obscure that it may be doubted whether the theory 

 of the top can be obtained more easily from the top itself, or from Euler's in- 

 vestigation, supposing it accurate. Throughout the whole of it, I cannot find 

 it distinctly brought out that the top's tendency to fall is converted by the ro- 

 tation into the precessional (or rather retrocessional) movement. That seems, 

 however, to be his meaning, but under symbolical expressions. At the same 

 time he clearly and distinctly assigns a cause of the top's rising to a vertical 

 position, not only different from that which I have given, but different from 

 that which he himself appears to assign as the cause of its not falling. He at- 

 tributes the rise to friction. In chapter xvii. he says expressly : — " Nunquam 

 enim turbo magis fiet erectus quam fuerat initio, siquidem nulla affuerit fric- 

 tio." Now the cause to which I ascribe the rise (whether correctly or not), 



