94 Mr C. Chree, On some Compound Vibrating Systems. [Oct. 27, 



Society, which will be published as a separate part of the 

 Proceedings. 



The President elect, Prof. G. H. Darwin, then took the Chair, 

 and the following Communication was made to the Society : 



(1) On some Compound Vibrating Systems. By C. Chree, M.A., 



King's College. 



(Abstract.) 



The vibrating systems treated in this memoir are bounded 

 either by concentric spherical or by coaxial cylindrical surfaces, 

 and the vibrations are of those types in which the displacements 

 are either wholly radial or wholly transverse. 



By a simple system is meant a spherical or a cylindrical shell 

 of a single isotropic medium ; by a compound system is meant 

 a stratified medium in which the surfaces separating adjacent 

 media, or layers, are spherical or cylindrical according as the 

 outer surfaces are spherical or cylindrical. 



Those functions which when equated to zero constitute the 

 frequency equations for a simple system are termed frequency 

 functions. A. method is developed whereby the frequency equation 

 for a compound system of any number of layers, composed of 

 different isotropic media, can be at once written down in a form 

 which involves the frequency functions of the several layers. 



The general result so obtained is employed in determining the 

 change in the pitch of the several notes in an otherwise isotropic 

 simple shell owing to the existence of a thin intercalated layer 

 of a different isotropic medium. The dependence of the magnitude 

 of the change of pitch on the nature of the difference between 

 this altered layer and the remainder of the shell, on the position 

 of the altered layer, and on the value of Poisson's ratio for the 

 unaltered medium is considered for the system of notes which 

 the vibrating system in question is capable of producing. 



The law of variation of the magnitude of the change of pitch 

 in solid spheres or cylinders with the position of an altered layer, 

 which differs from the remainder of the system in a given assigned 

 way, is represented by a curve or curves. Every such curve shows 

 in a very simple manner the comparative magnitude of the largest 

 possible changes of pitch, for all possible notes of the system, which 

 can arise from a given alteration of material, throughout* a layer of 

 given volume or of given thickness as the case may be. The cor- 

 responding positions of the layer may also be immediately derived 

 from the curves for all those notes of the system whose frequencies 

 are recorded. 



Tables are constructed showing the positions where a thin layer 

 differing in an assigned way from the remainder is most effective 



