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being transferred from the sea level to the mountain, or from 

 one of the earth's poles toward the equator, as the earth is a 

 spheroid slightly flattened at the poles. 



A very interesting experiment can be made to show the 

 influence of mutual attraction between masses. Take two well- 

 regulated astronomical clocks with seconds pendulums, place 

 them side by side, and cause each pendulum to oscillate simul- 

 taneously on the same side of the vertical, the pendulums will 

 oscillate to the right together, and to the left for a time together, 

 then they will change so as to oscillate in opposite directions and 

 will never depart from this motion. Another reason why a 

 pendulum loses on being transferred to the equator, lies in the 

 fact that the rotation of the earth gives rise to centrifugal force 

 at its surface. This, being zero at the poles, gradually increases 

 to a maximum at the equator; and, as it acts in opposition to 

 the force of gravity, it counteracts a gradually increasing pro- 

 portion of this force which shows in the time of oscillation. 

 The rotation of the earth on its axis also has another effect upon 

 the oscillation of the pendulum as you have just seen by the 

 demonstration of the pendulum of Foucault by Prof. Kellicott. 

 The error caused by the tendency of the pendulum to oscillate 

 in one given plane is reduced to a minimum by the use of short 

 ares of oscillation, and is of very little importance in comparison 

 with other errors. 



CYCLOIDAL PENDULUM. 



The arcs of oscillation of any ordinary simple pendulum are 

 a part of a circle with the point of suspension as a center. 



Now, a pendulum producing isochronal oscillations; namely, 

 producing unequal arcs in equal time is called cycloidal because the 

 center of oscillation must describe a cycloidal path during each 

 excursion on either side of the vertical line. 



This curve is one of the most interesting of any known, 

 both in respect to its geometrical properties and connection with 

 falling bodies, and is described in this manner: 



// a circle roll along a straight line on its own plane, a point 

 on its circumference will describe a curve which is called a 

 cycloid. The peculiar value of this curve in relation to the 

 pendulum will be better shown by inverting a cycloid curve as 

 we have here illustrated. V D A , 



