204 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1914. 
the pendulum to one side, and let go, either from rest, or with a 
certain amount of sidelong motion, when yot observe that the pen 
describes a flower-shaped path. (Fig. 11.) The path is shown for 
different amounts of sidelong motion. The peculiar appearance of 
these curves is due to the rapid falling off of amplitude produced by 
friction. 
When the flywheel is revolving there are, in general, two couples 
acting on the pendulum, one due to gravity, the other due to gyro- 
static action. At an instant at which the axis of the gyrostat is 
vertical the former couple is zero, and the latter one is a maximum, 
for at that instant the angular velocity with which the axis of the 
gyrostat is changing direction is greatest. When the pendulum is 
at one extremity of its swing the former couple is a maximum, and 
the latter one is zero. At that instant the deflection of the bob from 
the vertical is a maximum, and it is at rest, or is moving sidewise, 
according to the mode of starting, except in so far as the initial 
conditions have been interfered with by friction. By this relation 
of the couples the form of the path can be explained. 
Another mode of motion is possible which has a very mtimate 
connection with the theory of vibrations of light-emitting molecules 
in a magnetic field, as indeed I pointed out here several years ago in 
a Friday evening discourse.t| The bob can be made to move in a 
circle about the vertical through the point of support either with or 
against the direction of rotation of the flywheel. The two periods are 
different, and the motions correspond to the circularly polarized light 
of two distinct periods, which molecules, situated in a magnetic field, 
are found to emit. Thus the gyrostatic pendulum gives a dynamical 
analogue of the cause of the Zeeman effect. 
In 1907 Herr Otto Schlick introduced a method of employing 
a gyrostat to counteract the rolling of a vessel at sea. The gyrostat 
is carried on bearings placed athwart the ship. These bearings are 
in line with the flywheel, and a weight is attached to the frame of 
the gyrostat in a position in line with the axis. It will be seen that 
when the ship is on even keel the gyrostat rests with its axis vertical, 
and with the weight vertically below the center of gravity of the | 
flywheel. Heeling of the ship in one direction causes the gyrostat 
to precess in one direction on the bearings on which it is mounted; 
heeling in the other direction causes precession in the opposite 
direction, and couples resisting the rolling motion are brought to 
bear on the ship. The device may be employed in two ways. In 
the first place, if the bearings on which the frame of the gyrostat is 
carried within the ship are smooth, the effect of the gyrostat is to 
resist the rolling force of the waves, and to bring about a lengthen- 
ing of the free period of the ship, according to a mathematical theory 
1 See Nature, Apr. 13, 1899, and Aug. 24, 1899. 
