XXV11 



successive experiments, alternations in the violence of the twitchings 

 of the muscle were noticed, and in all forty-five maxima were 

 observed. Helmholtz claimed for this method the advantage that 

 the electrical oscillations were established on an unbroken conductor 

 between the coatings of the jar, so that no spark was produced. 



Two years later (1871) he returned to the same subject, and 

 determined an inferior limit to the rate of propagation of electro- 

 magnetic induction. Blaserna had published some experiments, from 

 which he concluded that in air this velocity was only 550 metre- 

 seconds. Helmholtz then proceeded to investigate the matter for 

 himself, using, with some modifications, the apparatus described above. 

 It is evident that if the time interval between the breaking of the 

 two currents were adjusted so as to give the maximum effect, the 

 same result would only be obtained when the distance between the 

 two circuits was increased, if the time interval were itself augmented 

 by an amount equal to that required for the induction to travel 

 across the additional space. Helmholtz found that the same adjust- 

 ment was equally good at all distances, and concluded that the 

 velocity of propagation must exceed 314,400 metre-seconds. These 

 experiments acquire an additional interest when we remember that 

 Hertz was a pupil of von Helmholtz, and was thus brought up in a 

 laboratory in which electrical oscillations had been the subject of 

 careful study. The seed sown by the earlier efforts of the master 

 brought forth fruit a hundred-fold. 



From 1870 onwards, Helmholtz published an important series of 

 papers on the theory of electro- dynamics. His point of departure 

 was the discussion of the mutual action of two current elements. 

 An expression for the potential of two such elements had been 

 formulated by F. E. Neumann, which differed from those deduced 

 from the theories of W. Weber and Clerk Maxwell respectively. All 

 three gave identical results in the case of closed circuits. 



Taking the elder Neumann's formula as the groundwork of his 

 investigations, Helmholtz sought to find the terms which must be 

 added to it, so as to produce the most general expression consistent 

 with the known behaviour of closed circuits. The result was an 

 expression consisting of the sum of two terms, which were multi- 

 plied respectively by 1 + k and 1 — it, where Jc is an undetermined 

 constant. 



The expression is equivalent to that given by Weber when k = — l r 

 to that given by F. E. Neumann when h = 1, and is in accord with 

 Maxwell's theory when h = 0. 



It was then proved that if k is negative the equilibrium of elec- 

 tricity at rest must be unstable, so that motion, when once estab- 

 lished, would increase of its own accord, and lead to infinite velocities 

 and densities. The assumption was, in fact, a violation of the law of 



