270 Lord Rayleigh on Acoustic Repulsion. 



ease it is pure ; in the latter it is mixed with other light pro- 

 ceeding from the objects behind, and moreover belongs to the 

 coarser turbidity of the lower layers of the atmosphere, for 

 which reason it is whiter. In the drier air of warmer coun- 

 tries the turbidity is finer, even in the lower strata of the at- 

 mosphere, and hence the blue seen before distant terrestrial 

 objects is more like that of the sky. It is to this circumstance 

 that Italian landscapes owe their clearness and richness of 

 colour." I fail to detect in this explanation, which was origi- 

 nally, I believe, due to Dr. Tyndall, the slightest resemblance 

 to that of Mr. Lockyer. 



I am, your obedient servant, 



A. M. WOKTHINGTON. 



XXXV. Note on Acoustic Repulsion. 

 To the Editors of the Philosophical Magazine and Journal. 



Gentlemen, 



PERHAPS the following explanation of the curious phe- 

 nomenon of the repulsion of resonators observed by 

 Dvorak and Mayer * may be of interest to the readers of the 

 Philosophical Magazine. 



The hydrodynamical equation of pressure for irrotational 

 motion is (in the usual notation) 



$ _ i TT 2 



dt 2 u • • • • w 



= J7 =R " 



If we suppose that there are no impressed forces, R = 0. Di- 

 stinguishing the values of the quantities at two points of space 

 by suffixes, we may write 



-i-«,= 5(*,-#i)-iU!+*u!. • • • (2) 



This equation holds good at every instant. Integrating it 

 over a long range of time, we obtain as applicable to every 

 case of fluid-motion in which the flow between the two points 

 does not continually increase 



fadt-feodt^iS^dt-iSTJUt- ... (3) 



Let us now apply this equation to the case of a resonator 

 excited by a source of sound nearly in unison with itself, 

 taking the first point at a distance from the resonator, where 

 neither the variation of pressure nor the velocity is sensible, 

 and for the second a point in the interior of the cavity, where 

 * Phil. Mag. September 1878, p. 225. 



