xxvi 



even if some of the views of Helmholtz should hereafter be decisively 

 rejected, his work on the theory of sound will always stand out in 

 the history of the science as the first great attempt to explain the 

 foundations of music by the laws of acoustics and by the construction 

 of the ear. The discussion was extended in the ' Tonempfindungen ' 

 from the cause of dissonance to the theory of musical scales ; a 

 natural relationship between the tones being sought, as before, in 

 the relationship of their partials. 



But though he maintained that these theories explained the physical 

 " reason of the melodic relationship of two tones," the author of the 

 ' Tonempfindungen ' was careful to point out that the principles he 

 enunciated had not always determined the structure of the scale and 

 do not determine it everywhere now. The selection of a series of 

 notes, which were afterwards found to obey certain natural laws, was 

 voluntary. The scale itself is not natural in the sense that it is not 

 a necessary consequence of the construction of the ear ; on the 

 contrary, it is the product of artistic invention. Thus music is not a 

 mere branch of mechanics, but an art. The architect and the com- 

 poser alike deal with materials which are subject to mechanical laws, 

 but they are alike free to fashion from them forms determined, not 

 by calculation, but by the sense of beauty. 



In the subjects which have been noticed experiment was used by 

 Helmholtz at least as much as mathematics. In his researches on 

 vortex motion and electricity the mathematical powers of his genius 

 were predominant. 



The great paper on vortex motion made an extraordinary advance 

 in the theory of the movement of perfect fluids, a subject which had 

 already attracted the keen scrutiny of the greatest mathematicians. 

 It is to Helmholtz that we owe the discovery of the fundamental 

 laws which govern vortex motion, and of those peculiar qualities 

 which have made it play so large a part in theories as to the con- 

 stitution of matter and of the ether. 



The electrical work of Helmholtz began early, and extended over 

 many years. An important paper, published in 1851, on the duration 

 of induced electrical currents, has been already referred to. It was 

 a bye-product of his researches on the propagation of nervous action. 



In 1869 he published an account of some experiments on electrical 

 oscillations. A falling pendulum completed two circuits at times 

 separated by a very small though measurable interval. Electrical 

 oscillations were thus induced in a secondary circuit, the terminals 

 of which were connected with the coatings of a Ley den jar. Imme- 

 diately afterwards the secondary circuit wa3 itself broken, and at the 

 same instant it was connected with a shunt which led through the 

 nerve of a frog's leg. As the time between the completing of the 

 primary and the breaking of the secondary circuit was increased in 



