THE SMITHSONIAN INSTITUTION. 183 



little, and the next resultant lies within this diminished angle ; and 

 so, by the continued pressure on the frame, the angle is reduced to no- 

 thing, by the complete reversal of the poles. At that moment, the two 

 forces coincide in direction ; and noiu, if the axis is jarred a little, the 

 angle is acute, the resultant lies within it, and tends to bring them to 

 immediate coincidence without upsetting the spheroid. We see, there- 

 fore, that there is a condition of equillbrlu in, whichever way the frame 

 is turned on a vertical axis, provided the spheroid revolves also on a 

 vertical axis ; but if the revolutions are in the same direction, the 

 equilibrium is stable ; if in opposite directions, it is unstable. 



We are now prepared to attend to the explanation and illustration 

 of the " Precession of the equinoxes." The earth is not an exact 

 sphere. If it was a sphere, and of uniform density, there would be 

 no such phenomenon as precession. The equator of the earth, as is 

 true also of the other planets, is a little bilged beyond the spherical 

 form, in consequence of its rotation. We conceive ol" the earth, there- 

 fore, as consisting of a sphere with a thin ring attached to its equator. 

 This equatorial ring is inclined about twenty-three and a half degrees 

 to the plane of the ecliptic. The sun is always in the ecliptic, and 

 the moon is always very nearly in it. By the attraction of these 

 bodies the equatorial ring is slightly pressed towards the ecliptic, and 

 the whole mass of the earth, being united to the ring, is thus urged 

 to turn into the plane of the ecliptic, on an axis passing through the 

 intersection of the two planes. But in the mean time the earth is also 

 turning on the axis which passes through its poles. By the composi- 

 tion of these two revolutions it begins to turn on a new axis very near 

 the original one, and between it and the line of equinoxes. But the 

 depressing force continues, tending to tip the equator towards the 

 ecliptic on a line still at right angles to the diurnal axis, and there- 

 fore shifts that axis again ; and thus the cause, and its consequent 

 effect, are repeated from moment to moment for ages. The earth's 

 axis is ever seeking a neiv position between its present one and another 

 at rigid angles to the present one. 



The rotascope illustrates this perfectly. I first set the horizontal 

 ring around the frame, to represent the ecliptic. The spheroid of the 

 rotascope represents the earth ; though, for convenience, it has an 

 excessive oblateness, the equatorial ring being even larger than the 

 enclosed sphere. The earth I set in rotation on its axis from west to 

 Fig. 8. east, and incline the equator to the ecliptic ; and 



now I attach this brass weight to the lower edge 

 of the inner ring ; the weight, by urging the 

 ring into a vertical position, of course presses the 

 equator of the spheroid into a horizontal plane — 

 that is, the plane of the ecliptic. The line of 

 equinoxes, you perceive, now lies east and west; 

 but if I leave the apparatus thus adjusted to itself, 

 this line commences a slow revolution from east 

 to west. This is the "Precession of equinoxes."* 



. *-" hi figure 8, the particles at A, revolving to the right with the spheroid, and urged towards 

 the observer by the weight W, take an intermediate direction ; that is, the equinoctial points, 



