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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.

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

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