BY SMALL OBSTACLES OF CYLINDRICAL AND SPHERICAL FORM. 



241 



and audibility of sound. If the diameter of the drops of water in a dense fog is 

 assumed to be '02 mm., there is no appreciable alteration in the audibility of sound ; 

 but, if the diameter of the drops of water is '002 mm., the presence of fog is distinctly 

 prejudicial to the audibility of sound. The former case is in agreement with 

 TYNDALL'S observations on the subject. 



In conclusion I desire to thank Prof. LAMB for much kind advice and encourage- 

 ment in the writing of this paper. 



1. In a viscous gas, if u, v, w be the components of the velocity at any point 

 x, y, z of the fluid referred to fixed rectangular axes, and if p be the pressure at this 

 point, the equations of vibration may be written in the form 



Bx 



V + l 



(1) 



where p (} is the equilibrium density, v is a small constant of dimensions LT ' 

 depending on the viscosity, $ has been written for div (u, r, ?/), and terms of the 

 order of the square of the velocity have been neglected. 



By a method very similar to that* used in the case of an incompressible fluid it is 

 found that the total rate of dissipation of energy within any closed surface S is 

 given by 



2F = $ vpo | [ f (a + b + c) 2 dx dy dz 



(f 



f) dx dy dz 



1 1 (lu+mv+nw) 



I, in, n 

 u, i\ w 



where </ is the resultant velocity at any point of the fluid, 8n denotes an element of 

 the normal to the surface S, /, m, n are the direction cosines of this normal drawn 

 inwards in each case from the surface element 8S. Further, a, b, c, f, 17, are given 

 by the relations 



_ cu , ov dw 



(3). 



dy 



When there is no motion of the gas parallel to the axis of z, and the motion is the 



VOL. ccx. A. 



* LAMB'S 'Hydrodynamics,' p. 540, 

 2 I 



