22$ Prof. A. McAulay on the Wave-Surface and Rotation 



Fix the attention on a tangent plane of R and the corre- 

 sponding point of S, and on the plane (tangential to R') and 

 point (of 8') into which these are strained. 



Let p be the coordinate vector (the origin being the given 

 one) of any point of the tangent plane of R, p' the corre- 

 sponding strained value of p, a the vector of the point on S, 

 and o 1 the strained value of a. Let % be the given strain, so 

 that ^' -1 is the reciprocal conjugate. Thus we have 



p' = xp, ^ = x'-^, (i) 



and 



Spcr = -1 (2) 



for all values of p (in travelling over the tangent plane). It 

 at once follows that 



S/oV= -1 



for all values of p ! . This proves the proposition. 



The equations that Mr. Heaviside uses in considering the 

 wave-surface are 



WH = cE = D, (3) 



-VVE = /*H=B, (4) 



where c and jjl are self-conjugate nonions, viz. permittivity 

 and inductivity respectively, and where H, E, B, D are as 

 usual. The medium is immovable, and c and p, have constant 

 values at all points. 



In order to bring these into harmony with the notation of 

 my paper ei On the Mathematical Theory of Electro- 

 magnetism " (Phil. Trans, vol. clxxxiii. 1892, A, p. 685 : 

 this paper will be referred to below as u M. T. E."), I prefer 

 to write them 



VV'H' = c'E' = D', (5) 



-Vv'E' =^ , H / =B / , (6) 



p 1 being the coordinate vector of an actual point of the 

 medium. 



Suppose now, in accordance with " M. T. E.," we write 



P'=XP, (?) 



where % is an arbitrary nonion, which, however, has a constant 

 value. If then we put 



H' = m- l wx!, c' = m-^cx', 



... (8) 

 m having the usual meaning with regard to %, (5) and (6) 



