PROFESSOIJ HORACE LAMB ON THE PROPAGATION OF 



Rt 



38 

 where 



The following numerical table is derived from one given on p. 155 of the paper- 

 referred to : 



* Extremes. 



The graphs of (/,, and v^ as functions of t, in the neighbourhood of the critical 

 epoch era, are shown in fig. 8, which may be compared with fig. 6.t The corresponding 

 orbit of a surface particle is traced in fig. 9, where the positive direction of z is 

 down wards ; it may be derived by a homogeneous strain from a portion of the curve 



whose polar equation is 



,* = ' cos 1 (6 - ITT). 



The amplitude of this part of the disturbance diminishes, with increasing distance 

 from the source, according to the law TO-"*. 



Complete expressions for the disturbance are obtained by generalizing (155) and 

 (156). They may be written 



H 



or o 



. ) du.d0 (169), 



TTO//, J a ovs . o 



I ^ V (0)- f f R ( - #" cosh u) du.de ... (170), 



Ja ot J() 



where U (0) and V (0) are the functions defined and tabulated in Art. 9. 



t See the footnote on p. 26 ante. 



