Hotatory Motion, the Gyroscope, 4'c. l-il 



that in the one ease the force of the impulse is spent, being accounted 

 for by the changed velocity, whilst in the other case the force is 7iot 

 spent. In the case of the continued pressure the wheel acts as though 

 points on its periphery were continually coming in contact with fixed 

 inclined guides, which have tlie effect of changing the courses of the 

 points, and consequently altering the position of the axis about which 

 they rotate. 



It may occur to some one to ask if the pressure on the point of 

 support exists also in the case of the earth ? There would be such a 

 pressure at right angles to the plane of the ecliptic, did the action on 

 the earth, corresponding to that of the weight on the gyroscope, take 

 effect on one side only of the centre. This action, however, takes effect 

 on both sides in the case of the earth. Thus, if in fig. 6, i J represents 

 the plane of the ecliptic, and G a a diameter of the earth ; there is a 

 force pressing at w, towards j, and another pressing at n, towards i. 

 The precession, as I have shown, gives rise to counter pressures, a and 

 o exactly balancing the pressures w and h respectively. If these pres- 

 sures, w and H, are equal, there will obviously be no pressure on the 

 centre r : for the pressures, w and G, pressing the centre one way, are 

 equal to the pressures, A and H, pressing it the other way. I leave it to 

 astronomers to decide if the forces at w and H are equal or not. When 

 the sun is towards J, the force at w may possibly be slightly the greater 

 of the two — if it is, there will be a slight pressure on the centre r, in 

 the same direction ; but this will be compensated for when the sun is 

 towards i, by a like pressure in the opposite direction. If the pressure 

 exists at all, it wiU merely amount to the difference between the forces 

 at w and h. 



I must now show how my explanation applies to the Fessel gyroscope, 

 in which the weight of the entire instrument constitutes the downward 

 pressure which changes the position of the axis. Referring to figs. 1 

 and 2, — if we remove from the sphere all but the segment shaded with 

 vertical lines, and shown separately in figs. 8 and 9 — we shall obtain a 

 sufficiently close approximation for our purpose, the centre of the sphere, 

 marked r in figs. 8 and 9, being still the point of support. The ten- 

 dency of gravity to produce rotation about a horizontal axis at right 

 angles to the axis a f, combines with the rotation of the wheel to 

 produce rotation about an intermediate axis, c c, fig. 7, supposed to be 

 very near a jt. At the instant the change of axis takes place, the wheel 

 is oblique to the line c c, but each material point in it immediately 

 endeavours to rotate in a plane at right angles to this line, c c, and the 

 horizontal components of the centrifugal forces due to the rotation 

 consequently act in directions parallel to the arrows, e. The centrifugal 



