The Treatment of Electrodynamics. 275 



When the resistivity o£ the wires is not very great, and 

 the frequency is large, the Bessel functions in these results 

 may usually be replaced by their ordinary asymptotic ex- 

 pansions for large argument, and tables cease to be necessary. 

 The solutions then approximate to that for an infinite 

 frequency, which is well known *. The formula (72), appli- 

 cable when the wires are very far apart in comparison with 

 their radii, is chiefly useful in determining a differential 

 effect, for the ends of the wires will have a great influence in 

 most cases to which the formula might be applied if the 

 wires were really infinite. 



Trinity College, Cambridge. 



XX. The Treatment of Electrodynamics. 

 By R. A. Lehfeldt, D.Sc'j 



IT has long been customary in English books to treat 

 magnetism before current electricity, and " explain " 

 the latter by analogy with the action of magnetic shells. 

 This mode of presentation has always seemed to the writer 

 unsatisfactory, putting the more obscure phenomenon as an 

 explanation of the simpler ; and now that the electron theory 

 has shown itself capable of application to all branches of 

 electricity, it is most inappropriate, since magnetism is 

 looked upon as an effect of molecular electric currents. An 

 attempt has therefore been made to put the treatment of 

 electrodynamics, including magnetism, on a more logical 

 basis. 



The experimental starting-point is the brilliant investi- 

 gation of Ampere on the forces between conductors carrying- 

 currents. The electrostatic forces, although out of all pro- 

 portion greater in amount, produce no effect, on account of 

 the equal quantities of positive and negative electricity in 

 each wire. Again, a charge in motion produces no effect, 

 so far as is known, on a charge at rest. There remain, 

 therefore, only the purely electrodynamic forces — the action 

 of one moving charge on another moving charge. These 

 forces can be explainel by means of the concept of a mag- 

 netic field, but it is better to begin with the forces themselves, 

 although their spatial relations are somewhat complicated. 



Let us suppose, then, a charge e, located at the origin and 

 moving with the \eetor velocity V, whose components are 

 (ill, »!, 0), i. e. the axis of z is chosen perpendicularly to the 



* Russell, 7. c. ante. 



t Communicated by the Author. From the Transactions of the South 

 African Association for the Advancement of Science, Grahamstown, 1908. 



