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points at the ends of a horizontal arm made to rotate round a ver- 

 tical axis through its middle point at a constant angular velocity, 

 w, and let a second cord bearing a weight be attached to the middle 

 of the first cord. The two cords being each perfectly light and 

 flexible, and the weight a material point, it is required to determine 

 its motion when infinitely little disturbed from its position of equi- 

 librium * . 



Let I be the length of the second cord, and m the distance from 

 the weight to the middle point of the arm bearing the first. Let x 

 and y be, at any time t, the rectangular coordinates of the position 

 of the weight, referred to the position of equilibrium O, and two rec- 

 tangular lines OX, OY, revolving uniformly in a horizontal plane in 

 the same direction, and with the same angular velocity as the bearing 

 arm ; then, if we choose OX parallel to this arm, and if the rotation 

 be in the direction with OY preceding OX, we have, for the equa- 

 tions of motion, 



d z x a n dy q 



o> 9 # 2w-^= ^x, 



dt* dt I 



If for brevit we assume 



we find, by the usual methods, the following solution : 



where A, a, B, ft are arbitrary constants, and and ^ are used for 

 brevity to denote the arguments of the cosines appearing in the 

 expression for x. 



The interpretation of this solution, when w is taken equal to the 

 component of the earth's angular velocity round a vertical at the 



* By means of this arrangement, but without the rotation of the bearing arm, 

 a very beautiful experiment, due to Professor Blackburn, may be made by attach- 

 ing to the weight a bag of sand discharging its contents through a fine aperture. 



