1891.] On the Theory of Electrodynamics. 533 



We conclude that the propagation of waves of transverse dis- 

 placement with this velocity KI~* is not a characteristic of any special 

 theory, but forms a part of any conceivable theory which admits 

 some sort of polarisation in the dielectric, and leads to the correct 

 results for Ampere's case of circuital currents. 



This cardinal result will still follow, even if x is anv function what- 

 ever. The degree of (mathematical) generality which this remark 

 imparts may be expressed as follows. In a complete circuit the one 

 thing essential to the established theory is that the electric force 

 integrated round the circuit should be equal to the time rate of 

 change of the magnetic induction through it, and, therefore, have an 

 ascertainable value, though its distribution round the circuit is a sub- 

 ject of hypothesis. The conclusion that waves of transverse dis- 

 placement will be propagated in a dielectric with velocity K^" 1 will 

 hold good if we assume any form whatever for the electric force 

 which does not violate this one relation, and also assume an electro- 

 static polarisation of , the medium, equal at each point to the electric 

 force multiplied i>y a constant Ki/4w. For the indeterminateness that 

 may exist in the vector potential (or electric momentum) PGH is of 

 the same type as that which may exist in the electric force PQR, 

 and, therefore, as the equations show, may be merged in the latter. 

 It would, perhaps, be difficult to conceive any more general hypothesis 

 than this. 



The increased generality which can be imparted to the theory 

 merely leads to .-various modes of .propagation of a condensational 

 wave. 



cCorpp orison with Experimental Knowledge. 



In the general theory, of polarisation sketched at the beginning of 

 this paper, 



therefore KI 



The specific inductive capacity of v the medium is 

 K 2 = /t = l-f-45rr. 



Thus K a 



the units being here electrostatic. 



Now, the results of various experimental investigations seem to 

 place it beyond doubt that for dielectrics of simple chemical consti- 

 tution the velocity of propagation varies as K 2 ~*. Thus, in the recent 

 experiments of Arons and Rubens,* the velocity of waves, 6 metres 



* Wiedemann's ' Annalen,' vol. 42, 1891, p. 581. 



