88 Dr. C. V. Burton on a 



introduced in the following seven paragraphs, which are 

 devoted to establishing certain simple relations amongst the 

 quantities concerned; the immediate object being to discover 

 whether there is any consistent set of values which does not 

 bring our theory into conflict with experience. 



27. From (32) 



F =V(f )• < 37 > 



As regards the primary disturbance, the problem (as in 

 § 11) may be simplified by limiting our consideration to a 

 single train of plane waves of definite wave-length X, the 

 greatest linear dimension of the region with which we are 

 concerned being but a small fraction of X, so that, to a 

 sufficient degree of approximation, the pressure variations at 

 any point within that region are given by 



p = Bsin(27rn£ — e), (38) 



n denoting the frequency of the disturbance. Equation (26) 

 now becomes 



G=5^BV=^.HVBV, . . . (39) 



since we are now limited to a single s, which is identical 

 with 2 7m. 



F, the extrusion of sether per unit mass of matter (§ 7) 

 suffers variations given by 



8F = -Hp=-HBsin(27™£-e). . . (40) 



Let the greatest numerical value of SF be £F ; then by 

 (40), (39), 



? 2 F 2 = H 2 B 2 = 2G/7r P? i 2 ; (41) 



or, remembering (37), 



«=.V(X> ••■■■■■■ <*» 



28. Let k denote the bulk-modulus of elasticity of the 

 tether, or 1/k its compressibility. By § 8 above, Her is the 

 additional setherial compressibility where there are cr grams of 

 atomic matter per cubic centimetre ; let this be equivalent to 

 yLtcr/*;, so that jjlct is a pure number. Thus 



R=fi/K (43) 



