Manchester Memoirs, Vol. xliv. ( 1 900), No. ft. 5 



investigations of the effect of an isolated impulse on the 

 surface of water, as interpreted by Lord Kelvin.* 



(4) For waves of flexure travelling along an elastic 

 rod, FocX'' ; the curve is then a hyperbola xy = a'^, and 

 0T=2PN. 



(5) For waves on a tense string every point of which 

 is urged towards its equilibrium-position by a force varying 

 as the displacement, 



Fee ^(a'^-t-A-) 

 where a is a constant. The curve has then the form of a 

 hyperbola 



V" x^ 



Ir a- 



and OT varies inversely as PN \ i.e., the group-velocity 

 varies inversely as the wave-velocity. 



Proc. Rov. Soc. Feb. 3, 1SS7. 



