Small Vibratory Motions of Elastic Fluids. 317 



for the obstacle presented to the wave by the chord, the density 

 at the given instant would have been Oe. The quantity ^ used 



above, varies as sin — — , and it is easily shewn that the resultant 



of the pressures on the chord varies in the same manner. This 

 being- premised, it will be possible to solve the problem of 

 sonances in the particular case in which the waves are incident 

 perpendicularly on the resounding body. It will be supposed 

 that every particle of it tends to return to its position of rest 

 by the same force, varying as the distance from this position ; and 

 the supposition is allowable if it be permitted to infer from what 

 has been said of the types of waves, that the primary form of 

 vibrating chords is the Taylorean Curve. Every point of the 

 chord will thus be acted upon by three forces; its own elas- 

 ticity, the pressure of the impinging wave varying as sin -^— , 

 and the fluids resistance varying as the velocity. Hence, 



d-s , ds . irat 



_+;,_+„«_,„ s.n — = o 



is the equation to determine the motion; p and m being small 



in comparison of n. This equation being integrated, and the 



ds 

 constants determined so that s = o, and -- = o, when t = o, the 



dt 



ds 

 equation for ^ will come out after all reductions, 



TTfl /-/ 7r-a"\ irat -Trap . irat 



, ■ — m \\n -^) cos — — + -— -=- sin -— - 



ds \ \\ \- J \ \ \ 



I 



I COS ht + ("+^rr )^ sin ht 



where h is put for \/n-^. The value of m is constantly the 



same for the same point of the chord, but different at different 

 points. 



