WITH AN APPENDIX BY PROFESSOR A. LODGE. 



89 



kc = 2. 



A plot of 4 (F~ -4- G 2 ) against 6 is given in fig. 1, curve A. 



The investigation for kc = 10 could probably be undertaken with success upon the 

 lines explained in ' Theory of Sound ;' but as it is necessary to include some 20 terms 



\ 



Curves 



of Intensity 



A, Ac 



B, Ac 



45 



60 



75 



90 

 Fig. 1. 



105 



120 



135 



150 



165 



180 



of the expansion in LEGENDRE'S series, I considered that it would be advantageous to 

 use certain formulae of reduction by which the functions of various orders can be 

 deduced from their predecessors, and this involves a change of notation. Formula 

 convenient for the purpose have been set out by Professor LAMB.* The velocity - 



' Hydrodynamics,' 267 ; ' Camb. Phil. Trans.,' vol. 18, p. 350 1900. 



VOL. CCIII. A. 



N 



