PRINCIPLES OF ALTERNATING CURRENT 197 



cycles per second. In the early days of alternating current 

 engineering a frequency of 133 was adopted as the standard 

 and recently it has been recommended that a frequency 

 of 15 cycles per second be used for railway motors of a certain 

 type. Sixty cycles is as low as can be employed for lighting 

 purposes; if a lower frequency than this is used, the result- 

 ant flickering of the lamp becomes tiring to the eye. 



For the transmission of messages by wireless telephony 

 and telegraphy a frequency of many thousand cycles per 

 second is used; machines have been built for this work 

 which generate as high as 200,000 cycles per second. 



FIG. 116. Curve Illustrating Mirror Symmetry. 



Shape of Wave. The shape of the curve representing 

 an alternating current or e.m.f . is sometimes very important. 

 In nearly all commercial circuits the forms of voltage and 

 current waves are simple sine curves as shown in Fig. 117; 

 there will always be more or less departure from the simple 

 sine form caused by the presence of sine waves of higher 

 frequency than the fundamental. 



Upper Harmonics Affect Wave Shape. A current which 

 has approximately the form of a 60-cycle sine wave is likely 

 to be distorted by the presence of other sine waves of 

 frequencies of 180 cycles per second, 300 cycles per second, 

 etc. These higher frequency currents are called upper 



