SHAPE OF THE EARTH FROM A PENDULUM. 531 

 THE SHAPE OF THE EARTH FROM A PENDULUM. 



By Prof. J. H. GORE. 



IT was tliouglit that a maximum paradox was reached when 

 the quotation ex pede Herculevi {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 ener- 

 gies of countless troops of observers, artisans, and laborers, sup- 

 ported 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, em- 

 ploying 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 cathe- 

 dral in the year 1583 would be the prototype of the accurate geo- 

 detic 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 direc- 

 tion as possible, it swings down a circular arc whose center is the 

 point of support. Wnen 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 ; 



