Cycles of Rainfall 9 



the epoch of the uniform circular motion. The 

 radius of the circle is the amplitude of the motion; 

 the time of going once around the circle is the 

 period of the motion; the ratio of A Q to the 

 circumference of the circle is the phase of the mo- 

 tion. 



If from each position of Q a perpendicular is dropped 

 upon the diameter of the circle, G H, the foot of the 

 perpendicular will describe a simple harmonic motion. 

 The amplitude of the simple harmonic motion is one- 

 half of the range of the motion, that is, one-half of G H, 

 or the radius of the circle. The period of the simple 

 harmonic motion is the interval between the passing 

 of the point P twice through the same position in the 

 same direction. The distance of the point P from the 

 middle of its range, 0, is a simple harmonic function 

 of the time, P =y =a sin (nt+e), where a is the radius 

 of the circle — or the amplitude of the simple harmonic 

 motion — e is the angle of epoch, and n is the angle de- 

 scribed by the moving point Q in the unit of thne. The 

 period of the simple harmonic motion is, in the above 



27r nt + e 



case, . Its phase is — ~ — . 



Figure 2 presents a graph of simple harmonic mo- 

 tion. As in Figure 1, the point Q moves uniformly in 

 the circle ; the point P performs simple harmonic motion 

 according to the formula y=a sin (nt-\-e), where a is 

 the amplitude of the motion, or radius of the circle, e 

 is the angle of the epoch, namely, AGE, and n is the 

 arc described by Q in the unit of time. If time is meas- 



