306 



Mr. R. Moon on Poisson's Solution, ^c, [Dec. 13, 



As to the marked difference of birds of the two kinds in relation to the 

 condition of their bones, the rationale is not very obvious. Perhaps an 

 approximation to the truth, or to the probable, may be made by com- 

 paring the bones of birds of the two kinds, which are possessed of similar 

 powers, the swift, for instance, and the buzzard, rivals in swiftness of 

 flight and enduring power of wing. How different are their humeri ! of 

 the former, very short, strong, and compact, provided with firm and large 

 processes for the attachment of muscles ; in the latter, long, hollow, and 

 light, and comparatively brittle, yet sufficiently firm to bear without fracture 

 the muscles which act on them. Here, have we not after a manner a kind 

 of substitution of qualities ? great strength and extended surface in small 

 space in the one, for lightness with greater length of leverage in the 

 other. Further, the one kind of bone, that which contains marrow, being 

 less brittle than that which contains air, and more yielding, may be 

 less liable to fracture ; a quality which, in the bird, before the ossification 

 is complete, may be of essential service ; so that, teleologically considered, 

 it may perhaps serve to account for the bones which are eventually 

 hollow having primarily marrow in place of air. 



December 13, 1866. 



WILLIAM BOWMAN, Esq., Vice-President, in the Chair. 



Among the Presents announced were two manuscript volumes, by 

 Solomon Drach, Esq., F.R.A.S., containing various Tables in Pure Mathe- 

 matics, presented by the author. 



The following communications were read • 



I. On Poisson^s Solution of the Accui'ate Equations applicable 

 to the Transmission of Sound through a Cylindrical Tube ; 

 and on the General Solution of Partial Differential Equa- 

 tions." By R. Moon, M.A., late Fellow of Queen's College, 

 Cambridge. Communicated by Prof. J. J. Sylvester. Re- 

 ceived November 14, 1866. 



(Abstract.) 



The pair of equations 



a 1) 



which constitute Poisson's solution of the accurate equations applying to 

 the transmission of sound through a cylindrical tube derived by La Grange's 

 method, have long attracted the attention of mathematicians. 



