| THE SHAPE OF THE EARTH FROM A PENDULUM. |
By Prof. J. H. GORE.
IT was thought that a maximum paradox was reached when the quotation ex pede Herculem (from the foot, Hercules) forced its way into use. Hercules, in laying out the stadium, the length of the running course in the Olympian games, used his foot as the unit, and made the stadium six thousand feet long. From this distance, which was preserved, Pythagoras obtained the length of the foot of Hercules, and from an arbitrary ratio between the parts of the body deduced his height, thus restoring from the foot, Hercules.
But we can now propound a greater paradox, and say from a pendulum, the earth. Not the world that one can put in a sling, but the earth's shape. This striving after the shape of the earth has occupied men's attention for centuries; to know this shape they have braved the cold within the Arctic Circle, endured the heat of the equatorial regions, and penetrated India's malarial jungles. Peaks have been climbed, deserts traversed, and hostile tribes subjugated. To the theoretical side of this problem scores of the world's most profound mathematicians have devoted their time, while the practical side has been pushed ahead by the energies of countless troops of observers, artisans, and laborers, supported by the expenditure of millions upon millions of dollars.
While this great work is going on, looking toward a solution of this problem, with staffs of specialists in sixteen nations, employing instruments most complicated and refined, making, as it appears, an onslaught on the earth itself to compel it to yield to direct measurement, it now seems that from a modified form of the device which regulates our clocks—the pendulum—we may expect the most accurate knowledge regarding the earth's shape.
When Galileo deduced from observation that a pendulum is isochronal—that is, would make all its oscillations in the same interval of time whether the arc be long or short—he did not dream that the swinging lamp in the dome of Pisa's great cathedral in the year 1583 would be the prototype of the accurate geodetic instrument of three centuries later.
If the ball of a pendulum be drawn away from the vertical and released, its first impulse is to descend perpendicularly; but being held in restraint by the string, or connecting rod, it does the next best thing, and, keeping as near to this perpendicular direction as possible, it swings down a circular arc whose center is the point of support. When the lowest point of this arc is reached, an amount of energy has been stored up and the ball ascends the other side of the arc until this supply of energy is exhausted;
