Five of Maxwells Papers | Page 3

our eye the motion of a rotating body, we find it
difficult to determine through what point of the body the instantaneous
axis passes at any time,--and to determine its path must be still more
difficult. I have endeavoured to render visible the path of the
instantaneous axis, and to vary the circumstances of motion, by means
of a top of the same kind as that used by Mr Elliot, to illustrate
precession*. The body of the instrument is a hollow cone of wood,
rising from a ring, 7 inches in diameter and 1 inch thick. An iron axis, 8
inches long, screws into the vertex of the cone. The lower extremity has
a point of hard steel, which rests in an agate cup, and forms the support
of the instrument. An iron nut, three ounces in weight, is made to screw
on the axis, and to be fixed at any point; and in the wooden ring are
screwed four bolts, of three ounces, working horizontally, and four
bolts, of one ounce, working vertically. On the upper part of the axis is
placed a disc of card, on which are drawn four concentric rings. Each
ring is divided into four quadrants, which are coloured red, yellow,
green, and blue. The spaces between the rings are white. When the top
is in motion, it is easy to see in which quadrant the instantaneous axis is
at any moment and the distance between it and the axis of the
instrument; and we observe,--1st. That the instantaneous axis travels in
a closed curve, and returns to its original position in the body. 2ndly.
That by working the vertical bolts, we can make the axis of the
instrument the centre of this closed curve. It will then be one of the
principal axes of inertia. 3rdly. That, by working the nut on the axis, we
can make the order of colours either red, yellow, green, blue, or the
reverse. When the order of colours is in the same direction as the
rotation, it indicates that the axis of the instrument is that of greatest
moment of inertia. 4thly. That if we screw the two pairs of opposite
horizontal bolts to different distances from the axis, the path of the
instantaneous pole will no longer be equidistant from the axis, but will
describe an ellipse, whose longer axis is in the direction of the mean
axis of the instrument. 5thly. That if we now make one of the two
horizontal axes less and the other greater than the vertical axis, the
instantaneous pole will separate from the axis of the instrument, and the
axis will incline more and more till the spinning can no longer go on,
on account of the obliquity. It is easy to see that, by attending to the

laws of motion, we may produce any of the above effects at pleasure,
and illustrate many different propositions by means of the same
instrument.
* Transactions of the Royal Scottish Society of Arts, 1855.
*** Address to the Mathematical and Physical Sections of the British
Association.
James Clerk Maxwell
[From the British Association Report, Vol. XL.]
[Liverpool, September 15, 1870.]
At several of the recent Meetings of the British Association the varied
and important business of the Mathematical and Physical Section has
been introduced by an Address, the subject of which has been left to the
selection of the President for the time being. The perplexing duty of
choosing a subject has not, however, fallen to me.
Professor Sylvester, the President of Section A at the Exeter Meeting,
gave us a noble vindication of pure mathematics by laying bare, as it
were, the very working of the mathematical mind, and setting before us,
not the array of symbols and brackets which form the armoury of the
mathematician, or the dry results which are only the monuments of his
conquests, but the mathematician himself, with all his human faculties
directed by his professional sagacity to the pursuit, apprehension, and
exhibition of that ideal harmony which he feels to be the root of all
knowledge, the fountain of all pleasure, and the condition of all action.
The mathematician has, above all things, an eye for symmetry; and
Professor Sylvester has not only recognized the symmetry formed by
the combination of his own subject with those of the former Presidents,
but has pointed out the duties of his successor in the following
characteristic note:--
"Mr Spottiswoode favoured the Section, in his opening Address, with a
combined history of the progress of Mathematics and Physics; Dr.

Tyndall's address was virtually on the limits of Physical Philosophy;
the one here in print," says Prof. Sylvester, "is an attempted faint
adumbration of the nature of Mathematical Science in the abstract.
What is wanting (like a fourth sphere resting on three others