PROFESSOR AT HEIDELBERG 271 



electrical charges accumulate at the open ends of unclosed 

 conductors, owing to the interpolation of insulating masses, 

 at each electrical disturbance along the conductor, these electric 

 charges being due to the electricity accumulated near the ends 

 of the conductor, and unable to traverse the insulator. 



Since the hypothesis resorted to by W. Weber (i. e. that 

 electricity has a certain degree of inertia like that of heavy 

 bodies) proved untenable, because the apparent inertia is due to 

 induction, Helmholtz next endeavoured to convert all these 

 laws into one single theorem, which should contain a still 

 undetermined constant, whence he could theoretically deduce 

 all the conclusions, and then test them empirically. 



The potential of the current elements of two linear 

 conductors due to one another proposed by Neumann, and 

 derived from Ampere's attractive force between two current 

 elements, was directly proportional to the product of the 

 length of the elements, the cosine of the angle between them, 

 and the product of current intensity in both, and indirectly 

 proportional to the distance between them, with a factor of 

 proportionality which is the negative square of the reciprocal of 

 the velocity of light ; the validity of this expression of potential 

 was tested and confirmed on closed currents. Helmholtz then 

 looked for the most general form of expression for the 

 potential of a single current element, which in all cases where 

 one of the currents is closed gave the same value as Neumann's 

 formula, and he finds this form expressed in the product of the 

 two infinitely small elements, and the second partial differential 

 quotients, taken with respect to the elements of a function of the 

 distance of these elements and of the current intensities. He 

 further submits this function to the condition that it shall be 

 proportional to current intensity, and inversely proportional to 

 distance, and obtains for the potential an expression which differs 

 from Neumann's in that, instead of the cosine of the angle of 

 the two elements, an expression is introduced which is linear 

 in respect of this cosine and of the product of the cosine 

 of the angle which the elements form with their distance 

 from one another, and which contains a new constant k. This 

 expression also includes the two different potential expressions 

 of the theories of W. Weber and Maxwell for each pair of 

 current elements. From the expression of the potential the two 



