532 THE POPULAR SCIENCE MONTHLY. 



then stopping for an instant the ball again descends, to ascend on 

 the other side, thus adding oscillation to oscillation. Were it not 

 for the resistance of the atmosphere and certain mechanical im- 

 perfections these arcs would be the same, but, what is more im- 

 portant, the times of oscillating are the same. 



The rapidity with which the pendulum descends depends upon 

 its length and the amount of this impulse to drop vertically. 

 This impulse is known as gravity. Therefore, with a pendulum 

 of constant length the time of oscillation will be dependent upon 

 gravity, and thus time and gravity are determinable one in terms 

 of the other. 



Newton had shown that gravity on the earth's surface de- 

 pended upon distance from the center of the earth, and also the 

 diminishing effect of the revolution of the earth on gravity. To 

 this theory other mathematicians made valuable contributions, 

 notably Clairaut, who demonstrated that the relative lengths of 

 the equatorial and polar radii could be ascertained directly from 

 the force of gravity at the equator and at one of the poles. Then, 

 since the gravity is obtained directly from the time in which a 

 pendulum makes an oscillation and its length, it was necessary to 

 simply swing a pendulum at the equator and at one of the poles 

 to have at once the coveted ellipticity that is, the ratio of the 

 difference between the equatorial and polar radii to the equatorial 

 radius. 



Unfortunately, it has not been possible to swing a pendulum 

 at one of the poles. This inability, however, is made of no mo- 

 ment by a law which gives the value of the polar gravity when- 

 ever the gravity of a given place is known, together with the lati- 

 tude of the place. 



From this it appears that the earth's figure becomes known 

 through a determination of the length of a pendulum and the 

 time required for it to make an oscillation at the equator (or near 

 it) and at the pole (or as near to it as possible). If the same pen- 

 dulum is used and the constancy of its length assured, it becomes 

 necessary to make sure of the length of time required for an oscil- 

 lation at these two places. Inasmuch as the pendulum appears to 

 stop for an instant when it reaches the highest point in its arc, 

 it is a difficult matter to determine with exactness the time of an 

 oscillation; but if one counts the number of oscillations in an 

 hour, in two hours, or in any number of hours, a simple division 

 will give the time of one oscillation. 



The figure of the earth desired is an ideal figure, such a figure 

 as it would have if one could remove all the land now standing 

 higher than the surface of the sea were a sea to occupy the place 

 of the land. Hence it is the sea-level earth whose figure we want. 

 Newton's law of gravity would require that a pendulum, if raised 



