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XVII. On the Energy acquired by small Resonators from 

 incident Waves of like Period. By Lord Rayleigh. 

 O.M., F.B.S.* 



i 



N discussions on photo-electricity it is often assumed that 

 a resonator can operate only upon so much of the 

 radiation incident upon it as corresponds to its own cross- 

 section f. As a general proposition this is certainly not true 

 and may indeed differ from the truth very widely. Since 

 1878 J it has been known that an ideal infinitely small 

 acoustical resonator may disperse energy corresponding to an 

 area of wave-front of the primary waves equal to \ 2 /7r, an 

 efficiency exceeding to any extent the limit fixed by the above 

 mentioned rule. The questions of how much energy can be 

 absorbed into the resonator itself and how long the absorption 

 may take are a little different, but they can be treated without 

 difficulty by the method explained in a recent paper §. The 

 equation (49) there found for the free vibration of a small 

 symmetrical resonator was 



Mg- +w + 4w^(l-^),J=0, . . . (1) 



in which p denotes the radial displacement of the spherical 

 surface from its equilibrium value r, M the mass, //, the 

 coefficient of restitution, a the density of the surrounding- 

 gas, and k = 2 7r-f- wave-length (X) of vibrations in the gas. 

 The first of the two terms containing a operates merely as 

 an addition to M. If we write 



M / = M + 47r<rr 3 , (2) 



(1) becomes 



M'g+ w -/.4™^g- = 0. . . . (3) 



Thus, if in free vibration p is proportional to e Vlt , where n is 

 complex, the equation for n is 



n 2 (-M'-fi.47T(7^ 4 ) +/"=0 (4) 



* Communicated by the Author. 



t See for example Millikan's important paper ou a direct determination 

 of Planck's constant " h " ; Physical Review, vol. vii. March 1916. p. 385. 

 X "Theorv of Sound,' § 319; X= wave-length. 

 § Phil. Mag. vol. xxix. Feb. 1915, p. 210. 



