526 Mr. R. T. G-lazebrook on the Application of the 



Rayleigh), A is infinite, and the right-hand side is 1/V 2 . If, 

 on the other hand, A vanishes (Thomson) , the right-hand side 

 is zero, and the equation becomes 



I iyv 1 n 2 



Y 2 -a 2 + Y 2 -b 2 + Y 2 -c 2 =0# * * ' ^ 

 which is FresneFs surface. 



To trace the form of the surface in general, let us find its 

 section by the principal planes. Suppose a, b, c to be in order 

 of magnitude, and let A/(A — B) = —k. Consider the section 

 by the plane of zx. Then m=0, and we have 



(Y 2 -b 2 )[Y 2 {l 2 (V 2 -c 2 ) + n%Y 2 -a 2 )} + k(Y 2 -c 2 )(Y 2 -a 2 )] = 0. (16) 



Thus the section consists of a circle given by Y = 6, and 

 the quartic curve 



Y%l + k)-Y 2 {(l 2 c 2 + n 2 a 2 ) + k(a 2 + c 2 )\+ka 2 c 2 = 0. . (17) 



The two important cases are given by k= — 1 (Rankine, Stokes, 

 Rayleigh) ; and k very small, probably zero (Thomson). 

 For the latter case, on solving the quadratic and neglecting k 2 

 and higher powers, the two roots are 



; . . . (18) 



\/ 2 -an+cl+ a 2 n 2 + cH i 

 and 



Thus the section of the surface of wave-slowness by this plane 

 will be, for the nearly transverse waves, the circle given by 



J=* 2 ; (20) 



and a curve differing from an ellipse by extremely small 

 quantities depending on k(a 2 —c 2 ) 2 , and given by 

 1 _ A 2 lc 2 P] k(a 2 -c 2 )H 2 n 2 . 



and for the condensational wave, the inverse of an ellipse, 

 given by 



r * - a 2 n 2 + cH 2 { Z) 



Moreover for the velocity of the condensational wave along 



the axis of x we find the value \ / a. If we substitute 



V 1 + k 



the values of a and k, this reduces to 



VA//V 



