ON THE PSYCHO-PHYSICAL YIE^Y OF NATURE. 487 



two dimensions — however coniplieuted or irregular that 

 motion might appear to be — could be mathematically 

 represented or calculated by the superposition or addition 

 of a larger or smaller number of simple periodic motions ; 

 as it were analysed and dissected into these simple move- 

 ments, just as any number can be looked upon as made 

 up by the addition of others — say of prime numbers. 

 Now, it was also known that sounds were produced by 

 wave-like tremors of the air set going by the vibrations 

 of strings or other sounding musical instruments ; further, 

 that definite musical notes were absorbed or transmitted 

 by neighbouring sounding bodies according as these were 

 in or out of tune with the vibrating source of sound. 

 This is the well-known phenomenon of resonance. Ohm^ 

 had applied Fourier's mathematical analysis to the ex- 

 planation of the partial notes, the ground tone and the 

 harmonic overtones (or upper partial tones), of which 

 musical " sounds are made up. Helmholtz invented a 



^ Ceo. S. Ohm, the same to See the introduction to his treatise 



wh(jni we are indebted for the on the galvanic current ('Ges. 



well-known law which obtains in I Werke,' p. 6'i). 



electric currents, published in 1843 - Cagniard de la Tour had in- 

 a paper in Poggendorfs ' Annalen ' } vented (1819) and Seebeck the 

 (reprinted in ' Gesammelte Ab- younger had improved (1841) the 

 liandlungen,' 1892, p. 575), "On first mechanical counter for the 

 the definition of a tone and the frequencies of musical sounds, the 

 theory of the sii-en," in which he i siren ; and the latter as well as 

 applied the mathematical methods Duhamel had studied the corn- 

 introduced by Fourier in his ' The- position of such sounds out of their 

 orie analytique de la Chaleur' elements or simple notes. A sug- 

 (1822) : as he had already done in gestion had been thrown out as to 

 liis earlier work on the galvanic , the part played by the up])er 



current (1827). In fact, Ohm was 

 one of the first to recognise the 



partial tones which accom])anied 

 the ground tone. Hehnholtz treats 



value of Fourier's conceptions in ' first of this subject in a lecture 



contradistinction from Laplace's, ' (1857), reprinted in 'Vortriige und 



which were bound up with certain Reden,' vol. i. p. 79, dealing with 



hypothetical notions as to the "the psychological causes of musi- 



niolecular constitution of bodies. I cal harmony." 



