224 



rvutory varied, once seven and one-half seconds, and at 

 another time, five seconds in twenty-four hours; at that time it 

 was not well understood what caused these sudden variations in 

 a pendulum having a known daily equation. But later experi- 

 ments have shown this error to be caused by seismic waves. 



From the simple observation of the lamp swinging- from the 

 roof of the Cathedral at Pisa, more than three hundred and forty 

 years ago has grown the thought included in the foregoing laws. 

 The laws of inverse squares and mutual attraction as shown in 

 the simple pendulum, the properties of the cycloid and cycloidal 

 pendulum, the influence of the linear and cubical dilatation, the 

 intluence of atmospheric pressure on the pendulum, and the 

 centrifugal force from the revolution of the earth on its axis, 

 and by reducing all these errors to a minimum we are furnished 

 with an instrument that performs its work with as much accu- 

 racy as any piece of mechanism ever produced by man. 



NOTE A. 



The length of the pendulum rod is just double the diameter 

 of the generating circle. Now, from relations of parts of the 

 cycloid, it is shown that the time of falling down the semi-cycloid , 

 is to the time of fall through the diameter of the generating 

 circle, as a quadrant is to a radius. 



