ELECTRIC OSCILLATIONS AND ELECTRIC WAVES. 211 



117. Superposition of waves A principle of extremely wide 

 application in physics is the so-called principle of superposition. 

 From the physical point of view a general statement of the prin- 

 ciple of superposition is scarcely possible and therefore the 

 following examples must suffice : 



(a) A person at A, Fig. 147, can see window No. I and another 

 person at B can see window No. 2 at the same time. This 

 means that two beams of light a and b can travel through 

 the same region at the same 

 time without getting tangled 

 up together, as it were, each 

 beam behaving as if it were 

 traveling through the region 

 alone, (b) Two systems of 

 water waves can travel over 

 the same part of a pond simul- Fig. 147. 



taneously, each system behav- 

 ing as if the other system were non-existent, (c) Two forces 

 F and G exerted together on an elastic structure produce a de- 

 formation which is the sum of the deformations which would 

 be produced by the forces separately, provided the two forces 

 together do not exceed the elastic limit of the structure. There- 

 fore each force may be thought of as producing the same effect 

 that it would produce if it were acting alone. 



All of the effects in physics which are thus superposable 

 and this includes the majority of effects in mechanics, heat, 

 electricity and magnetism, light and sound are expressible in 

 terms of linear differential equations. Thus equations (i), (2), 

 (3) and (4) of Art. 116 are linear differential equations, and any 

 number of electric waves can travel over a transmission line 

 simultaneously, each behaving as if it were alone. The voltage 

 across the line at any point is the sum of the voltages at that point 

 due to the separate waves, and the current in the line at a point* 

 is the sum of the currents at that point due to the separate waves. 



* Outflowing current in one wire and returning current in the other wire. 



