274 Prof. J. J. Miiller on a Mechanical Principle 



somewhat, I imagine, as loaded strings* of graded lengths and 

 diameters would act in similar circumstances. The vibrations 

 of the composite wave fall upon the membrane placed near the 

 reed as they fall upon the membrane of the tympanum ; and 

 these vibrations are sent through the stretched fibres (or delicate 

 splints of rye-straw, which I have sometimes used) from the 

 membrane to the tuned forks, as they are sent from the mem- 

 brana tympani through the ossicles and fluids of the ear to the 

 rods of Corti. The composite vibration is decomposed into its 

 vibratory elements by the covibration of those forks whose vi- 

 bratory periods exist as elements of the composite wave-motion ; 

 so the composite sound is decomposed into its sonorous elements 

 by the covibrations of the rods of Corti, which are tuned to the 

 elementary sounds which exist in the composite sonorous vibra- 

 tion. The analogy can be carried yet further by placing the 

 forks in line and in order of ascending pitch, and attaching to 

 each fork a sharply-pointed steel filament. If- the arm be now 

 stretched near the forks, so that the points of the filaments nearly 

 touch it at points along its length, then any fork will indicate 

 its covibration by the fact of its pricking the skin of the arm, 

 and the localization of this pricking will tell us which of the 

 series of forks entered into vibration. The rods of Corti shake 

 the nerve-filaments attached to them, and thus specialize the po- 

 sition in the musical scale of the elements of a composite sono- 

 rous vibration. Thus a complete analogy is brought into view 

 between our experiment and Helmholtz's comprehensive hypo- 

 thesis of the mode of audition. 



[To be continued.] 



XL. On a Mechanical Principle resulting from Hamilton's Theory 

 of Motion. By J. J. Muller, Professor at the Polytechnic 

 in Zurich-^. 



WHEN a system of material points moves under the influ- 

 ence of forces proceeding from the reciprocal attraction 

 and repulsion of the points, all the integral equations of the mo- 

 tion can, as Hamilton has shown J, be represented by the par- 

 tial differential quotients of a function of the coordinates (the 

 primary function), in a manner similar to that in which, accord- 

 ing to Lagrange, its differential equations can be represented by 

 aid of the partial differential quotients of the force-function. 

 Therein the primary function satisfies two partial differential 

 equations ; but even one of these equations, as Jacobi demon- 



* For discussions of the vibratory phenomena of loaded strings, see Don- 

 kin's ' Acoustics/ p. 139, and Helmholtz's Tonempfindungen, p. 267. 



t Translated from PoggendorfF's Annalen, vol. clii. pp. 105-131. 



% Phil. Trans. 1834, 1835. 



