Plane Waves of Soimd, 19 



I have obtained as an approximation to the amplitude of 

 the progressive part, due to the wave 



> = Hcos — ' (<7/ - .t) 

 c A. 



set up at a region where the density is D^ the expression 



while the amplitude of the retrograde wave is 



H,/5oAXsin^" 

 V D X 



where A\ is extremely small. 



Let us suppose that A and B are two planes of constant 

 density at some little distance apart, and that at A, the 

 progressive part of a wave travels towards B, through the 

 slowly varying gas between ; then at every part of its 

 course we have a reflected wave so that the progressive part 

 which passes B is not exactly the same as it would have 

 been, if the gas between A and B and beyond B had been 

 absolutely uniform. If we were to consider, however, that 

 the density between the planes was allowed to become 

 uniform so that the change of density at B would be sudden, 

 then the same wave passing A would travel unchanged to 

 B, part being reflected there, while the progressive wave 

 passing B would differ infinitesimally from the progressive 

 wave passing B when the gas varies continuously. These 

 considerations will guide us in the discussion of the problem 

 in hand. 



Let .... A,_i A A^^i .... be planes of constant density, 

 the difference of density at any two consecutive planes 

 being excessively small, and suppose that all bodily forces 

 producing the variation of density are annihilated, the 

 planes being prevented from consequent motion by properly 

 applied surface forces. Gravity is here supposed to be the 

 cause of the variation and acts in the direction A^-i A,. 



