IV. On the theory of internal resistance and internal friction in fluids ; and on the theories of sound and of auscultation

The author shows in the first instance, that when sound is propagated 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 element. He considers that the amount of the force thus called into play (whether it be accelerative of, or retarding the motion) in anelement of given magnitude in a given indefinitely short interval, will depend solely on the amount of compression or dilatation developed 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 ±b 2 (dy /dx )-1 d 2 y /dxdt ' wherex denotes the distance from the origin of the element when the air is at rest,y the same distance at the timet when the air is in motion,b 2 constant depending on the compressibility of air under given circumstances; so that the accurate equation of sound (variation of temperature being neglected) will standd 2 y /dt 2 =a 2 (dy /dx )-2 d 2 y /dx 2 ±b 2 (dy /dx )-1 d2y/dxdt '(1) in which equation the upper or lower sign ofb 2 is to be taken according as the motion of the particles is in the direction in whichx is measured positively, or the contrary.