90 Dr. C. V. Burton on a 



Using (50) in conjunction with (44) and (45) respectively, 



-as w 



"-MSP)' ■ ' ' <K) 



while from (43) 



*=w (54) 



30. An expression is readily found for the maximum 

 translational velocity attained by any element of aether in 

 the primary wave-motion, half the square of this velocity 

 multiplied by the density of the aether being equal to the 

 maximum kinetic or maximum potential energy per unit 

 volume ; that is, equal to B 2 /2/c. From (47) the desired 

 expression is at once obtained, and only requires to be divided 

 by 27m to give the semi-amplitude of vibration (maximum 

 displacement), and multiplied by 27m to give the maximum 

 acceleration of any aether-element. Remembering (50) the 

 three expressions are : — 



Maximum displacement from mean position = — 2\/\ q t? )» (****) 

 Maximum velocity = —a /( J, (56) 



Maximum acceleration = a/{ — ^ J (57) 



31. Bearing in mind § 9, and in particular equation (3), 

 we have also, for any particle of neutral matter considered 

 with respect to the ather, 



Maximum displacement from mean position = 2 \/(—^r\ (*>%) 



Maximum velocity = — \/( — o — ), (59) 



Maximum acceleration = 2a /( — - — - J: (60) 



these three equations of course concern only that motion of 

 matter with respect to the aether which is directly due to the 

 primary wave-motion. 



