Dr. Oliver Lodge on Opacity. 403 



theory, a sort of Fresnel-like theory, which he has given 

 for infinitely thin films of finite conductance ; it is of remark- 

 able simplicity, and may give results more in accordance 

 with experiment than the theory of the universal opaque 

 medium without boundary, hitherto treated : a medium in 

 which really the source is immersed. 



Let a film, not so thick as gold-leaf, but as thin as the 

 black spot of a soap-bubble, be interposed perpendicularly 

 between source and receiver. I will quote from i Electrical 

 Papers,' vol. ii. p. 385 : — " Let a plane wave ^j 1 =:/jlvH 1 

 moving in a nonconducting dielectric strike flush an ex- 

 ceedingly thin sheet of metal [so thin as to escape the need 

 for attending to internal reflexions, or the double boundary, 

 or the behaviour inside] ; letE 2 = //uH 2 be the transmitted wave 

 out in the dielectric on the other side, and E 3 = — /jlvH 3 be the 

 reflected wave *. 



* General Principles. — It may be convenient to explain here the 

 principles on which Mr. Heaviside arrives at his remarkably neat 

 expression for a wave-front in an insulating medium, 



E = pvH, 

 or as it may be more fully and vectorially written, 



VOE) = ^H, 

 where E is a vector representing the electric intensity (proportional to 

 the electric displacement), H is the magnetic intensity, and v is unit 

 normal to the wave-front. E and H are perpendicular vectors in the 

 same plane, i. e. in the same phase, and E H v are all at right angles to 

 each other. 



The general electromagnetic equations in an insulating medium are 

 perhaps sufficiently well known to be, on Mr. Heaviside's system, 



curl K = KE and —curl E = ^H, 



where " curl " is the vector part of the operator v, and where Maxwell's 

 vector-potential and other complexities have been dispensed with. 



[In case these equations are not familiar to students I interpolate a 

 parenthetical explanation which may be utilised or skipped at pleasure. 



The orthodox definition of Maxwell's name " curl " is that b is called 

 the curl of a when the surface-integral of ft through an area is equal to the 

 line-integral of a round its boundary, a being a vector or a component 

 of a vector agreeing everywhere with the boundary in direction, and b 

 being a vector or component of vector everywhere normal to the area. 

 Thus it is an operator appropriate to a pair of looped or interlocked 

 circuits, such as the electric and the magnetic circuits alwa}-s are. The 

 first of the above fundamental equations represents the fact of electro- 

 magnetism, specially as caused by displacement currents in an insulato?', 

 the second represents the fact of magneto-electricity, Faraday's magneto- 

 electric induction, in any medium. Taking the second first, it states the 

 fundamental law that the induced EMF in a boundary equals the rate of 

 change in the lines of force passing through it ; since the EMF or step 

 of potential all round a contour is the line-integral of the electric intensity 

 E round it, so that 



EMF = f Eds = - ^=-fTBe?S=-ff«HrfS : 



J cycle at J J JJ 



