Figure by means of the Pendulum. ■ 447 



determined. Let us first understand what kind of quantities 

 we are dealing with. The difference between two radii of the 

 earth, one being polar and the other equatorial, is about thirteen 

 miles. This bears the same relation to the whole radius that 

 one inch bears to twenty-five feet. So that had we a model of 

 the earth in its true proportions it would be quite impossible 

 to see with the naked eye whether it was flattened at the poles 

 or not. The first practical demonstration of a change of the 

 force of gravity with a change of latitude was had a little over 

 200 years ago when a clock was carried from France to Guiana. 

 This clock kept accurate time in Paris but lost two minutes 

 per day in Cayenne. The pendulum had to be shortened 

 about y 1 -^ of an inch in order to make it beat seconds, as it 

 had done in a more northern latitude It was thus seen that 

 the pendulum could be used to measure the force of gravity. 

 The change in the time of one oscillation over limited areas is, 

 however, very small ; one mile in distance making a difference 

 of one two-millionth of a second in the time of vibration ; or 

 stated in another way, a pendulum thirty-nine inches long that 

 beats seconds at the equator would only have to be lengthened 

 by -J- of an inch to make it beat seconds at the pole. When 

 we consider that one-quarter of the entire circumference of the 

 earth only changes the length of the second pendulum by its 

 2^-q part, it is evident that a change of latitude even for a 

 country as large as the United States affects the pendulum by 

 what may be called a minute quantity. Then the force of 

 gravity changes with the elevation ; but our highest mountains 

 only alter the time of oscillation by l5 1 00 part when distance 

 alone is considered, and the effect is even less than that if the 

 attraction of the mountain is taken into account. Of this we 

 shall speak later. It is thus seen that in all work pertaining 

 to the measurement of the force of gravity we are obliged to 

 deal with very small quantities and that methods must be 

 devised delicate enough to appreciate them. How far these 

 have been successful may be judged from the fact that in- 

 dependent determinations of the time of an oscillation do 

 not differ as much as the one hundred thousandth part of a 

 second. It is not asserted that differential gravity is always 

 known to this degree of accuracy, but simply that there is no 

 difficulty in making the pendulum repeat itself with no greater 

 error than that mentioned. When we come to measure the 

 absolute force of gravity, besides determining an interval of 

 time, we are required to measure an interval of space. This 

 can be accomplished with a degree of precision far exceeding 

 that attained in the time measures. Not only is it much easier 

 to obtain the one hundred thousandth part of a meter than to 

 get the corresponding fractional part of a second, but the effect 



