218 



Presents. 



[May 17, 



end be "free" a difficulty arises. At such an end the solution 

 requires the existence of a radial stress U oc (2i + l) 3 r (a 2 — r 2 )/Z 3 , 

 where i is an integer depending on the number of the harmonic of the 

 fundamental note and I denotes the length of the bar. The value 

 given above for k thus answers to a problem differing to a certain 

 extent from that occurring in nature in the case either of "fixed- 

 free " or of " free-free " vibrations. There will thus be a difference 

 in these cases between the results of experiment and those of the 

 accepted theory, even as amended by Lord Rayleigh. This divergence 

 will increase rapidly with the order of the harmonic, and though very 

 small for a long thin bar will increase rapidly as the ratio of the 

 diameter to the length is increased. Since in dealing with the condi- 

 tions at the curved surface, terms of the order (ajl) 5 were neglected, 

 the same remarks apply, though to a smaller extent, in the case of the 

 "fixed-fixed " vibrations. 



From the values of u and w, which are obtained explicitly, it is 

 shown that the hypothesis made by Lord Rayleigh is true as a first, 

 and only as a first, approximation. 



The Society adjourned over the Whitsuntide Recess to Thursday, 

 May 31st. 



Presents, May 17, 1888. 



Transactions. 



Alnwick: — Berwickshire Naturalists' Club. History. Vol. XI. 

 Nos. 3-4 8vo. Alnwick 1887. The Club. 



Batavia : — Bataviaasch Genootschap van Kunsten en Wetenscbap- 

 pen. Dagh-Register gehouden int Casteel Batavia. Anno 1653. 

 8vo. Batavia 1888; Notulen. Deel XXV. Aflev. 4. 8vo. 

 Batavia 1888. The Society. 



Berlin : — Konigl. Preuss. Akademie der Wissenschaften. Politische 

 Correspondenz Friedrich's des Grossen. Bd. XV. 4to. Berlin 

 1887. The Academy. 



Bombay: — Royal Asiatic Society (Bombay Branch). Journal. 

 Vol. XVII. No. 46. 8vo. Bombay 1887. The Society. 



Brussels : — Musee Royal d'Histoire Naturelle de Belgique. Bulle- 

 tin. Tome V. No. 1. 8vo. Bruxelles [1888]. 



The Museum. 



Cambridge, Mass. : — Harvard College. Museum of Comparative 



Zoology. Bulletin. Vol. XIII. No. 8. Vol. XVI. No. 1. 8vo. 



Cambridge, Mass. 1888. The Museum. 



Cordova : — Academia Nacional de Ciencias. Boletin. Tomo X. 



Entrega 1. 8vo. Buenos Aires 1887. The Academy. 



Gottingen: — Konigl. Gesellschaft der Wissenschaften. Abhand- 



lungen. Bd. XXXIV. 4to. Gottingen 1887; Nachrichten. 



Jahrg. 1887. 8vo. Gottingen. The Society. 



