194 ANNUAL OF SCIENTIFIC DISCOVERY. 



rotation. This can be shown experimentally by pressing with the fingers upon 

 these two parts of the edge. As soon as the motion round the vertical axis 

 begins, the horizontal components of the original rotation no longer retain 

 their parallelism with the disc. But the tendency to preserve this parallelism, 

 in other words, the tendency of the disc to preserve unchanged its plane of 

 rotation, generates forces which act on the top of the wheel to the left and on 

 the bottom of the wheel to the right. These forces, acting by leverage, tend to 

 lift the wheel, as may be seen by pressing in the same way with the fingers. 

 When friction is excluded, this uplifting force is an exact balance of gravity, 

 and the wheel neither rises nor falls. 



" The results of these experiments are remarkable, as showing how differ- 

 ently gravity acts upon a body at rest and upon the same body in motion. 

 "When it acts upon a body at rest, it tends to give it a motion round a hori- 

 zontal axis, but not about a vertical axis. "When a body is rotating in a ver- 

 tical plane, gravity tends to give it no descending motion round a horizontal 

 axis, but simply to turn it upon a vertical line. This apparent mechanical 

 paradox is beautifully illustrated in the Precession of the Equinoxes. The dis- 

 turbing influence of the sun and moon, which represent the gravity to be con- 

 sidered in this astronomical example, would make the equator drop down into 

 coincidence with the ecliptic, if the earth were not spinning on its axis, and 

 would make the precession an unknown phenomenon. But the same forces, 

 acting upon the rotating earth, move the line of equinoxes backward, 

 and leave the obliquity essentially unchanged. It follows, from the experi- 

 mental illustration, as well as from the mathematical theory, that, if the disturb- 

 ing forces were greater, the precession would be greater ; and if the earth's rota- 

 tion were diminished, cceteris paribus, the precession would be increased. 



2. The Polytrop of Magnus consists of two rotating vertical discs, arranged 

 upon an axle as the two wheels of a carriage. These discs can be set in motion 

 by cords wound upon the hub of each disc, the free ends of the cords being 

 attached to the same handle. The axle which carries the discs is movable at 

 its centre around a vertical and also a horizontal axis, but either of these mo- 

 tions can be prevented at pleasure. If both discs are made to rotate in the 

 same direction, or if only one disc rotates, it is not easy to turn the whole appa- 

 ratus on its horizontal axis. But if the machine is prevented from moving 

 round a vertical axis, there is no difficulty in disturbing it around its horizon- 

 tal axis. 



" Thus it appears in this experiment, as well as in those made with the 

 Bohnenberger and Fessel machines, that a force acting upon a free body is 

 prevented from producing motion in its own direction by the conical motion 

 which exists around a rectangular axis. The same experiments can be made 

 with the Bohnenberger apparatus, by holding or releasing the middle ring. In 

 mechanics, a body has lost its stability of rotation when it has lost its freedom : 

 and the most complete stability is consistent with perfect freedom. Astro- 

 nomy hangs up for ever in the sky a splendid illustration of this principle. It 

 cannot be that a less noble law prevails in the kingdom of mind than in that of 

 jjaatter. When the two discs are made to rotate in opposite directions with the 

 velocity, there is no stability, even when the apparatus is most free. For 



