98 THE PRINCIPLES OF SCIENCE. 



He showed that if a string is affected by two kinds of 

 vibrations, we may consider each to be going on as if the 

 other did not exist. We cannot perceive that the sound 

 ing of one musical instrument prevents or even modifies 

 the sound of another, so that all sounds would seem to 

 travel through the air, and act upon the ear in independ 

 ence of each other. An exactly similar assumption is 

 made in the theory of tides, which are really great waves. 

 One wave is produced by the attraction of the moon, and 

 another by the attraction of the sun, and the question 

 arises, whether when these waves coincide, as at the time 

 of spring tides, the joint wave will be simply the sum of 

 the separate waves. On the principle of Bernoulli this 

 will be so, because the tides on the ocean are almost 

 indefinitely small compared with the depth of the ocean. 



The principle of Bernouilli, however, is only approxi 

 mately true. A wave never is exactly the same when 

 another wave is interfering with it, but the less the dis 

 placement of particles due to each wave, the less in a still 

 higher degree is the effect of one wave upon the other. 

 In recent years Helmholtz was led to suspect that some 

 of the phenomena of sound might after all be due to 

 resultant effects overlooked by the assumption of previous 

 physicists. He investigated the secondary waves which 

 would arise from the interference of considerable disturb 

 ances, and was able to show that certain summation or 

 resultant tones ought to be heard, and experiments subse 

 quently devised for the purpose showed that they might 

 be heard. 



Throughout the mechanical sciences the Principle of the 

 Superposition of Small Motions is of fundamental im 

 portance y, and it may be thus explained. Suppose 

 that two forces, acting from the points B and C, are 

 simultaneously moving a body A. Let the force acting 

 y See Thomson and Tait s Natural Philosophy/ vol. i. p. 60. 



