ELECTROMAGNETIC WAVE THEORY 395 



velocity; but by tradition he eliminates one of these variables, obtains a 

 second order differential equation in the other and calls it the 'wave equa- 

 tion.' Thus he loses sight of the interdependence of force and velocity 

 waves . . ." (p. vii). Still, it is surprising to see that one has started with 

 two constants co and /xo, and recognizing the fundamental importance of 

 their product, \'et has not enquired about their ratio. 



Then, the reader will ask, how can the Theory of Relativity give a leading 

 role to the velocity of light and not mention the impedance of free space. 

 Has Einstein no use forrjo? Well, he has, and he has not. First, an essential 

 point in Special Relativity is the merging of the magnetic and the electric 

 fields into one skew-symmetrical tensor. When doing this in the MKS sys- 

 tem, homogeneity requires the use of the components of E and of 770//; but 

 the factor 170 is not apparent, for instance, in the equations on p. 44 of "The 

 Meaning of Relativity" (by A. Einstein, Princeton Univ. Press, 1923) which 

 uses a system of units in which 770 = 1. Secondly, if we try to connect the 

 universal constant rjo with other members of this interesting family, we find 

 that Tjo times a (charge)^ has the dimensions of "action," and more precisely 

 that 



•) 2/t 



■nae = :rwz. 



13/ 



(c = charge of the electron, h = Planck's constant). We see from this that 

 there is more to 770 than appears in Special Relativity, the first step in the 

 successive Einsteinian extensions of Maxwell's theory. 



We have dealt at length with this question of the "impedance of free space" 

 because it exemplifies the spirit of the whole work. It occurs in the course 

 of a short but apt presentation of the "Fundamental Electromagnetic Equa- 

 tions" (Chapter IV), immediately applied to harmonic oscillations. The 

 book as a whole is devoted not to Electromagnetism in general but, as 

 specified in the title, to Electromagnetic Waves. 



Three preliminary chapters introduce the more advanced mathematical 

 tools which will be used, but sparingly, in what follows: such topics as con- 

 tour integration, Bessel and Legendre functions. Chapter V is a short and 

 original presentation of Network Theor}^ 



The central part of the book begins with Chapter VI, "About Waves in 

 General," a sort of preview of the questions which will be treated in detail 

 later, during which we are introduced to radiation from given currents, 

 propagation along wave guides, and to such general tools as electric and 

 magnetic current sheets, the method of images and conformal representation. 



In the following four chapters, we meet the most thorough treatment 



- See Quarterly of Applied Matlienmtics, 1, 78 (1943). 



