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affirmed by Galileo to be made in the same interval of time, 

 whether the arcs were long or short 



That there is a difference, although very slight, between 

 long and short arcs, where the distance passed over is not too 

 great, is nevertheless true; and it was not until 1658 that 

 Huvghens discovered and proved that long arcs required more 

 time than short arcs to perform the oscillations of the same 

 vibrating length of pendulum. I will add here, as the question 

 is often asked, what constitutes the length of a pendulum. It is 

 the distance from the point of suspension to the center of oscil- 

 lation. This point is in theory very near the center of gravity 

 of tlie pendulum ; and it described as being just below the gravity 

 point. In order to describe the center of oscillation more clearly, 

 I will make this simple illustration. 



If a blow is struck with a club and the impingment takes 

 place beyond the point of concussion, the blow is partial^ inflic- 

 ted on the hand; and the same result is experienced if the 

 impingment takes place between the hand and the point of con- 

 cussion, only in a reversed manner. The full force of the blow 

 is obtained only when the exact 'point of concussion meets the 

 object. Now, it is true that the center of oscillation in the 

 pendulum is identical with the point of concussion in the club, 

 and the time producing qualities of a pendulum depend entirely 

 on the above mentioned oscillating point. 



LAWvS. 



I will first call your attention to the laws of motions con- 

 trolling the simple pendulum, and wall refer to the cycloidal 

 pendulum later. First, the pendulum is a falling body, and is 

 controlled by laws governing such a body, and when at rest 

 points directly toward the center of the earth. Next, the square 

 of the time of oscillation is directly at its length, and inversely 

 as the earth's attraction. 



For instance, a pendulum vibrating seconds at the level of 

 the sea, in the latitude of New York city, would be 39.02 inches, 

 and a pendulum vibrating two seconds in the same location 

 would be the square (of the time) or two seconds, which squared 

 would be four, multiplied by the length of the one second 39.02 

 pendulum, which is equal to 156.08 inches, something over 13 

 feel long. This rapid increase in length for a comparatively 



