1831 .] 
Philosophy in Sport. 
23 
Notes on the above passages. 
(a) You will observe the non sequitur which occurs here. In consequence of his 
dropping a link in the chain of his argument, the Author is led to the false conclu- 
sion, that a top sleeping upon a plane inclined to the horizon will have its axis 
of rotation perpendicular, not to the horizon, but to the inclined plane, (bj 
To suit his theory, the author here converts friction into impulse, powers 
which are wholly dissimilar. Friction, in this case, would act only by retarding the 
motion of the top, and causing it to gyrate as explained by Dr. Arnott (see Glean- 
ings, vol. i. p. 368). It is true, that this friction may, from irregularities in the he- 
mispherical shoulder of the top, and of the surface on which it revolves, and from the 
elasticity of both bodies, be accompanied by a bounding motion of the top ; but this 
very phenomenon is fatal to Dr. Paris’s theory; according to which, these bounds 
ought to consist in a slight depression of the lower end of the axis of rotation, and a 
raising of the other, this slight revolution being performed round an imaginary 
centre of motion, placed betweeen the tangential portion of the shoulder and the 
lower end of the axis of rotation. Now it is remarkable, that the actual phenome- 
non is the reverse of this ; consisting in a raising of the lower end of the axis of rota- 
tion and depression ol the upper ; and for this very obvious reason, that the top’s 
centre of inertia is placed between the shoulder, and not the lower end of the axis, 
but the upper. Dr. Paris has overlooked the position of the top’s centre of inertia, 
and accordingly misstated the consequence of an impulse applied to the shoulder of 
the peg, besides making the inadmissible supposition, that friction is impulse : and 
his theory, like Dr. Arnott’s, is disproved by the fact, that a top may sleep perpendi- 
cularly to the horizon, on a plane inclined to the horizon, in which situation it would, 
according to these authors, of necessity gyrate or sleep in a position perpendicular 
to the said plane, (c) As Dr. Paris has not favored the world with the details of the 
reasoning from which he traces an analogy between the precession of the equinoxes 
and the gyrations of a top, I can only state, that it is invisible to me, and that Dr. 
Arnott’s explanation is quite satisfactory. 
Of the last paragraph above transcribed, some conclusions are not deducible from 
what preceded ; part is unintelligible, and altogether it has the air of a crude transla- 
tion from the French. I shall quit this subject with remarking, as the explanation 
which I attempted in the 1st vol. of the Gleanings , p. 368, is probably original, and as 
Dr. Paris says, that the subject has been unduly neglected, that the word special, 
which appears there, is a misprint for spiral. 
The Swing. — It struck me, on looking over the above work, that an excellent il- 
lustration of the pendulum might have been drawn from the facility with which a 
person standing in a swing can extend its excursions at pleasure, by swaying the 
upper part of his body forwards when he is at the forward limit of the oscillation, 
and backwards when at the backward limit ; thereby forcibly carrying the centre op 
oscillation beyond the point which it would have attained, if the person had remained 
passive, and so extending the limits of each oscillation by the impetus thus acquired. 
I have read Dr. Lardner’s treatise on Mechanics, in his Cyclopaedia ; and, as far 
as I can judge, it is a correct, though, from its limits, necessarily a slight work. 
One mistake the Author has committed, while searching for a familiar illustration of 
expansion by heat, — a thing which is not easily found. At p. 22 he states, as an in- 
stance of this kind, that “ in warm weather, the flesh swells, the vessels appear filled, 
the hand is plump, and the skin distended,” apparently unaware that this distension 
is merely a consequence of the relaxation of the sanguiferous tubes, and the greater 
facility with which the blood then enters them. 
These observations may appear hypercritical ; but in works especially addressed 
to the general reader under the sanction of great names, it is reasonable to expect 
