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

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

 Earth's motion. By J. C. Maxwell, B.A., Professor of Natural Philosophy 

 in Marischal College, Aberdeen. 



(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, search- 

 ing 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 in- 

 tricacies 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. La- 

 grange has incorporated his own analysis of the problem with his general treat- 

 ment of mechanics, and since his time M. Poinsot 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 in- 

 struments 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 experi- 

 ments 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. 



The top which I have the honour to spin before the Society, differs from that 

 of Mr Elliot in having more adjustments, and in being designed to exhibit far 

 more complicated phenomena. 



The arrangement of these adjustments, so as to produce the desired effects, 

 depends on the mathematical theory of rotation. The method of exhibiting the 

 motion of the axis of rotation, by means of a coloured disc, is essential to the 

 success of these adjustments. This optical contrivance for rendering visible the 

 nature of the rapid motion of the top, and the practical methods of applying the 

 theory of rotation to such an instrument as the one before us, are the grounds on 

 which I bring my instrument and experiments before the Society as my own. 



I propose, therefore, in the first place, to give a brief outline of such parts of 



VOL. XXI. PART IV. 7 M 



