above the level of the sea, would make its oscillation in a longer time than when swinging at sea level. Therefore it is necessary to know the elevation of the station in order to ascertain the force of gravity in that latitude on the ideal earth.
If the parallels were perfect circles and if observations were absolutely correct, it would be necessary to swing a pendulum at only two points on the earth's surface in order to determine its shape. However, the results obtained by combining observations two and two are not harmonious; not only because the observations may be affected by errors, but the attraction of dense matter immediately beneath a station might seriously impair the observations made there; and as we never know the exact constitution of the earth's crust at any point, it becomes necessary to eliminate, as far as possible, this uncontrollable error by making observations at many places.
The ideal pendulum would consist of a ball of symmetrical form suspended by a wire stiff and uniform. Like all ideal conditions, these are never attained, but a close approximation is sought. In seeking rigidity the pendulum rod must be so large in cross section as to make the instrument cumbrous. This was a serious feature when, in order to avoid slips in counting, it was not thought feasible to use a pendulum that made an oscillation in less than a second of time—that is, a pendulum about thirty-nine inches long. Again, as the pendulum was provided with sharp knife-edges on opposite sides near its upper end, shaped like a V, on which it swung, the greater the weight of the pendulum the more wear there would be on these knife-edges. This becomes a serious matter, as the length of the pendulum is estimated from the line of support furnished by these same knife-edges. Then, too, the swinging of a large and heavy pendulum was liable to induce a swinging motion in its support, unless the latter were exceedingly rigid, thereby vitiating the results.
Several years ago it was realized that the resistance of the atmosphere would vary with different conditions of moisture and density, and hence retard the pendulum more at some times than at others, more at some elevations than at others. Therefore it seemed necessary, in the absence of any well-accepted correction for these hurtful resistances, to swing the pendulum always under the same atmospheric pressure and surrounded by similar conditions as to moisture. This could be done only by inclosing the entire pendulum in a chamber in which the air could be maintained at the same density and dryness. One can readily see how difficult this would be with an apparatus more than four feet in length and weighing many pounds.
Although the shortcomings of the ordinary pendulum forced themselves into recognition one by one, still the readiness with
