272 



Dr. J. Larmor. A Dynamical Theory 



"A Dynamical Theory of the Electric and Luminiferons 

 Medium. Part III. Relations with Material Media." By 

 Joseph Larmor, F.R.S., Fellow of St. John's College, 

 Cambridge. Received iVpril 21 — Read May 13, 1897. 



(Abstract.) 



1. It was shown by Maxwell that the theory of electric current 

 systems flowing in rigid conductors could be formulated dynamically 

 if the current in each circuit, which is supposed constant all round 

 it, is taken as a generalised velocity : a formal development in his 

 manner of the properties of the current system, from the single 

 dynamical foundation of least action, was given in the first of the 

 present series of papers. It is implied in such a view that the 

 positions of the linear conductors and the intensities of the currents 

 that are flowing in them control completely, it may be in an entirely 

 unknown manner, the motions that are going on in the surrounding 

 eether ; just as in the cyclic irrotational motion of a perfect fluid the 

 positions of the rigid cores round which the circulations take place, 

 and the amounts of these circulations, determine the motion. But it 

 was pointed out that, whereas the vorticity of such a core is dynami- 

 cally a momentum, on the other hand in order to satisfy the facts 

 the currents in the circuits must be considered dynamically as 

 velocities ; so that there is not any real analogy between the two 

 cases. 



This simple dynamical formulation is no longer available when 

 attention is not confined to complete rigid circuits, for example 

 when the mechanical forces acting on a portion of a circuit are in 

 question. It is insufficient also when the electromotive force 

 (integrated electric force) between two points of a circuit carrying 

 a current is to be discussed, that quantity being realisable and 

 measurable by bridging the two points through the incomplete con- 

 ducting circuit of an electrometer. 



A knowledge of the electric force at a point, as well as of its 

 integrated value round a circuit, is also essential when the current 

 in the circnit is in part conducted and in part arises from changing 

 electric displacement : it is thus essential in the theory of electric 

 waves and radiation, though unimportant in ordinary electrodynamie 

 applications ; and for this reason that part of electric theory re- 

 mained unsettled until Hertz showed how to produce and investigate 

 free electric waves. 



Previous to that time, the theory had been completed hypothetically 

 in various ways, by extending the range of the dynamical formulae 

 (with such generalisations as were admissible) from the complete 



