xxiv.] EMPIRICAL KNOWLEDGE, EXPLANATION, &c. 541 



rated, and conducted by a longer passage, so as, on rejoin- 

 ing the other half, to be one-quarter of a vibration behind- 

 hand, the two portions would exactly neutralise each 

 other. This experiment has been performed with success. 

 The interference arising between the waves from the two 

 prongs of a tuning-fork was also predicted by theory, and 

 proved to exist by Weber ; indeed it may be observed by 

 merely holding a vibrating fork close to the ear and turn- 

 ing it round. 1 



It is a result of the theory of sound that, if we move 

 rapidly towards a sounding body, or if it move rapidly 

 towards us, the pitch of the sound will be a little more 

 acute ; and, vice versa, when the relative motion is in the 

 opposite direction, the pitch will be more grave. This arises 

 from the less or greater intervals of time elapsing between 

 the successive strokes of waves upon the auditory nerve, 

 according as the ear moves towards or from the source 

 of sound relatively speaking. This effect was predicted 

 by theory, and afterwards verified by the experiments of 

 Buys Ballot, on Dutch railways, and of Scott Kussell, in 

 England. Whenever one railway train passes another, 

 on the locomotive of which the whistle is being sounded, 

 the drop in the acuteness of the sound may be noticed at 

 the moment of passing. This change gives the sound a 

 peculiar howling character, which many persons must have 

 noticed. I have calculated that with two trains travelling 

 thirty miles an hour, the effect would amount to rather 

 more than half a tone, and with some express trains it 

 would amount to a tone. A corresponding effect is pro- 

 duced in the case of light undulations, when the eye and 

 the luminous body approach or recede from each other. It 

 is shown by a slight change in the refrangibility of the 

 rays of light, and a consequent change in the place of the 

 lines of the spectrum, which has been made to give impor- 

 tant and unexpected information concerning the relative 

 approach or recession of stars. 



Tides are vast waves, and were the earth's surface en- 

 tirely covered by an ocean of uniform depth, they would 

 admit of exact theoretical investigation. The irregular 

 form of the seas introduces unknown quantities and com- 



1 TyuJalV Sound, pp. 261, 273. 



