316 James Elliot on certain 



But the demonstration is as yet incomplete ; for, although I 

 may have shown that the point which was the lowest at first 

 will no longer be the lowest, unless I can also show that 

 the neiu lowest point will not be lower than that which was 

 previously the lowest point, the top will fall, in spite of this 

 secondary preserving motion. How, then, can it be esta- 

 blished that it will not be so % It cannot be proved gene- 

 rally : to do so would be to prove too much ; for a top some- 

 times does fall : but the same theory, a little extended, will 

 show under what circumstances it will fall, and under what 

 it will not. 



The same things being assumed as before, let us further 



has no connection whatever with friction, and is the very same with that which 

 I have maintained prevents its fall. Practically also I have endeavoured to 

 deprive my model of friction as far as possible, and yet it rises equally well. 

 No doubt the peg is prevented from sliding or rolling from its place by con- 

 finement to the agate cup, and if that were what Euler means by friction, or 

 if it served the same purpose, the matter would be simple enough; but he ap- 

 pears himself expressly to say otherwise ; for he goes on : — " At frictio cessare 

 nequit nisi cuspis turbinis in eodem loco persistat," indicating clearly that he 

 does not consider confinement of the peg to a particular place as identical 

 with friction. In fact it is on this last statement that a peculiar position is 

 taken by a writer in the Cambridge Journal (in an article also pointed out to 

 me when the first part of this communication was read to the Society), who 

 attempts to explain and support Euler. He offers to rest the practical proof 

 of Euler's theory on the fact that a top cannot be made to rise when spinning 

 on a very fine point. I showed to the Society a top rising to a vertical position, 

 and spinning perfectly well on the point of a fine sewing needle. 



Poisson is much more clear in regard to the conversion of the fall or rise into 

 the conical motion of the axis, but I cannot find that he enters into any expla- 

 nation of a top of the common form (that is, with the centre of gravity above 

 the point of support) rising towards a vertical position. Still his demonstrations 

 are quite sufficient for establishing my main point, the identity of the top's 

 motions with those of the earth in their principle; and if I had seen his work 

 previously, I might have satisfied myself with quoting it, instead of entering 

 so fully into the subject. 



Professor Whewell follows pretty closely in Euler's track, adhering to the 

 same cause assigned by the latter for the rising of the top, viz., friction, but 

 putting it forward with hesitation, and not supporting it by any demonstra- 

 tion. {Dynamics, Book iii., Sect, ii.) 



I have also been referred to the Lectures and Tracts of Professor Airy. 

 These bring out the theory clearly and explicitly with reference to the earth it- 

 self : but in regard to it, I have advanced nothing as new : my subject is — not 

 the earth, but the model. 



