Lord Rayleigh on Waves. 277 



mented on by Professor Guthrie. The approximate formula 

 for the length of the simple equivalent pendulum correspond- 

 ing to (N) is 



3i(l + 2<T^), . . . . (Q) 



or, when I is considerable, 



R-r- 3-832 simply (R) 



Professor Guthrie compares his observations with a pendulum 

 of length R-f-4, and finds a fair agreement, which, however, 

 would be improved by the substitution of the theoretical for- 

 mula (R), 



According to (0) the place of zero elevation and depression 

 occurs when 



According to observation, 



r=§R=*6667R. 



From the Tables of Bessel's functions it appears that the am- 

 plitude at the edge of the vessel is *403 of that at the centre. 

 Professor Guthrie makes this *5. 



For the next set of vibrations in a circular dish u is of the 

 form 



u— sin 0Ji(jcr), 



where the admissible values of #R are 1*841, 5*332, 8*536, &c. 

 Hence for the gravest of this group the length of the equiva- 

 lent pendulum is 



R-f- 1-841 (S) 



In this group of modes the elevation vanishes at all points along 

 a certain diameter (0=0). 

 In the third group we have 



u = sin 20 J 2 (kt), 



and the admissible values of kR are 3*054, 6*705, 9*965, &c. 

 For the gravest of these the length of the equivalent pendu- 

 lum is 



R-r-3-054, (T) 



if the depth be sufficient. The elevation vanishes along two 



7T 



perpendicular diameters (0 = 0, 0— -). 



In the fourth group there would be three diameters for which 

 n = ; and the length of the pendulum isochronous with the 

 gravest mode will be 



R^-4-201 (U) 



