1854.] OF THE ROYAL INSTITUTION. 395 
length near the end carrying the bar, upon a horizontal axis, 
capable of moving freely round a vertical pillar. At the lower end 
of the first axis is a weight which more than counterpoises the 
upper part. 
If then there be no rotation in the bar about the first axis, the 
effect of the weight is to produce a rotation about the second alone, 
bringing down the first axis into a vertical position. 
If now the first axis be held horizontally or obliquely, and a rota- 
tory motion be given to the bar about it, on letting the axis go, we 
compound both rotations ; and the resulting effect is, that the weight 
will no longer bring the axis down, or alter its inclination at all: 
but will cause it to take a new position, or make the whole to turn 
round the vertical, in a direction opposite to that of the rotation. 
Thus, although confessedly not new in principle, to make public 
an experimental illustration in so simple a form may not be without 
its use for a great majority of students. 
Even the theoretical principle is capable of being stated in a way 
quite intelligible to those acquainted only with the very first rudi- 
ments of theoretical mechanics, presenting itself in close analogy 
to that well known first principle, the composition of rectilinear 
motion. 
As in this last case, if a body be in motion in one direction, and 
any cause tend to make it move in another, it will move in neither, 
but in an intermediate direction,—so we have the strictly analogous 
case in rotatory motion; when a body is rotating about an axis, and 
any cause tends to make it rotate about another axis, it will not 
rotate about either, but about a new axis intermediate to the two. Thus 
the result of compounding the two rotations will be, that the axis 
(carrying with it the rotating body) will simply take a new position, 
or will move ina direction determined by the nature of the impressed 
motions. 
Professor Magnus, in the very able, but rather prolix and obscurely 
written Memoir, before referred to, speaks (p. 223) of the conse- 
quences of such a law as evinced in the resulting rotations, but without 
any distinct or explicit statement of the essential theorem of the 
composition of rotatory motion. He gives, however, some singular 
and even paradoxical exemplifications of it. We may allude to one 
of these, which is capable of being put into a form at once more 
simple, and at the same time more paradovical, than that in which 
he describes it. It consists in this: a wheel at one end of an axis, 
and a weight at the other, are suspended in equilibrio ; which is, of 
course, unaltered, whether the wheel be at rest or in rotation: the 
weight is then slid so that the balance is destroyed: now if the wheel 
be set in rapid rotation, the equilibium is restored. This is nothing 
but a simple case of the principle just stated, as shewn by the author’s 
apparatus. 
Besides certain other cases traceable to a different cause, Professor 
Magnus’s immediate object is to explain a curious observed anomaly 
