223 



IV. " On the Theory of Internal Resistance and Internal Fric- 

 tion in Fluids ; and on the Theories of Sound and of Aus- 

 cultation." By ROBERT MOON, Esq., M.A., late Fellow of 

 Queen's College, Cambridge. Communicated by ARTHUR 

 CAYLEY, Esq. Received April 3, 1858. 



(Abstract.) 



The author shows in the first instance, that when sound is propa- 

 gated along a cylindrical tube filled with air, the compression which 

 takes place in any element calls forth a resistance which diminishes 

 the velocity of the particles in the element, at the same time that 

 the dilatation which takes place in any element calls into play a force 

 which will tend to increase the velocity of the particles in the ele- 

 ment. He considers that the amount of the force thus called into 

 play (whether it be accelerative of, or retarding the motion) in an 

 element of given magnitude in a given indefinitely short interval, 

 will depend solely on the amount of compression or dilatation deve- 

 loped in the element in the interval, and the state of density in the 

 element at the time ; and he is thus led to the conclusion, that to 

 the ordinary equation for the transmission of sound through a column 

 of air must be added a term of the form 



" \dx) dx~dt' 



where x denotes the distance from the origin of the element when 

 the air is at rest, y the same distance at the time t when the air is 

 in motion, 6 2 a constant depending on the compressibility of air under 

 given circumstances ; so that the accurate equation of sound (varia- 

 tion of temperature being neglected) will stand 



in which equation the upper or lower sign of W is to be taken accord- 

 ing as the motion of the particles is in the direction in which x is 

 measured positively, or the contrary. 



On the same principles the author shows that, in the case of 

 elastic fluids, the general equations of motion, when internal resist- 

 ance is taken into account, must be written as follows : 



VOL. IX. R 



