certain the number of oscillations made by a pendulum within an interval of several minutes without counting them. This at once suggested that the danger of making a slip in counting the oscillations, should they be as frequent as two in a second, might be avoided, and thus a short or half-second's pendulum be employed. This shortening resulted, of course, in a lightening, and each ounce of diminution added to the safety of the knife-edge, thereby contributing to the permanency of the pendulum. Nor was this all: the parts now became of such wieldy size that the whole could be incased in a chamber sufficiently air-tight to maintain a constant atmospheric pressure either by exhausting a portion of the air near sea level or forcing air in when stations at great altitudes are occupied.
With a pendulum so compact one can visit places heretofore inaccessible with the larger forms, and require distant islands and inhospitable climes to give a voice in determining the earth's shape. Large land areas are needed for the measurement of arcs, and hence less than one fourth of the earth only is available to determine geodetically its shape. But now each party sent out on a voyage of discovery or to observe astronomic phenomena can take one of these compact pendulums along and make stations within the bounds of the three fourths so that they may not be encompassed by a figure dictated by the minority.
Now that differential methods are used almost universally that is, comparing the times of oscillation of the same pendulum at different places—it is essential that the length may continue to be what it was when swinging at the base station, or station where absolute gravity had been determined. Supposing that due correction has been made for such changes in length as would be occasioned by differences of temperature, the only possibility for variation in length could come from disarrangement or wear of the knife-edge. Any chipping of this knife-edge—made of agate—could not be rectified, and dullness could not be removed without making in so doing a new pendulum, thereby destroying its differential value. In swinging, this agate V rests on a steel plane, and as this plane, forming no part of the pendulum proper, is less liable to injury or derangement, the idea occurred to the survey officers to let these parts change places. So now we have a pendulum with a slit in the upper end of its rod, having for its upper surface a plane of hard steel. This plane rests on the agate knife-edge which projects into the slit. If now the agate becomes dull or injured it can be repaired or a new one substituted, and the pendulum remain the same.
As already stated, the usual procedure has been, when observing with a pendulum, to note the number of oscillations made in a given interval of time; then, by dividing this interval by the