[From the Transactions of the Royal Society of Edinburgh, Vol. XXI. Part IV.] 



XV. On a Dynamical Top, for exhibiting the phenomena of the motion of a 

 system of invariable form about a fcced point, with some suggestions as to 

 the Earth's motion. 



(Read 20th April, 1857.) 



To those who study the progress of exact science, the common spinning-top 

 is a symbol of the labours and the perplexities of men who had successfully 

 threaded the mazes of the planetary motions. The mathematicians of the last 

 age, searching through nature for problems worthy of their analysis, found in 

 this toy of their youth, ample occupation for their highest mathematical powers. 



No illustration of astronomical precession can be devised more perfect than 

 that presented by a properly balanced top, but yet the motion of rotation has 

 intricacies far exceeding those of the theory of precession. 



Accordingly, we find Euler and D'Alembert devoting their talent and their 

 patience to the establishment of the laws of the rotation of solid bodies. 

 Lagrange has incorporated his own analysis of the problem with his general 

 treatment of mechanics, and since his time M. Poins6t has brought the subject 

 under the power of a more searching analysis than that of the calculus, in 

 which ideas take the place of symbols, and intelligible propositions supersede 

 equations. 



In the practical department of the subject, we must notice the rotatory 

 machine of Bohnenberger, and the nautical top of Troughton. In the first of 

 these instruments we have the model of the Gyroscope, by which Foucault has 

 been able to render visible the effects of the earth's rotation. The beautiful 

 experiments by which Mr J. Elliot has made the ideas of precession so familiar 

 to us are performed with a top, similar in some respects to Troughton's, though 

 not borrowed from his. 



