The results of all these forces must affect the position of all the stars and planets as seen from our earth. Their longitudes being reckoned from the equinoxes, the precession of these points would increase the longitude; but as it affects all the stars and planets alike, it would make no real or apparent change in their relative positions. Nutation, however, affects the celestial latitudes and longitudes, as the real motion of the earth’s polar axis changes the relative positions. So great is the change that our present pole star has changed from 12° to 1° 24; in regard to the celestial pole, the gradual approximation will continue until it is with 0° 30´, after which it will leave the pole indefinitely until in 12,934 years α Lyræ will be the pole star. So far we have given only the causes that affect the meridian, and consequently our standard for time; but that point being established for the yearly and diurnal revolutions, it becomes necessary to find some means to divide the day into minute fractional parts, such as seconds and parts of seconds. This, it has been stated, is effected by means of an isochronous pendulum. On this instrument no comment is required but of the causes that disturb its accuracy much is needed. In 1672, at Cayenne, the astronomer Richter, while taking transits of fixed stars, found his clock lost 2´ 28´´ per day. This was an error that arrested his attention, and he immediately attributed it to some variation in the length of the pendulum--due to other causes than atmospheric changes and expansion. He determined the length of a pendulum beating seconds in that latitude, which was 5° N. in South America. He found that that pendulum was shorter than one beating seconds in Paris, by 0833+ of an inch. Now, if the earth was a sphere, the attraction of gravitation at all places on its surface would be equal, and the oscillations of a pendulum would also be equal, + or - the disturbing effect of centrifugal force--an amount that can be easily determined. The real reason of the variation is found in the configuration of the earth. The amount of the attraction of gravitation at any point of the earth’s surface is found by the distance traversed by any body during the first second of its fall. The pendulum is a falling body, and may be by the same analysis reasoned on that pertains to the laws of gravitation; the centrifugal force is measured by any deflection from a tangent to the earth’s surface in a second.